text:
ChaparralFilms
Tractor Derby
Mechanics face off in a time-crunch contest to see who can assemble the most badass tractor build to compete in the ultimate tractor derby.
Building shows have exploded and audiences now more than ever are tuning in to watch how experts ply their trade. This show feeds the appetite for getting your hands dirty to make something exceptional from scratch using heavy equipment like a fine craftsman.
Dig Perfect
The world's best diggers from around the world race against the clock to see who can excavate the best, most arduous construction project. The challenge is different every time and requires every ounce of skill, patience, experience and talent that they can muster!
A new kind of competition show that pits contestants against each other with a fresh twist. Players must endure the most visceral challenges & lose the use of a sense. Like intense discomfort with scorching heat or biting cold or loud noises or rites of passage. Imaginative tests like a cold room or noise assault with interesting tasks to perform that require communication, quick-thinking and working together to problem-solve and succeed to move on.
Ancient Sports
Modern day athletes are challenged to play and win odd games from the past or that are played around the world that no one knows about. Sports that were played long ago that have been forgotten. Rare games played that are dangerous or strange: Buzkashi, Pitz, Pankration, etc. Crown the finalist after points accrued playing and winning all these thrilling and death-defying contests .
Phantoms of the Battlefield
Tour the battlefields of the ancient world with a combat veteran paranormal expert to reach out and experience sites haunted by the legions of dead who fell there in battle centuries ago. Watch closely in wonder as our host medium conducts chilling ceremonies to conjure spirits from the past and hear their grisly and sad tales of loss, tragedy and horror.
Gamermania
A celebrity on-the-road pop-up video game match. Take a tricked-out luxury RV. Park it at a huge venue. Set up a kick-ass stage with massive screens. A YouTube gamer host engages celebs as they duel it out live, playing their favorite video game in front of a wild audience. Broadcast live!
Gaming culture has exploded and audiences now more than ever are tuning in to watch popular figures indulge. This show feeds the appetite for celebrity culture, takes advantage of the biggest worldwide venues, their massive audience and the vast social media potential.
It couldn't be more simple. Kids love to throw things. Especially at targets! Make it a challenge and you've got yourself a game and all the drama and stakes of competition. From sports to the carnival booths to obstacle course game shows, hitting targets is a part of our culture. Let's get kids of all ages out there to work as a team to conquer the most challenging obstacles courses yet to be seen on TV.
Teleporter
Sci-Fi/Thriller – When a team of scientists led by the brilliant CLAUDIA successfully test a device that can teleport objects through space, all Hell breaks loose at the giant conglomerate Orinoco, Inc. where they work in research and development. After she mysteriously disappears during a failed demonstration, her friend and colleague BANDU must fend off the greedy corporate executive SANDY and her sinister head of security DENTON to find out the truth behind her disappearance. This drama unfolds and upsets the innocent lives of roommates the shy artist ADLER, the bull-headed tugboat captain MARA and slick car salesman KEITH ALAN. As the clock ticks down on finding the ground-breaking machine and it's elusive inventor, the stakes are raised to a fever pitch where the lives of all those involved hang in the balance. And an honest detective VICTOR who's hot on the trail to see justice is served.
A weekly show that begins with four celebrities, a comedian host and a seasoned PGA veteran who will play a round of golf together at a world-renowned course. We get a peek at who these people really are as they travel the world together, take in the foreign sights and culture and talk some friendly and not-so-friendly trash on the course.
Instagram Makeover
IG Makeover is a digital popularity contest. Every episode rates how our candidates are performing. And social media plays a huge part since on the program, they will either create or enhance their platforms..This new digital era sees us reaching out to others in ways never dreamed of. This show embraces our fascination with being connected in a way never been done before. And uses social media to unlock potential and make dreams come true. The contestants must compete to build the most successful and popular social profile.
Back from Extinction
A show eons in the making that does three simple things. First, this program identifies and follows the movers and shakers in the realm of environmentalism. Second, what efforts these brave souls are taking to make the world a better place and the positive results of their actions. And lastly, what stands in the way against the daily struggle to defeat the forces of evil that threaten to destroy our planet. This show has been a long time coming. It's time to take precious wildlife off the endangered list and replace them with the culprits who are thwarting efforts to save our planet because of lethargy, ignorance and corporate greed.
Hide + Seek
Weekend warriors are secreted away to a remote location where they are given a limited timeframe to reach a distant finish line before being hunted down by deadly opponents. Their mission: use their survival skills to evade capture, master the hostile environment and it's hidden traps to win the game.
Jr Flips
In 2017, Six Elementary School Kids ages 7 to 13 years old grew tired of playing video games and watching TV – so after an inspirational chance meeting with Oprah Winfrey along with seed money from one of the parents they partnered up and launched Junior Flips, LLC (Jr Flips) thanks to the leadership and inspiration of young entrepreneur Alianna Hines and her industrious family.
Tuesday's fine
Family Feel-Good – Set in rural 1970's Oklahoma, Tuesday's Fine follows the story of a rural American family through the eyes of a young boy, the fledgling artist HALSEY. The tale traces the break-up his family and the uncertain aftermath that follows. Halsey's dad, the local doctor SETH returns from Viet Nam a crippled and hardened man. And his wife, the broken ex-blues singer SCOTTY yearns for the exciting youth and romance she fell in love years before. It's at the blaring racetrack, smoky bars and dingy diners that Halsey comes of age under the watchful eye of his best friend, salty and sober ex-race car driver DEKE and his seasoned sidekicks, ARLENE, LEE and FATHER VERNON.
The World Awaits
Our show follows four Instagram celebrity influencers around the world to the greatest global events of 2018. From Carnival in Rio to the Monaco Grand Prix in France or the World Cup in Russia, each week our cast is flown first class to a high-end resort to enjoy the sights and sounds of a new country and culture. Every step of the way the cameras are rolling as the girls pose for still shoots in the most remote exotic locations. And take time out to give back and support local charities that support communities in need. Audiences around the world can finally see just what life in the fast lane is really like. And get to know these social media megastars!
Kids News Network
KNN is a live newscast for children of all ages to bring them up to date on the goings-on around the world. From schools to the latest fashion. Sports and entertainment. What movies are out and what kids are into today. Our show informs our youth from education to current events and gets kids involved. This program will inspire children around the world to make the most out of life and themselves.
Sci-Fi/Horror – Snow White is a sci-fi action-packed thrill ride that keeps you on the edge of your seat. In the vein of Terminator and I Am Legend, the movie follows a battle-hardened vet WOLF who awakens to a world gone mad. Los Angeles after some unknown apocalypse that has wiped out humanity. Survivors hide like rats from terrifying mannequins that roam the wastes like grim reapers and appear at the mention of a cryptic phrase.
Action/Thriller – A trained intelligence officer stumbles across an illegal covert operation while on a dangerous assignment overseas that results in her and her estranged sister being hunted down like fugitives. They unravel a government conspiracy that reaches to the highest levels of power and sadly, forces one of them to pay the ultimate price. Just as their once frail bond of sisterhood is rekindled.
Time 2 Dance
With instruction from four young dance coaches and encouragement from an energetic host, ordinary kids selected from a studio audience compete in an inspirational dance-off.TIME 2 DANCE!
Kid VS. Beast
What if there was a new breed of game show? One where kids square off against…that's right, animals! Obstacle courses designed to showcase a particular animals' ability and strength. Paired with or opposed by young kids of all ages who pit their best alongside or against these wonders of nature to win a simple competition. It's new. It's innovative. And it will warm the hearts of viewers of all ages in a way never been done before.
Picture's Up
Hollywood slang for when you're about to roll camera, Picture's Up is a competition show where a different group of kids work together to make a movie every episode. The contest is simple. Whoever makes the best movie wins the show. A panel of celebrity kid judges monitors their progress and critiques their films in the season finale. Each crew is assigned a movie genre and given a specific time frame to complete their film. At the end of the season, the best movie wins. It's Project Greenlight for kids, and we get to experience the fireworks and pitfalls of filmmaking through the lens of childhood.
Out To Pasture
Out To Pasture follows the lives of four good friends dealing with life in Los Angeles today. From the psychiatrists couch to the movie sets, these deep and troubled men lead very different lives yet share the same hopes and doubts. Ordinary guys trying to cut away from the herd, from bachelorhood to marriage to divorce and all the ups and downs along the way.
Peddler
The show follows the lives of Crawford Boyle, a young writer living in Los Angeles today. He dreams of penning the great American novelist but has gotten caught up in the nasty world of drug dealing to make ends meet until his ship comes in.
Sadly, he's good at it and those he cares about most suffer the penalty for his inability to escape this world of decadence and evil.
Action/Adventure – Hardened Iraqi war vets led by a bloodthirsty madman have sequestered themselves from the world in a hideaway compound deep in the back country, far from prying eyes. Every year, these killers travel to the far corners of the globe to find six dangerous candidates to compete in a terrible contest. Violent criminals or lethal down-and-out characters who have made terrible mistakes and the world will not miss. They are secreted away to where the deadliest game of all awaits: the hunt! And they must pit their wits and survival skills against these evil hunters in order to escape.
Musical – Talented country girl moves to the big city to make her dreams come true. But life is hard in Hollywood and getting back doesn't come easy. Lured to a glitzy, jetset lifestyle by a fallen angle with dreams like her, our heroine learns the hard way that it's not all wine and roses. After facing her fears, she chooses the right path and earns her break break to let her talents shine through. This modern telling of a classic, heartfelt tale, exciting dance numbers and soaring songs galore make this a special foray into life in tinseltown today.
Eagle Of The Desert
Epic/Action – Set in North Africa during WWII, Eagle Of The Desert tells the tragic tale of lives brought together and torn apart against the terrible backdrop of war and some of history's most awe-inspiring characters. Spun around the charismatic and rebellious fighter ace Joachim Marseille, the story follows one of the most decorated and colorful pilots in history. His passion for flying, disdain for authority and wild comrades in the field were the stuff of classic Greek tragedy. Especially his fateful plight fighting for yet railing against a cruel Nazi regime he neither believed in nor obeyed. This defiance would ultimately lead to his untimely demise and overshadow his fearsome feats in the skies. Even the deep forbidden love he found in the desert would fall prey to a destiny fraught with peril and loss.
Mechanical Failure
Action/Horror – Horror films are driven by concept rather than stars. They have relativly low cost with high potential return. Due to Horror's rabid and loyal audience, Horror projects perform as well if not better in the ancillary markets ( Video, DVD, Cable, etc. ) than in the box office. Great saleability both domestically and internationally. Basically, there is always a market for Horror amongst the largest movie-going demographic – teenagers.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to minmax normalize data and build as json in postgresql Let's say I have a simple table tracking values over time for different users as a postgres database that looks like this:

