Spherical Pythagorean theorem - finding length of longer side

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Discussion Overview

The discussion revolves around the application of the spherical Pythagorean theorem in a specific geometric context, focusing on the lengths of sides in a spherical triangle. Participants explore the implications of the theorem in relation to the sides labeled a1 and a2.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes a contradiction in the spherical Pythagorean theorem when applying it to sides a1 and a2, questioning if they are missing something.
  • Another participant clarifies that a1 is not part of a great circle, implying a distinction in the application of the theorem.
  • A later reply acknowledges a misunderstanding regarding the sides, suggesting that a2 was intended instead of a1.

Areas of Agreement / Disagreement

Participants express differing views on the application of the theorem to the sides of the triangle, indicating that the discussion remains unresolved regarding the correct interpretation of the theorem in this context.

Contextual Notes

There is a potential limitation in understanding the relationship between the sides and their definitions within the context of spherical geometry, which may affect the application of the theorem.

Plutoniummatt
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Picture of the problem:
Untitled-3.jpg


As seen by the diagram above, a2 < a1

But the spherical Pythagorean theorem states that cos c = (cos a)(cos b).

The triangle can either have a1,b,c or a2,b,c as its sides, which means the above equation contradicts itself. Am I missing something?

thanks.
 
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Hi Plutoniummatt! :smile:
Plutoniummatt said:
But the spherical Pythagorean theorem states that cos c = (cos a)(cos b).

he he :biggrin:

a1 isn't part of a great circle :wink:​
 
hehe thanks, this is what happens when I look up a formula and not bother to read the text that goes with it :P but I assume you meant a2
 
oops! :biggrin:
 

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