Pi vs. Tau
Pi vs. Tau
[On the left is a "forbidden"-style slashed circle with the π symbol, captioned "Pi". On the right is a "forbidden"-style slashed circle with 2π, captioned "Tau". Between these is 1.5π, captioned "Pau".] [Caption below the panel:] A compromise solution to the Pi/Tau dispute
Possibly, Randall used Wolfram|Alpha to calculate the result (he uses it a lot, for example What-if 70: The Constant Groundskeeper or What-if 62: Falling With Helium ).
However, when the comic was published, there was a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed.
This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, twice and once, respectively. There are 4 occurrences, however, in the first three hundred and ten (310 in base 8 equals 200 in base 10) digits:
Expansion that long indeed does contain 666 (the number of the beast ) four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.
In the first 500 digits of the actual octal expansion of pau, we also find that 6666 occurs once, and 666 occurs two other times:
(Note that this contains 500 digits after the decimal point.) No other run of 3 or more repeated digits (e.g. 111) occurs as many times, although 1111 occurs once, 111 occurs once elsewhere, and 333 and 777 also occur once each. 9 other strings of 3 digits occur 4 times, namely 164, 362, 521, 644, 432, 730, 43, 216, and 450, and only 573 occurs more often, as it occurs 6 times. Therefore, if 6666 is counted as two occurrences of 666, it is actually the joint second most common string of three numbers in the first 500 digits.
Coincidentally , e+2 is also very similar to 1.5 pi, although only to a few digits.

This is yet another of Randall 's compromise comics . A few mathematicians argue as to whether to use pi , which is the ratio between a circle's circumference and its diameter, or tau , which is the ratio between a circle's circumference and its radius.
Some consider pi to be the wrong convention and are in favor of using tau as the circle constant; see the Tau Manifesto , which was inspired by the article " Pi is wrong! " by mathematician Robert Palais and publicized by Vi Hart .  Others consider proponents of tau to be foolish and remain loyal to pi (see the Pi Manifesto ). Of course, regardless of which convention is used, the change is merely in notation — the underlying mathematics remains unaltered. Still, the choice of pi vs. tau can affect the clarity of equations, analogies between different equations, and how easy various subjects are to teach.
Most people know π (pi) by the approximation 3.14, but do not know τ (tau) which, by definition, is twice as large as pi. Randall is suggesting using "pau", which is a portmanteau of "pi" and "tau", as a number situated, appropriately enough, halfway between pi and tau, i.e. 1.5 pi or 0.75 tau. But of course his number would be inconvenient, as this value does not naturally turn up when working with circles or other mathematical constructs, so there are no commonly used formulas that would use pau.
The title text claims that pau can be approximated by e+2, as both values are roughly 4.71 — a similarity that holds little since it requires another irrational constant, e (although knowing the value of pau is somewhat more helpful in remembering e to 2 digits). It also attributes the nickname "Devil's Ratio" to pau, due to the sequence 666 supposedly appearing four times in the first 200 digits of pau when expressed in the octal base. However, this is not the case, and was likely due to an error in the computer system used by WolframAlpha; for more details see below.
The Tau/pi controversy was later mentioned in 2520: Symbols .
[On the left is a "forbidden"-style slashed circle with the π symbol, captioned "Pi". On the right is a "forbidden"-style slashed circle with 2π, captioned "Tau". Between these is 1.5π, captioned "Pau".] [Caption below the panel:] A compromise solution to the Pi/Tau dispute
Possibly, Randall used Wolfram|Alpha to calculate the result (he uses it a lot, for example What-if 70: The Constant Groundskeeper or What-if 62: Falling With Helium ).
However, when the comic was published, there was a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed.
This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, twice and once, respectively. There are 4 occurrences, however, in the first three hundred and ten (310 in base 8 equals 200 in base 10) digits:
Expansion that long indeed does contain 666 (the number of the beast ) four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.
In the first 500 digits of the actual octal expansion of pau, we also find that 6666 occurs once, and 666 occurs two other times:
(Note that this contains 500 digits after the decimal point.) No other run of 3 or more repeated digits (e.g. 111) occurs as many times, although 1111 occurs once, 111 occurs once elsewhere, and 333 and 777 also occur once each. 9 other strings of 3 digits occur 4 times, namely 164, 362, 521, 644, 432, 730, 43, 216, and 450, and only 573 occurs more often, as it occurs 6 times. Therefore, if 6666 is counted as two occurrences of 666, it is actually the joint second most common string of three numbers in the first 500 digits.
Coincidentally , e+2 is also very similar to 1.5 pi, although only to a few digits.