user_id
date
value

1
'2021-01-01'
1

1
'2021-01-02'
2

1
'2021-01-03'
3

2
'2021-01-01'
1

2
'2021-01-02'
2

2
'2021-01-03'
3

And I want to return this data as an array of json objects so I do something like this...
select
  user_id,
  coalesce(
    json_agg(
      'date', date,
      'value', value
    ),
    '[]'
  ) as values
from user_table
group by user_id

But let's say that I also wanted to return another column of json objects called values_normalized where it's the same thing except the values are minmax normalized between 0 and 1.
My assumption is that I could do something like this -
select
  user_id,
  coalesce(
    json_agg(
      'date', date,
      'value', ((values - min(values) over ())::float / (max(values) over () - min(values) over ())::float)
    ),
    '[]'
  ) as values
from user_table
group by user_id

But this is giving me an error "aggregate function calls cannot contain window function calls"
Anybody know how to do this?

A: With a simple subquery that is easy:
SELECT user_id,
       coalesce(
          json_agg(
             'date', date,
             'value', (value - minvalue)::float /
                      (maxvalue - minvalue)::float
          ),
          '[]'
       ) AS values
FROM (SELECT user_id, date, value
             min(value) OVER () AS minvalue,
             max(value) OVER () AS maxvalue,
      FROM user_table) AS subq
GROUP BY user_id;

redpajama_set_name: RedPajamaStackExchange


text:
Red Wings Latest News
Season begins against Anaheim
By Christy Oct 2, 2007, 10:53pm CDT
Share All sharing options for: Season begins against Anaheim
The Detroit Red Wings open the regular season on Wednesday evening at home at 7pm. The game will be shown on Versus.
If you live in the metro Detroit area, you can still buy tickets to the game. I know the team has had a harder time selling tickets this year, but I'm surprised that the season opener hasn't sold out. All those in attendance will receive a free magnet schedule courtesy of Belle Tire.
Not only did Anaheim kick Detroit out of the playoffs this year, but two former Wings jumped ship for the defending Stanley Cup champs. Wings fans will not get to see former defenseman Mathieu Schneider as he is currently out with a broken ankle. However, we will see Todd Bertuzzi play and it'll be interesting hearing the crowd's reaction on this one.
Feel free to leave any comments or reactions about the game on this post- I'd love to hear what you guys have to say. I'm just so happy that hockey is starting back up!
Here's hoping that Detroit gets some sort of retribution on the Ducks for ending our postseason too early.
If you haven't seen the interview already, I suggest you go read it or at least skim it right now. The Detroit News did a great job holding a roundtable discussion with the five masterminds behind the Red Wings and it really is a great read. You get to hear insight from team owner Mike Ilitch, GM Ken Holland, Asst. GM Jim Nill, former coach and current advisor Scotty Bowman, and senior vice president Jimmy Devellano.


Have the flu? That's unfortunate. It doesn't have to be completely miserable, however, as there are certain foods that can soothe side effects while also helping boost your immune system. Here are five foods to try when you have the flu.
These can soothe a sore throat, swollen throat, and a dry throat. They also help you stay hydrated, which is essential when successfully fighting the flu. Staying hydrated keeps your mucus thin and helps ease congestion. Try to eat popsicles made from 100% fruit juice, as these will give your body nutrients rather than sugar water.
Turkey sandwich. Turkey is lean protein, which is a great component of a healthy diet. The more energy you have, the more easily your body can fight off illnesses.
You may not feel up to eating a salad while sick, so try a glass of vegetable juice instead. You'll get the antioxidants you need while doing so. Not a fan of veggies? Try 100% fruit juice instead.
Chicken soup. It's good for the soul and good for the flu! Chicken soup helps you get the fluids you need while also providing nourishment. Hot chicken soup can help improve the tiny hair-like parts in the passages of your nose protect your body from bacteria and viruses.
This seasoning can help boost your immune system and can also lower your risk of developing more colds.


