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by cobertos 1173 days ago
Geometrically, this happens when alpha is 45. The two lines in the diagram from the article will be parallel and never converge. 2*alpha = beta+alpha

I was waiting for them to break this out into a special case or something but the article never did. Can't find any other material on this proof that mentions it
1 comments
scotty79 1173 days ago
You can divide partial sums first and then take the limit at infinity instead summing first and then dividing.

Not sure how much that helps with "infinite triangle" with two 90deg and one 0deg angles.

That's btw how you get sin90=1 which doesn't have any geometrical sense when we consider finite triangles.

Or in case of triangle with 45, 45, 90 maybe you could just pick different angle than 90 to be 2alpha.

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cobertos 1173 days ago
On the partial sums, okay, I see.

Though, still for the 45-45-90 I don't think you can pick a different angle? At least for alpha > 45 (because it also doesn't work for this, the lines diverge), you can always swap it so beta is > 45 for those cases. If you pick something other than 90 to be 2 alpha, the reflection mentioned in step 1 can't be done

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