MHB Consequences of the Pythagorean Theorem

[Perlita]

Hello!
I have a homework for tomorrow. The question is: What are the consequences of the Pythagorean theorem??
On Wikipedia, they mixed the consequences and the uses of the theorem in one paragraph:

5.1 Pythagorean triples
5.2 Incommensurable lengths
5.3 Complex numbers
5.4 Euclidean distance in various coordinate systems
5.5 Pythagorean trigonometric identity
5.6 Relation to the cross productI assume that the first two are the consequences, and the rest are the uses of the theorem, but I want to be 100% sure.
Any help?

 

[Deveno]

I think this question is "too vague" to have a definitive answer. In particular, there is no "firm line" in mathematics between "consequence" and "use" of ANY theorem.

I suspect what your instructor wanted you to do is RESEARCH this, and arrive at some understanding of how the Pythagorean theorem came to be regarded as so important. "Copypasta" from Wikipedia isn't really doing that, is it?

 

[sweer6]

Are you perhaps asking in what situations the Pythagorean theorem can be used and in what situations it cannot?