text:
Due to the Covid-19 Pandemic tourism in Hawaii has halted. Our offices are closed due to the stay-at-home orders by the State of Hawaii. We apologize for any inconvenience. Please stay healthy. We hope to see you soon.
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Franklin D. Roosevelt was President of the United States when Pearl Harbor was attacked. The next day, he asked Congress to declare war on Japan. In his speech, Roosevelt mentioned the date of the attack—December 7, 1941—and called it "a date which will live in infamy." He meant that in the future, that date would be remembered as a day when something terrible happened. Many decades after the attack, that date does indeed continue to live in infamy.
In his speech, President Roosevelt also said that the United States had been at peace with Japan and was hoping to maintain that peace. That hope was shattered on December 7. As a direct result of the attack, the United States entered World War II.
Roosevelt had made Pearl Harbor the headquarters for the US Pacific Fleet earlier in 1941. He did this as a sign to Japan that the America was preparing for war, a move that he was warned against making. Roosevelt knew moving the fleet could trigger an attack. But he thought it was more important to show that America was powerful and ready to stop Japan from continuing to expand its territories.
Many people believe that Roosevelt could have prevented the attack on Pearl Harbor. They say he failed to act on information he received about a planned attack, though this has never been proven.
The military at Pearl Harbor was under the command of Admiral Husband E. Kimmel, who worked alongside General Walter Short. Not long after Kimmel was put in charge, he voiced his concern about Pearl Harbor being at risk of a surprise attack. However, he didn't make any changes to prepare for such an attack.
Adm. Husband E. Kimmel
It has been said that both Kimmel and Short were given numerous warnings that an attack was possible, but neither one took any action. They were sent a message from General Marshall, Chief of Staff of the United States Army. The message stated that the military at Pearl Harbor should prepare for an attack in such a way as to avoid causing alarm among the civilian (non-military) population. However, no action was taken.
And on December 3, 1941—just four days before the attack—a final warning letting Kimmel know that war with Japan was close at hand was again ignored.
On the day of the attack, Kimmel and Short had planned to play golf. Instead they faced terrible destruction. Could it have been prevented? The question remains.
Both men admitted that they hadn't expected an air attack. However, Short claimed that the government hadn't provided the right resources. He stated that their ability to protect the base was limited, even if they had warning.
Kimmel and Short were removed from command ten days after the attack. The search for the truth about what happened at Pearl Harbor lasted for the rest of their lives. The two men kept trying to clear their names of any wrongdoing.
Admiral Chester W. Nimitz, who took command of the US Pacific Fleet after Kimmel, thought it was better that Kimmel hadn't prepared for the attack. He said that if they had prepared, the fleet of ships would have left Pearl Harbor and gone out to sea. There, they all would have been destroyed, and more than five times as many American sailors would have been lost.
Short died in 1949, and Kimmel died in 1968. In 1999, both men were cleared of wrongdoing by the US Senate.
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text:
Q: Join three Lists in CAML Suppose that we have three tables(Three Lists in SharePoint).The relations between tables are described by the following image.

I want to translate the following query to CAML query:
select c.* from TableB b inner join TableA a on
b.TableAId=a.Id inner join TableC c on
c.TableAId=a.Id
where b.Nam='ABC'
order by c.InsertDate

I know that in CAML I can join first Table B and Table A and then
with the resulted Table A.Id ,then query Table C.
But this is two step fetch data and also I lose order by c.InsertDate  in first query.
And also if I want to limit only 10 result from TableC, In first CAML query(join query) I must fetch all data in first query.
Is there better approach to implement this query in SharePoint?

A: For such complex cases you might need to create DataContext and use Linq to SharePoint.. SPMetal command utility is used to create .CS code file for Entity Context..
Using this generated class you can easily query using LINQ..
Have a look at these:
Using LINQ to SharePoint
How to: Query Using LINQ to SharePoint


So taking the Costum Bokeh on and off works like a charm. Replacing the Bokeh with another "Preset" is easy as well. So far I got the diamond shaped Bokeh, and a heart which i will not post any pictures of since its a total cliche.


text:
Soccer Betting Tips EUROPE: Euro 2020 - Qualification
Wales vs Slovakia
EUROPE: Euro 2020 - Qualification
Best tip posted by : wampecc
Wales vs Slovakia - Best Bet Tips
League: EUROPE: Euro 2020 - Qualification
Bet on Wales vs Slovakia and claim your 100% bonus with Unibet !
This will be just the fourth meeting between Wales and Slovakia, with the Dragons winning two and losing one – most recently a 2-1 victory at Euro 2016 in the group stages.
In Slovakia's only previous visit to Wales in any competition, they ran out 5-1 winners in a Euro 2008 qualifier at the Principality Stadium back in October 2006.
Wales have won their opening match in their last two major qualifying campaigns, beating Moldova 4-0 in World Cup 2018 qualifying, and Andorra 2-1 in EURO 2016 qualifying.
This will be Wales' 15th European Championships qualification campaign, with the Dragons looking to secure successful back-to-back attempts after reaching their first European Championship finals in France in 2016.
Slovakia are winless in their last six away matches in all competitions (D1 L5), since a 2-1 victory in Lithuania back in June 2017.
Under Ryan Giggs, Wales have won two and lost two of their four previous competitive matches, falling to a 1-2 defeat in their last such match versus Denmark. Indeed, Wales have not lost back-to-back competitive matches since September 2013 (a run of three).
During Wales' 1-5 defeat to Slovakia back in October 2006, Gareth Bale scored what was his first ever goal for his country.
Should he feature, Ashley Williams will make his 85th appearance for Wales, moving third alongside Gary Speed in the all-time cap list. Indeed, only Neville Southall (92) and Chris Gunter (94) have made more than Speed for the Dragons.
EUROPE: Euro 2020 - Qualification action continues with Wales taking on Slovakia. We propose the best bet prediction for the game Wales vs Slovakia, valid for the EUROPE: Euro 2020 - Qualification, which will be played on 24.03.2019 14:00. Look for the best betting odds and free bets for EUROPE: Euro 2020 - Qualification offered by the best bookmakers.


text:
Spartans to say farewell to Munn Arena on senior night
Chris Solari
A few were Tom Anastos' first recruits. A few were holdover commitments. Michigan State's eight hockey seniors, along with redshirt junior David Bondra, will take the Munn Arena ice Saturday night one final time as Spartans.
"Being here — the full experience, from hockey to school to social life to everything — has been absolutely unbelievable," senior captain Michael Ferrantino said this week.
They will be honored after the Spartans' home finale against Ohio State, which faces off at 7 p.m. Here's a look at the outgoing class (stats prior to Friday's game against the Buckeyes).
► David Bondra, F, Annapolis, Md.: The son of NHL great Peter Bondra has a goal and four assists in 67 career games. He expects to graduate in May but could return for a fifth season.
► Matt DeBlouw, F, Chesterfield: A seventh-round pick of the Calgary Flames in 2012, DeBlouw has 25 goals and 27 assists in 125 career games, including seven goals and seven assists this season.
► John Draeger, D, Fairbault, Minn.: A third-round pick of the Minnesota Wild in 2012, Draeger has three goals and 27 assists in 128 career games, including a goal and seven assists this season.
► Michael Ferrantino, F, Plymouth: Three-time captain Ferrantino has a career-best 24 points this season and is MSU's active leader in goals (33), assists (44) and games played (145). He has nine goals and 15 assists this season.
► Jake Hildebrand, G, Butler, Pa.: A first-team All-American and the Big Ten Player of the Year last season, Hildebrand is allowing 3.10 goals per game with a .904 save percentage this season. He ranks second all-time in saves at MSU and third in career shutouts with 13.
► Justin Hoomaian, F/D, Novi: Hoomaian has two goals and four assists in 96 career games. He transitioned to defense in the middle of this season due to injuries on MSU's blueline.
► Ryan Keller, F, Farmington Hills: Keller has 17 goals and 21 assists in 108 career games, including three goals and four assists this season.
► Nate Phillips, G, Jackson: A walk-on, Phillips has provided depth in practice during his five seasons.
► Travis Walsh, D, Haslett: The grandson of former MSU coach/athletic director Ron Mason, Walsh has three goals and 41 assists in 138 career games. He has a goal and 11 assists this season.


