text: # Search by Topic
  
  #### Resources tagged with Spheres similar to When the Angles of a Triangle Don't Add up to 180 Degrees:
  
  Filter by: Content type:
  Stage:
  Challenge level:
  
  ##### Other tags that relate to When the Angles of a Triangle Don't Add up to 180 Degrees
  Geodesics. Non Euclidean Geometry. Mathematical reasoning & proof. Spheres. Games. Real world. Visualising. Maths Supporting SET. Surface and surface area. Working systematically.
  
  ### There are 5 results
  
  Broad Topics > 3D Geometry, Shape and Space > Spheres
  
  ### When the Angles of a Triangle Don't Add up to 180 Degrees
  
  ##### Stage: 4 and 5
  
  This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
  
  ### There and Back Again
  
  ##### Stage: 3 Challenge Level:
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
  
  ### Ball Packing
  
  ##### Stage: 4 Challenge Level:
  
  If a ball is rolled into the corner of a room how far is its centre from the corner?
  
  ### Three Balls
  
  ##### Stage: 4 Challenge Level:
  
  A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?
  
  ### Mouhefanggai
  
  ##### Stage: 4
  
  Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
explanation: The provided text is a collection of titles and brief descriptions of resources or problems related to the topic of spheres in mathematics. Each entry seems to be a separate problem or article, and none of them contain a direct question and answer format. However, they do present problems or topics that could be explored further.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Search by Topic
  
  #### Resources tagged with Spheres similar to When the Angles of a Triangle Don't Add up to 180 Degrees:
  
  Filter by: Content type:
  Stage:
  Challenge level:
  
  ##### Other tags that relate to When the Angles of a Triangle Don't Add up to 180 Degrees
  Geodesics. Non Euclidean Geometry. Mathematical reasoning & proof. Spheres. Games. Real world. Visualising. Maths Supporting SET. Surface and surface area. Working systematically.
  
  ### There are 5 results
  
  Broad Topics > 3D Geometry, Shape and Space > Spheres
  
  ### When the Angles of a Triangle Don't Add up to 180 Degrees
  
  ##### Stage: 4 and 5
  
  This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
  
  ### There and Back Again
  
  ##### Stage: 3 Challenge Level:
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
  
  ### Ball Packing
  
  ##### Stage: 4 Challenge Level:
  
  If a ball is rolled into the corner of a room how far is its centre from the corner?
  
  ### Three Balls
  
  ##### Stage: 4 Challenge Level:
  
  A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?
  
  ### Mouhefanggai
  
  ##### Stage: 4
  
  Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a collection of titles and brief descriptions of resources or problems related to the topic of spheres in mathematics. Each entry seems to be a separate problem or article, and none of them contain a direct question and answer format. However, they do present problems or topics that could be explored further.
  
  Label: multiple-question