Murderous Maths

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Emmett has been reading and re-reading and re-reading all of the Murderous Maths books, and enjoying them immensely. He told me that you can't have a right triangle with an obtuse angle in it. I, being a geek and kind of mean, said, "Well, you can't unless the triangle is on the surface of a sphere." We've talked about triangles on spheres before, but I was a bit surprised when he confidently responded, "Correct!" His dad, not to be outdone, wondered about a triangle on a hyperbolic plane (shaped like a pringle), but shortly concluded that it could only be done in spaces with positive curvature. Emmett has it coming at him from all sides...

Comments

Suji said…
I love the geek-talk. And now you have me curious about curvature! Off to google it!
12:07 AM
Stephanie Ozenne said…
The easiest way to think about a triangle with angles adding to more than 180 degrees on a sphere (for me at least) is this: Imagine standing on the equator and walking to the North Pole. Then turn right 90 degrees and walk back to the equator. Turn right 90 degrees again, and you can walk back to your starting location. That triangle has angles that add to 270 degrees!
3:34 PM
Suji said…
Thanks for replying Stephanie! And for your comment on my blog post earlier too. :) I can visualize it now...you explain it so well! :)
11:09 AM
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