text:
National Scenic Riverway WI, MN
Recreation of a voyageur carriying two 90 lb packs of fur across a portage to avoid rapids or move to another river
By the late 1600s, French fur traders had entered the St. Croix valley and begun interacting with both the Dakota and the Ojibwe. The fastest way to get to the St. Croix from the east took months. Fur traders went through the Great Lakes, up the Bois Brule River (which flows north into Lake Superior) and portaged to the headwaters of the St. Croix, which then flows south to the Mississippi River or took other similar routes. Everything the voyageurs brought to and from the valley had to fit in their canoes and at points be carried between rivers on their backs. To make the most of their long and arduous journeys voyageurs enlisted the help of the Dakota and Ojibwe to acquire the beaver and other fur pelts and then trade them for western goods. These sashed frontier entrepreneurs set up trading throughout the valley, connecting the St. Croix's inhabitants and resources to the wider world economy.
While the fur traders of the Midwest and north woods are the romanticized figures of the early American frontier, much of their industry took place as a subplot to intertribal conflicts in the St. Croix valley. The Ojibwe were just moving into the St. Croix Region at the time the voyageurs reached the area. The Ojibwe had previously traded with voyageurs as they moved to the region from the east. The Dakota which occupied most of Minnesota and part of Wisconsin prior to this time had had limited contact with the fur trade and were eager to gain trade goods including guns. The Ojibwe helped them establish trade. The Ojibwe would become their most common rival in the valley as both vied for expanded territory as the Northwoods became over hunted and could no longer nutritionally sustain both groups. The fur-trade contributed to this conflict, but did not instigate it.
Traders both limited and aggravated tribal conflicts amongst the Dakota and Ojibwe. In some instances, traders encouraged tribes to expand their hunting ground into the territory of other groups they felt were not trapping enough, which led to violence. However, in other cases they attempted to broker peace, because the tribes hunted smaller areas in times of war. As the fur trade in the valley transitioned from French to British in the 1760s and then finally to American control after the War of 1812, federal Indian agents began to play a greater role in regulating the industry's impact on tribal conflict. Adopting a policy of separation, agents actively discouraged traders from working with both Ojibwe and Dakota at the same locations and sought to stop them from building trading posts near the territorial borders. In one instance in 1832, federal agent Henry Schoolcraft burned down a trading post near the 1825 boundary separating Dakota and Ojibwe territory (near the site of Taylors Falls, MN).
You too can hike the trail used by fur traders and Ojibwe to travel from the Namekagon River to Lake Court Oreilles
Throughout the valley there are a number of locations that have been historically connected to the fur trade as portages and trading posts. The most noteworthy portages are the St. Croix-Bois Brule at the headwaters, the Namekagon – Lac Courte Oreille portage below Hayward and the Namekagon-Lake Owen portage near Cable. Fur trading posts were known to exist in many locations throughout the valley including two known locations along the Riverway. In 1753, French fur traders established a post near the mouth of Sunrise River, under the order of New France official Louis-Joseph Gaultier de La Verendrye. In 1784, Michel Cadotte opened a post near the Lac Courte Oreilles portage. Two fur posts located on tributaries to the St. Croix have been rebuilt and can be visited today. These are Fort Folle Avoine near Webster, Wisconsin on the Yellow River and the North West Fur Company post on the Snake River near Pine City, Minnesota. A visit to either of these sites will help one understand and visualize the fur trade.
401 North Hamilton Street
St. Croix Falls , WI 54024


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It's August 29th, and it's time for Pin-spired!
As always, as the first of the month approaches (and we like to do it over a weekend), I partner up with Shay at Mix and Match Family and Mel at The Larson Lingo to Get Pin-Spired!
We're hoping that all of you will join in the fun!
The focus of the post today is a super simple look.
Instead of a black sweater, I wore my black MUST HAVE shirt.
Remember to size down in this shirt. I am wearing an x-small.
Kendra Scott is having a Labor Day sale with 15% OFF and FREE SHIPPING off of your entire order with the code 2014LDW.
All women's Converse at Nordstrom HERE.
Accessory Concierge is extending us a 20% OFF code.
Just enter the code PTMT20 and you're all set!
I can't say enough great things about THIS bracelet or THIS necklace.
Love them both so much!
*There's also a Labor Day sale going on at Accessory Concierge!
Click HERE to see a spiky necklace for $12 that looks like the gold spikey S and D bracelet!
Click HERE for a sky blue multi strand necklace.
If you want a closer look at the Converse that are similar to mine, here you go!
These have zippers, and I LOVE the zippers!!!! Totally wish mine had the zippers actually.
Click HERE (only 6 sizes left when the post went live)!
They are 33% OFF right now making them only $43.51!!!!!
Make sure you order 1/2 size down.
If you prefer to NOT have the zippers, click HERE for all of the other women's converse choices.
I like the light grey, the black, the white, and the navy!
I JUST SAW THAT NORDSTROM IS RUNNING A SPECIAL PROMOTION RIGHT NOW on the classic converse.
Converse are regularly $44.95 , but right now they are BUY 2 FOR $75 !
Buy 2 for you…or Buy 1 for yourself and and 1 for your daughter…or anybody else!
This next outfit was the first outfit I pinned after I ordered my converse last year.
It was super simple, and I already had all of the needed pieces.
That's all you need! If you already have the other 3 pieces, just add in the converse and you're set!
So here's a side by side of the looks.
Totally simple, but Totally cute.
Here is a collage of just a handful of times I've worn my grey ones since purchasing them.
Remember to order a 1/2 size down!
Thinking they might be on my Christmas list.
Look at this next pinterest inspiration and tell me you don't want to wear that entire outfit.
Click HERE for a similar shirt that I found last night at Nordstrom!
Look below and see how cute and FRESH white converse are!
Click HERE for the classic white. Click HERE for shoreline version with the elastic back.
Aren't those images pretty convincing?
They all have this cool and laid back (BUT SUPER CUTE AT THE SAME TIME) vibe.
And look at these outfits with dark converse.
Totally DYING over that look on the far left. How darling is she?!
And I never in a million years would have thought I would be a fan of the black ones. But I am.
So, that was my Pinspired look for the month!
MUST HAVE jeans, MUST HAVE shirt, and converse.
You can't get any easier than that!
eden bracelet HERE, similar pink cardigan HERE with amazing reviews!
I think this next picture illustrates nicely how the flats add a great pop of color to an otherwise basic outfit.
Must have wedges on the left (sold out), MK Mandarin Moccasins on the right!
If your size is no longer available in the MK mandarin moccasins, and now you are dying for some pop of color moccasins, there is an option HERE that comes in coral, turquoise, and yellow!
And they are UNDER $45!
The spikey bracelet (in rose gold) that looks like my Stella and Dot renegade bracelet HERE.
Pendant necklace HERE that is now UNDER $9 in both white and turquoise.
ANTHROPOLOGIE IS AN ADDITIONAL 20% OFF OF SALE ITEMS today through the weekend!!!! Click HERE to shop the entire sale.
Click HERE for my kelly green lace top (also comes in navy and white, but you have to wear a cami under the white).
And I'm totally smitten with THIS Anthro shirt. Has anybody seen it in person?
The regular price was totally out of my reach at $168, but now that it's an additional 20% OFF of $89.95 I'm considering it!
A military anorak vest HERE.
LOFT is 50% OFF select new fall items with lots of great choices!
Nordy app open! Thanks for all the ideas!!
sounds amazing esp after just finishing our bottle of wine!
LOVED the e-mail! You sound like my kind of girls!
Julie and Susan…or Susan and Julie….not really sure the order! ha!
I also got this picture from Ashley, one of my regular readers, when she was on her anniversary trip in Playa Del Carmen! So cute!
Ashley is wearing the magenta Rayne necklace and the neon yellow Morgan studs!
This would be a great time to pick up my favorite abalone elle earrings for fall!
If you want to take advantage of the code but need help deciding what you want, you can review the MUST HAVE announcement of the Kendra Scott jewelry HERE.
You'll get to see lots of different pieces styled lots of different ways!
And you'll get to see my favorites!
Click HERE if you are new here and want to see a MUST HAVE review!
Wanna win $500 to William Sonoma?
UM. OF COURSE YOU DO.
Yesterday marked the 3 year anniversary of my friend Shay's Mix and Match Mama site!
Shay is hosting a super easy contest where you just pin some of her images to enter!
Go over HERE to read about the contest….pin like a crazy person…and then cross your fingers that you'll be the winner!
Get Pin-spired: Brought to You Today by the Most Worn Item In My Closet!
Oh my heavens! The zippers on those Converse are just about the cutest thing I have EVER seen! Love them!! And your black was so simple and yet perfect at the very same time. Yay for Friday friend!!
You may have just sold me on the converse!
I wear my white converse all of the time but I think I need the gray zipper pair too! Love the must have shirt, distressed jeans and converse combo! Thanks for hosting the linkup!
Girl!!! You know I'm a fan of the Converse! This year…Ebby Lee is too!!
Great post, but the link for the moccasins under $50 takes me to a V-neck t shirt that's styled in a really weird way.
Hi Peggy! I fixed the link! Thank you so much for bringing it to my attention. And that t-shirt that the link originally went to? That is my favorite white v-neck. But I agree 100%. Not a fan of how it was styled!
Pretty sure I need some Converse in my life!!
Wow. You really do wear that shirt a lot.
The link to the Converse sale takes us to the Destroyed jeans. Sorry.
Hi Riley! I don't know why all of the links are acting up today! I fixed it!!! Thank you so much for letting me know!!!!
Converse are the best! I have a grey pair and a polka dot pair, Love them! You rocked your looks! I had the pendant necklace in my cart yesterday and told myself I didn't need it…. but you just confirmed I do! HAHA! Order placed 🙂 Can't be $9! Have a GREAT weekend!
I just ordered a pair of earrings and necklace from the Kendra Scott website AND they were on sale AND THEY WERE 15% OFF!!!!! HOLLA!!!!!!
P.S. They were Elle earrings and the Rayne necklace.
I love that you've embraced Chucks. They are one of my all time favorite shoe and really do go with so much!
And YES to the Kendra Scott sale! Heading over now to shop!
I love the blue/gray crossbody bag in the last of your converse pictures! What's the brand?
Hi Sarah! It's Rebecca Minkoff. I got it for Christmas last year and it's been sold out since December. Sorry I don't have better news!
Hi there! Thanks for all your tips!! And fyi…jcrew is having an additional 40% off sale items with code 'weekend'! Have a great Labor Day weekend!!
How does the green anthro top fit? I looked at the reviews and saw both true to size and runs large, so I want your take.
Hi Christine! I would say true to size. I got a small.
Oh my goodness, Sheaffer, once again so many cute looks! I have never owned any Converse sneakers before, but with so many cute outfit combos, I'm reconsidering adding some to my closet. Also, now I must head over to the Kendra Scott sale to scope out more fun things to add to my wardrobe. Thanks for hosting this linkup — it's so fun!!
Just adorable! I'm looking forward to weather where we can start wearing sneakers again this fall. They are so cute with cuffed jeans!


