TITLE: Non-Euclidean Geometry for Children
QUESTION [35 upvotes]: I should've asked this question two years ago when my son (at that time, 9 years old) came to me and said: "Dad, today in school our teacher drew a line on a paper and said this is a straight line, it goes from both directions and doesn't meet itself". I answered, "Okay, what is wrong with that". He said, "but I think it meets itself". I told, "how come?" Then, he drew a line on a piece of paper, made a cylinder with the paper and showed me how. At that time, I knew there is an element of truth in his idea, but being afraid of destroying the originality of his thinking I didn't add anything and instead promise him to think of his idea. I didn't keep my promise! But last night, he (now eleven) came back to me with the same idea thinking of what happens on a sphere. Again, I promised him  that we discussed it later on (that is supposed to be today). The question is how can I help him to develop his ideas. The question for you is: Are there any sources available?

REPLY [8 votes]: Actually, there is a perfectly nice non-euclidian geometry that does not require any extra imagination: spherical geometry. Just do the usual math and discover tons of cool stuff such as existence of a triangle with three right angles.