- Which did you find most compelling for why great circles
are intrinsically straight and shortest distance paths?
a) string pulled tightly
b) masking tape
c) toy car
- Why is the Pythagorean theorem false on the sphere?
a) Because we can create triangles with a hypotenuse the same length
as the other sides, making
a2 + a2
= a2 false for a triangle with nonzero sides.
b) Because we can create the two base sides a and
b with string, flatten and
create flat_c, and put it back on the sphere to see that it is too
a2 +b2 = flat_c2 >
c) Futurama says so
d) all of the above
e) none of the above, because the Pythagorean theorem is true
on the sphere