The Mesa Public Library was designed by Nationally-Renowned Architect Antoine Predock. The building featured a lobby, meeting rooms, a bookstore, private reading areas, children's areas, and stacks. The entry featured a courtyard, reading garden, and children's multi-purpose area.


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Meta and other tech giants are laying off workers and slowing down. Here's what that means for Boston.
A general view outside the Meta office in King's Cross, London. Dan Kitwood / Getty Images
By Anissa Gardizy, Aaron Pressman, The Boston Globe
The Massachusetts technology sector has benefited over the past decade from the expanding operations of West Coast giants such as Google, Meta, and Amazon, which created thousands of local jobs.
Now, that trend is reversing. Meta, the parent company of Facebook, on Wednesday announced the largest layoff in the company's 18-year history, cutting more than 11,000 people, or 13 percent of its workforce. Google is also in cost-cutting mode, trimming projects, limiting travel, and slowing hiring, chief executive Sundar Pichai has said. And last week, Amazon said it would "pause" hiring for its corporate workforce until next year.
The economic pressure on the West Coast tech giants, which all have substantial operations in Massachusetts that they were planning to expand before the slowdown hit, could lead to more local job losses.
"It's the first time in over a decade that these Big Tech firms are losing momentum," said Mohamad Ali, chief executive of IDG, a leading tech industry research firm based in Needham. "This is a macroeconomic issue and Boston is seeing the effects."
Amazon opened one of two gleaming new offices in the Seaport in June, with plans to house 4,500 employees there, and runs its global robotics division from North Reading and Westborough. Google said in May that it could more than double its workforce of 2,100-plus in Kendall Square as part of an office expansion. And last December, Meta announced plans to triple its office space in Cambridge, where it employs 500 people.
All of those growth plans are showing signs of slowing down.
In June, Amazon held a ribbon-cutting event at its new Seaport office at 111 Harbor Way. – Jonathan Wiggs / The Boston Globe
Amazon declined to say how Massachusetts operations would be affected by its hiring pause. But in a message to employees, Beth Galetti, senior vice president for people and technology, said hiring would resume next year and top executives "remain excited about our significant investments in our larger businesses," as well as initiatives such as Prime Video and Alexa. Many of the company's employees in Boston work on the Alexa voice-assistant team.
"Our long-term intention and commitment to the communities where we have a presence remains unchanged," Amazon said in a statement.
Amazon said in June that it employed 4,500 people in corporate and tech roles in Boston and had an additional 1,000 open positions. The company would not confirm its current headcount in Boston. It has 330 local job openings listed on its website, and it's unclear how many may have been filled since June.
Earlier this year, Meta was gearing up to triple its real estate footprint in Kendall Square after leasing a 250,000-square-foot office building. But in July, a spokesperson said Meta was pausing the expansion, without providing a timeline for revisiting it.
On Wednesday, CEO Mark Zuckerberg wrote in a memo to employees announcing the layoff that "as we shrink our real estate footprint, we're transitioning to desk sharing for people who already spend most of their time outside the office."
Meta did not immediately disclose how many cuts would be made in its Cambridge offices. Prior to the layoff, it said it employed about 500 people locally, mostly engineers and technologists, including some working on the company's "metaverse" ambitions.
Exterior of 50 Binney Street in Cambridge where Facebook parent Meta Platforms Inc. was renovating office space. – David L. Ryan / The Boston Globe
The company said in June that its Reality Labs, the division working on virtual reality, augmented reality, and the metaverse, was a "growing presence in the Boston area." (The division also contributed $3.7 billion in losses last quarter, while the rest of the company made $9.3 billion.)
Patrick Bench, founder of Boston public affairs firm Benchmark Strategies, said Meta's slowdown in Kendall Square represents "lost growth," and not just for tech jobs. He expects the move will affect small businesses, from catering companies to restaurants to custodial services.
Meanwhile, Google's local expansion has been in the works since before the pandemic, when the company planned to lease most of a 16-story office tower at 325 Main St. in Kendall Square before it was built. Liz Schwab, head of Google's external affairs for New England, said in May that the company's local workforce could grow to 5,000 people when its office expansion is complete, though she did not provide a timeline.
Google's new office on Main Street in Kendall Square. – Jonathan Wiggs / The Boston Globe
Google's local headcount of more than 2,100 people has not changed since May, a spokesperson said.
The company planned to open the new 380,000-square-foot office in late 2022. The spokesperson said the office will open in the "near future," but Google has not set an opening date.
C.A. Webb, the former president of the Kendall Square Association, said she thinks Google will continue its growth in the area, "just maybe not quite at the clip that they planned." Meta, on the other hand, "looks more vulnerable," given the fundamental shifts going on inside the company.
Meta "may just end up cutting their losses and letting the talent in this market be remote, versus feeling the need to sustain the [office] overhead that they've been carrying," she said.
And then, of course, there's Twitter: Last Friday, Elon Musk began cutting half of the company's 7,500 worldwide employees, and the Boston office is losing about 55 people, according to a letter from Twitter to the state. About 300 employees had previously reported to the Boston office and recent cuts have hit the marketing, curation, and communications teams, according to a source familiar with the matter.
The latest moves come after some prominent local companies have slashed payroll to adapt to the slowing economy and tighter financing market.
Last month, struggling wireless Internet service Starry said it would cut half its workforce, including 175 jobs in Massachusetts, while cybersecurity companies Cybereason and Snyk each announced layoffs of about 15 percent. And in August, online retailer Wayfair cut 870 jobs, 400 in Boston, and reduced its office space.
"The number of families and individuals who lost their jobs is brutal," said tech recruiter Joe Suliman, partner and head of Daversa's Boston practice, referring to the spate of job cuts across the industry. "The companies that recently had to do major layoffs were managed irresponsibly over the last few years and they should bear the responsibility of that miscalculation."
The local presence of Big Tech firms has long played an integral role in Boston's innovation scene, said venture capitalist Jeff Bussgang of Flybridge Capital Partners.
"It's provided a massive magnetic force for great technical and startup talent to be employed and trained in Boston," he said.
But he also thinks the aggressive expansion of the tech giants actually hurt local startups. "They were soaking up all the talent, and that had not been the case eight to ten years ago," said Bussgang, who also teaches at Harvard Business School. "It [became] really hard for our startups to hire."
Paul English, the cofounder of travel-tech firm Kayak, just recruited an executive from Meta to run one of his venture studio's new startups, a review app called Deets.
"One of the reasons I was able to recruit him away from Facebook, where he's paid a zillion dollars, is the chill in Big Tech," English said. "For startups that are hiring, I think they like seeing Big Tech slow down a little bit."
Ultimately, that's why Webb thinks Boston won't see an exodus of tech workers as the big companies retrench. "Maybe that engineer isn't going to get to raise her salary 20 percent," Webb said. "But there is another company waiting to employ her here in five minutes."
History shows, in any case, that the tech giants will not survive indefinitely, IDG's Ali said.
"Every company out there . . . gets to a point where they peak and they either come down — there's the Polaroids and the Kodaks — or they remake themselves," Ali said. "Tech will continue to be super important in our economy, but I think we'll start seeing some weeding out. And there'll be new tech companies that emerge. There'll be the next Google, the next Amazon, or the next Facebook."
Visit Channel 4 tests a 6 p.m. newscast without a sports report
Sam Trabucco, a Roxbury Latin and MIT grad, got rich trading crypto. Now he's the odd man out in the FTX saga.
International Place, a mainstay of the Financial District, to get a $100 million new look
Caroline Ellison and FTX co-founder Gary Wang plead guilty to fraud


