Kenneth Jones

Jason Birch

Worksheet to be completed by a class who would be presented with this material.

Review Questions:

Fill in the blank

  1. The sphere is locally ______, but in reality has a ______curvature equal to 1.
  1. The covering argument concerning the sphere would create an infinite number of ______and in hyperbolic space would create an infinite number of ______.
  1. Dr ______is the best math teacher out there!
  1. Surfaces like the ______and ______are isometric with the xy-plane.

Challenge Questions:

  1. Can you think of a way to preserve the geometry of one path on a globe when flattening?
  1. What do you think occurs at the edge of the universe if = 1 (Remember when omega is equal to one the universe works towards a finite volume)?
  1. The value is actually a function of time based on the mass and volume of the universe, how is it that a function with infinite inputs can be a static value?

Answers to worksheet:

Review Questions:

Fill in the blank

  1. The sphere is locally (flat), but in reality has a (Gauss) curvature equal to 1.
  2. The covering argument concerning the sphere would create an infinite number of (slices or segments) and in hyperbolic space would create an infinite number of (over laps).
  3. Dr (Sarah) is the best math teacher out there!
  4. Surfaces like the (cylinder) and (cone) are isometric with the xy-plane.

Challenge Questions:

  1. Can you think of a way to preserve the geometry of one path on a globe when flattening?

Orientate that path as the equator.

  1. What do you think occurs at the edge of the universe if = 1 (Remember when omega is equal to one the universe works towards a finite volume)?

I dunno, I have a problem thinking that the universe doesn’t curve back around to itself.

  1. The value is actually a function of time based on the mass and volume of the universe, how is it that a function with infinite inputs can be a static value?

Consider limits as t approaches infinity. Time is endless so in theory it is the limiting value we are concerned with and not so much an instantaneous value.