- How can a 3-torus be formed?

a) identify opposite edges of a square straight across

b) identify opposite faces of a cube straight across--left to right, top to bottom, front to back

c) sweep a cube perpendicular to itself in the fourth dimension and connect the edges

d) identify opposite faces of a cube with a 90 degree rotation

e) other

- Which application of higher dimensions do you find most compelling?

a) a separating plane for higher dimensional data like heart disease, breast cancer, or big business and high finance

b) protein modeling in biology on a hypersphere

c) artificial intelligence and machine learning using a hypersphere

d) artistic representations

- Which best describes what you think about the geometry of the universe?

a) Euclidean/flat (satisfying the laws of Euclidean geometry) (NASA says so)

b) hyperbolic (*Heart of Mathematics*says so)

c) spherical (Einstein based his theory of relativity on this, and Jeff Weeks said this best resolved the problem of the missing fluctuations)

d) I think we've reached the limits of our current technology and it is too big for us to know (but we might know some day)

e) other

1. b)

2. answers will vary

3. answers will vary