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"Marcus Aurelius Antoninus." Encyclopedia of World Biography. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
"Marcus Aurelius." UXL Encyclopedia of World Biography. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
Marcus Aurelius (Marcus Aelius Aurelius Antoninus) (mär´kəs ôrē´lēəs), 121–180, Roman emperor, named originally Marcus Annius Verus. He was a nephew of Faustina, the wife of Antoninus Pius, who adopted him. Marcus married Antoninus' daughter, another Faustina. From youth he was a diligent student and a zealous Stoic. With his adoptive brother, Lucius Verus, as colleague, Marcus succeeded Antoninus in 161. Verus allowed him to dominate, and from 169 Marcus was sole emperor. His reign was spent defending the empire against Parthians, Germans, and Britons. He won a victory over the Marcomanni (167–168), which was commemorated by the Antonine column (Piazza Colonna, Rome), erected by his son and successor, Commodus. Devoted to his duty and humanitarian in his conception of it, Marcus Aurelius was concerned with improving living conditions for the poor, particularly minors. He was always lenient with political criminals and tried to decrease the brutality at gladiatorial shows. He did, however, persecute the Christians, whom he regarded as natural enemies of the empire. His Meditations, available in several translations, expresses with great beauty and humanity a philosophy with a Stoic basis. The virtuous character of Marcus Aurelius is revealed in his letters to his tutor Fronto.
See biography by A. R. Birley (1966); study by J. H. Oliver (1970).
"Marcus Aurelius." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
Marcus Aurelius (121–180) Roman Emperor (161–180) and philosopher of the Stoic school, b. Marcus Annius Verus. From 161 to 169, he ruled as co-emperor with his adoptive younger brother, Lucius Aurelius Verus (d.169). The much-admired Meditations, his one surviving work, is a collection of philosophical thoughts and ideas that occurred to him during his campaigns, on the last of which he died.
"Marcus Aurelius." World Encyclopedia. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
Marcus Aurelius: see Marcus Aurelius.
"Aurelius, Marcus." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
Student of Philosophy. Originally named Marcus Annius Verus, the future emperor called Marcus Aurelius was raised by his grandfather and mother. He was attracted to the study of philosophy when he was only twelve years old. Epictetus was a great influence on him, which is evident in his work commonly called the Meditations, though probably called by him Notes to Himself. This was probably a kind of philosophic diary, not intended for publication, which probably was written as an older man and possibly during his campaigns against the Germanic tribes. He seems also to have incorporated elements of Platonism. In fact, the diary was lost and recovered only in the fourth century c.e. Like Epictetus, Marcus Aurelius was concerned with the making of moral choices in life and with the role of divine providence in events. He believed that one is to avoid those things that distract him from making correct choices, including power and glory, which are transitory anyway, and to forego his personal satisfaction for the sake of a greater good.
Philosopher Emperor. Aurelius became co-emperor, along with his half brother Lucius, when Antoninus died in 161. The new emperors were immediately faced with revolts in the borderlands and sent armies to quell the disturbances. Lucius, then known as Verus, died of plague while both emperors were leading Roman armies in Dacia. After several serious military setbacks, the Romans were able to push northern incursions out of Italy, but Aurelius had spent much treasure in the effort. He spent nearly the rest of his rule dealing with warfare in the borders, until his death in the north in 180.
Anthony Birley, Marcus Aurelius: A Biography, revised edition (New Haven: Yale University Press, 1987).
Mark Forstater, The Spiritual Exercises of Marcus Aurelius (New York: Harper-Collins, 2000).
"Marcus Aurelius." World Eras. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.


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Why are Microsoft and Warburg Pincus wooing BrowserStack
Software maker Microsoft, which signed a business partnership BrowserStack in March, has also offered to invest around $40M in the company at a valuation of $400-500 million over the past few months Madhav Chanchani&Shadma Shaikh | ET Bureau | May 23, 2017, 08:20 IST
Web-testing platform BrowserStack is being wooed by a slew of investors - strategic and financial - as they hunt for the next big winner in a sector, which combines rapid business growth with steady profits and offers a stark contrast to cash guzzling consumer internet startups that have dominated the funding cycle in recent times.
Mumbai-based BrowserStack, a bootstrapped venture - a term that denotes a company which has not raised any institutional funding - has received interest from marque venture funds including Sequoia Capital and Warburg Pincus, according to three people aware of the development.
Software maker Microsoft, which signed a business partnership with BrowserStack in March, has also offered to invest around $40 million in the company at a valuation of $400-500 million over the past few months, said two of the sources cited above.
"But the company is holding out for a (higher) valuation," the sources said, adding that it is looking for a $800 million to $1-billion valuation. Microsoft and Warburg Pincus did not reply to email queries from ET. Sequoia Capital responded saying, "this information is incorrect".
Founded by IIT-Bombay batchmates - Ritesh Arora and Nakul Aggarwal - in 2011, BrowserStack is the fourth venture for the duo, and the first to succeed. The company helps developers visualise what their code will look like and how it will perform across browsers and operating systems. A code has to work across multiple browsers - Windows' Internet Explorer, Apple's Safari and Google's Chrome. Each browser has its nuances and the behaviour of codes varies on different platforms.
Arora, 33, did not confirm the investment talks but said his company interacts with venture capital firms on a regular basis to explore choices.
"I've known the Sequoia folks for four years now and Warburg for over a year. We speak to a lot of VCs but there's nothing substantial that has developed in terms of funding," he said.
Arora, 33, who along with Aggarwal was a winner of the inaugural ET Startup Awards in the Bootstrap Champ category in 2015, told ET that, "we have been open to the option of fundraising, we don't have a timeline though and haven't decided on how much to raise. It's very open-ended at the moment."
BrowserStack's annual recurring revenue is estimated to be about $40 million to $50 million, with about 76,000 paying customers including companies like Adobe, Microsoft, Twitter, AirBnB, Spotify and Amazon.
For investors, the Indian enterprise SaaS space is attractive as companies offer competitive pricing and requires less upfront investment. What's more, with global giants including, Apple, Intel and Nutanix shopping for such startups, the chances of exits are also bright. So far, 67 SaaS startups have received funding this year.
Freshdesk, one of India's best known product software makers, was valued at about $700 million when it raised a round led by Sequoia Capital in November and is estimated to have an annual revenue run rate of $60-70 million.
Other bootstrapped Indian SaaS startups include Zoho, which competes globally with the likes of Salesforce and Microsoft, Delhi-based web-testing platform Wingify, hospitality SaaS provider Rategain and FusionCharts, a data visualisation company that has over 25,000 consumers across 118 countries.
"From a company's perspective, if there is good customer traction and the numbers look good, there is no harm in raising external funding, as long as there is a vision for what the money is going to be used for," said Naganand Doraswamy, founder of IdeaSpring Capital.
Tags : Internet, BrowserStack, Warburg Pincus, Microsoft, Funding


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text:
Q: Prove the identity $\frac{1}{\tan (x)(1+\cos( 2x))} = \csc(2x)$ $$\frac{1}{\tan (x)(1+\cos(2x))} = \csc(2x)$$
I really don't know what to do with denominator. Sure, I can use the double angle formula for cosine, and get:
$$\frac{1}{\tan(x)(2 - 2\sin^2(x))} = \csc(2x)$$
But what's next?

A: $$\frac{1}{\color{#0F0}{\tan x}(\color{#00F}{1}+\color{#F00}{\cos 2x)}}=\frac{\color{#0f0}{\cos x}}{\color{#0f0}{\sin x}(\color{#00F}{\sin^2 x+\cos^2 x}+\color{#F00}{\cos^2x-\sin^2 x})}$$
$$=\frac{1}{2\sin x\cos x}=\frac{1}{\sin 2x}=\csc 2x$$

A: There's a better form of the double-angle formula for this purpose: remember there are three different forms of the cosine double-angle formula,
$$ \cos{2x} = \cos^2{x}-\sin^2{x} = 2\cos^2{x}-1=1-2\sin^2{x}. $$
Hence
$$ 1+\cos{2x} = 2\cos^2{x}. $$
Now, you also know $\tan{x}=\frac{\sin{x}}{\cos{x}}$ (right?), so you have
$$ \frac{1}{\tan{x}(1+\cos{2x})} = \frac{\cos{x}}{\sin{x} \cdot 2\cos^2{x}} = \frac{1}{2\sin{x}\cos{x}} = \frac{1}{\sin{2x}} = \csc{2x}, $$
using the sine double-angle formula.

A: We have to prove $$\frac{1}{\tan(x)(1+\cos(2x))}=\csc(2x)=\frac{1}{\sin(2x)}$$ Multiply both sides by $\tan(x)$ and apply $\sin(2x)=2\sin(x)\cos(x)$ and you arrive at $$\frac{1}{2{\cos^2(x)}}=\frac{1}{1+\cos(2x)}$$ raise both sides to the power of -1, and divide both sides by two and arrive at $$\cos^2(x)=\frac{1}{2}+\frac{1}{2}\cos(2x)$$ which is a well-known result that can be easily derived using Euler's formula.

A: Here's one more -- this is being a bit "cute", but it is related to another trigonometric relation you should be meeting soon, if you haven't already.
$$ \frac{1}{\tan (x)(1+\cos(2x))}  \ = \  \csc(2x) \ \ \Rightarrow \ \ \frac{1}{\tan (x)(1+\cos(2x))}  \ = \  \frac{1}{\sin(2x)} $$
$$ \Rightarrow \ \ \tan (x) \ = \ \frac{\sin(2x)}{1+\cos(2x)}  \ \ . $$
If we now identify $ \ 2 \ x \ $ as the angle $ \ \theta \ $ , then $ \ x \ = \ \frac{\theta}{2} \ $ and we have
$$ \Rightarrow \ \ \tan \left(\frac{\theta}{2}\right) \ = \ \frac{\sin(\theta)}{1+\cos(\theta)}  \ \ , $$
which is one form of the "half-angle formula" for the tangent function.  To prove your original relation, you can start from this equation and work backwards.


Issued to brethren to form a Lodge in BALLYMONEY, Co. Antrim, 1 October 1789.
Grand Lodge of Ireland – Roll of Lodges, compiled by Bros. J.J. Nesbitt and William Scott for Bro F.C. Crossle – c. 1889.
Warrant issued 1 Oct. 1789 to Ballymoney, Co. Antrim to James Walker; Dan. McAllister and John McConlish.
1 October, 1789 – Ordered a Warrant to Brs. Jas. Walker, Danl. McAllister and Jno. McConlish to hold a Lodge in the town of Ballymoney, Co. Antrim.
Volume 3 of the extant Grand Lodge Registers record Jas. Walker; Danl. McAllister and Jno. McConlish registered 1 October, 1789. No registration of Master or Wardens.
A further 21 brethren registered up to 4 November, 1803.
No indication as to Master or Wardens.
A total of 54 brethren either transcribed from a previous volume or registered here up to 26 October, 1822.
Warrant 703 was issued on the 1st October, 1789 to James Walker, Daniel McAllister and James McConlish. This lodge was immersed in the activities of 1798 and the Seton revolt. The warrant was compounded for arrears in 1812, suspended in 1824, restored in 1824 and finally cancelled on the 7th July, 1825. It is interesting to note that the brethren were still in touch with Grand Lodge up until 1828 trying to get their warrant back.
Crossle Vol. 4.p. 339. Vol. 5.p. 440. Vol. 7.p. 60, 135. Vol. 10.p. 160, 162.
At a Meeting of Lodges, Nos. 135, 240, 655, and 703, of Free and Accepted Masons, Assembled together at Ballymoney, in the county of Antrim, in Monday the 14th of January, 1793.
Resolved unanimously, That at a time when the attachment of some to the Constitution is doubtful, we are happy in this opportunity, thus publicly to avow our sincere and strong Affection for his MAJESTY's PERSON and INDEPENDENT GOVERNMENT of this KINGDOM; and our wishes that his Crown may descend in succession to his latest Posterity.
Resolved unanimously, That we conceive he best merits, the appellation of a good Citizen who supports the laws of his country, and endeavours to promote the peace and good order of the Community to which he belongs; we will therefore support the Civil Magistrate in the execution of the laws of the land, collectively as well as individually, without respect to persons, regardless of religious distinctions, unsullied by any spirit of party and purely, from a with to maintain inviolate the INESTIMABLE BLESSINGS of our CONSTITUTION.
Resolved unanimously, That we shall be happy to meet and co-operate with any Lodge or Lodges of Free and Accepted Masons, who have by any public declaration shown, or shall hereafter show, a familiar attachment to the present CONSTITUTION, in order to pursue such measures as may be thought necessary to promote the peace and happiness of all his Majesty's Subjects in IRELAND.
Resolved unanimously, That united in sentiment as we are in love, we will carefully watch over the interests of our Brethren, and we will hold constant communication with each other for the common safety of all; and in case of danger will risk all we hold dear for our mutual safety.
`To Freemasons' - Whereas we, the Masters, Wardens, and Brethren of Lodges Nos. 240, 655, and 703, assembled on our Lodge-rooms in Ballymoney, have excluded Robert King, of Ballymoney aforesaid, from the benefits of Masonry, of which all concerned are hereby desired to take notice.
Given under our hands this 14th day of December, 1796.
Northern Star 2 December, 1796.
Resolved - "That, at this critical period, when the Loyalty of many are called in question, that we come forward to assert our attachment to our beloved King and Constitution in the most unequivocal manner; that we will pay a due respect to our most excellent laws, and be vigilant in detecting all Conspiracies whatever."
Resolved - "That it is with the utmost concern and detestation that we have heard of divers attempts and constitutions formed for the purpose of assaulting our worthy Brother, George Hutchinson, Esq."
Resolved - "That we, as Masons, pledge ourselves collectively and individually to our Brother G. Hutchinson, that we will, to the utmost of our power, aid and assist him in the due execution of his office as a Magistrate, and that we will watch the disaffected in this part of the Country, not only from injuring him, but from associating together either to promote treasonable or seditious purposes."
Resolved - "That our unfeigned thanks be returned to our Brother Hutchinson, for his promptitude at all times, in assisting the Craft, and for his unremitting attention to the Peace and Good Order of this Country."
Resolved - "That the motto belonging to our Ancient Order, to wit "Fear God, Honour the King, and Love the Brotherhood", shall never be violated by us; and we call on all the Fraternity to Show the world what they have ever individually been, that id loyal and peaceable subjects.
James Walker, Master of No. 703.
We the Masters & Brethren and Wardens of Lodges Nos. 235, 240, 571, 703, 730, 779, 844, 940, 942 return their thanks to the Rev. Benjamin Mitchell for the excellent and well adapted sermon preached to them at his Meeting House on Monday the 24th June inst., being the Anniversary of St. John.
N.B. We beg leave to return our thanks to the Delegated Free Masons met at Ballyeaston on the 25th May last for their worthy exertions in detecting Angus the Impostor.
Vol. 7.p. 135. & NP. Vol. D.p. 28.
At a Meeting of the Representatives of the following Lodges of Free and Accepted Masons, viz.:- Nos. 229, 235, 240, 365, 380, 397, 408, 414, 424, 431, 432, 655, 700, 703, 730, 754, 779, 818, 829, 844, 851, 905, 940, 955, 969 - convened at Ballymoney, on Monday the 14th of April, 1806 - the Worshipful Alexander Simpson, of Lodge No. 235, in the Chair - the following Resolutions were unanimously passed and ordered to be transmitted, signed by our Chairman, to the Right Worshipful the Grand Lodge of Ireland.
1st Resolved, that on the Resolutions of the County Antrim Meeting, convened at Belfast on the 20th of January last, being laid before us, we do most highly approve of them, and are resolved to abide by them.
2nd. That the Resolutions of the County Down Meeting, convened at Dromore on Tuesday the 18th of February, 1806, being laid before us, we do most highly approve of them, and are resolved to abide by them, and sincerely recommends it to all K.T's. and Royal Arch Masons in this Kingdom to do the same.
3rd. That it would be the Greatest satisfaction could be by the Right Worshipful the Grand Lodge afforded to us, if our Worthy Brother Irvin, Late Grand Secretary, would be restored to that Office, which he filled in the Grand Lodge, with high Honour to himself and great Satisfaction to us.
4th. That we would highly recommend to the Right Worshipful the Grand Lodge, that when a New Rule is moved for the Good of the Craft by them, that a statement of it would be sent to Country Lodges, that they might send their Memorials, according to their wishes to the Right Worshipful the Grand Lodge and a Majority of them should take place, and afterwards there could be no complaining.
5th. That we, having nothing more at heart that for the Good and Welfare of the Craft, and the Support of our Mother Lodge.
6th. That a Memorial be now drawn up by us, conveying our Sentiments, together with a Copy of these Resolutions to the Right Honourable and Right Worshipful the Earl of Donoughmore, G.M. of the Free and Accepted Masons in Ireland.
"To the Right Honourable and Right Worshipful Richard, Earl of Donoughmore, Grand Master of the Free and Accepted Masons in Ireland, May it please your Lordship, the Memorial of the Representatives of 25 Masonic Lodges, confined at Ballymoney, on Monday, the 14th April, 1806.
That your Memorialists, with the greatest respect, perceive that the Grand Lodge of Ireland, has recently been harassed by the baneful Effects of Party Spirit, disgraceful to any Society, but particularly unbecoming the Craft which is founded on Love, and devoted to Charity.
It further appears to Memorialists that many of the ancient Regulations of our Institution have been charged, an old and confidential officer displaced, a new office created, with a large salary annexed; and also, that attempts have been made to control those higher Orders of Masonry, hitherto unknown to the Grand Lodge - and to levy extraordinary Dues for defraying the Expenses of these new and complex systems.
These Innovations have produced Division, and the Press has groaned beneath the cumbrous Weight of exaggerated Facts on the one part, and vindictive Caution on the other, both condescending to use impassioned Language, highly unbecoming the heads of an ancient, honourable, and enlightened Institution, who should live together in Unity.
Memorialists, actuated by the most fervent desires for the Welfare of the Order, are most respectfully of opinion that your Lordship's fostering hand, and your Lordship's ONLY, can cure these rankling wounds, which, if not speedily healed, may endanger the Masonic Constitution in Ireland.
Memorialists therefore look up to your Lordship for Redress, most earnestly praying that you will be pleased to use the well-known Influence of your Lordship's highly exalted Character and Station, to put a final Stop to these Dissension's - to restore Unanimity, Tranquillity, and Love amongst those who have the Superintendence of the Craft, and to rescind those novel and pernicious Innovation's which have a Tendency to irritate the Feelings not only of our Constituents, but also of the respectable Brethren throughout Ireland.
On loan from Brother Dyson Atha, of Belfast:— Certificate issued 9 June, A.D. 1806, and of Super Excellent Masonry 3806, by Lodge No. 703, Ballymoney, Co. Antrim. It is to the effect that Charles Hamill" was initiated into the Sublime Degrees of a Royal Arch super Excellent Mason, and subsequently dubb'd a Knight of the Most Ancient and Right Honorable order of Sir Knight Templars." Signed by Archibald Harford, H.P., James Hay, C.C., Archibald Baines, G.M., Robert Johnson, Secretary. The Certificate is printed on parchment with red wax impression of a Royal Arch Seal attached to red ribbon. Also black wax impression of K.T. seal attached to black ribbon.
Lodge worked the Royal Arch and Knight Templar Degrees in 1806 as is evidenced by a Certificate dated 6 June 1806, confirming that Charles Hamill "was initiated into the Sublime Degree of a Royal Arch Super Excellent Mason, and subsequently Dubb'd a Knight of the Most Ancient and Right Honourable Order of Sir Knight Templars."
The Certificate is printed on parchment with red wax impression of a Royal Arch Seal attached to red ribbon. Also black wax impression of a Knight Templar seal attached to a black ribbon.
The following Masonic Lodges viz. Nos. 229, 235, 240, 380, 414, 703, 754, 818, 905, 910 & 955 return their sincere thanks to the Revd. Daniel McKee, for the very proper discourse delivered to them, on the 24th inst. from the following Text - Exodus 3rd Chap. & 3rd Verse.
Compounded for arrears, May 1812 but restored on the 7th May on paying £2. 10s. 0d. [£2.50] in lieu of arrears to Grand Lodge.
11 Oct. 1827 – Letter from Isaac Cochran appealing against the fines etc. against the Lodge.
6 May, 1828 – Further letter from the above noting that the Warrant will not be restored without the debts being cleared – requests debts waived.
"Warrant cancelled 7 July, 1825." – Fifty-four brethren registered.
From 1880 the Grand Lodge Correspondence is unsorted and held in yearly boxes.
The following are extracts taken from these yearly boxes ignoring routine correspondence, for example letters enclosing G.L. Dues, requests for G.L. Certificates and Half-Yearly returns etc. Included are some Royal Arch and H.K.T. Returns etc.
Up to 1939 G.L. replies are contained in "Letter Books" – from 1939 in the main the typed copy of the G.L. reply is attached to the Lodge letter etc.
22 May, 1946 - Read Memorial from various brethren praying for a warrant to establish a Lodge in Ballynahinch in the County of Down to be called the Spa. Recommended.
G.M.L. 6 June, 1946 – Confirmed.
Warrant No. 703 to Ballynahinch, Co. Down as "Spa Lodge", 7 June, 1946.
Arthur J. Heanen, Merchant (1009); Thomas J. Graham, Retired Army Officer (439) and Hutchinson P. Fishbourne, Cattle-trade (301) registered along with twenty-two others from various lodges, two marked "did not join" registered 7 June, 1946.
A total of 50 brethren registered up to 15 February, 1952. In most cases the dates when the issue of certificates is shown, together with the occupation of the brother.
A total of 86 brethren registered up to 16 April, 1982. In most cases the dates when the issue of certificates is shown, together with the occupation of the brother.


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