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 product

I 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?

 

[Quaid]

Is your question a matter of semantics?

For example, it's a consequence of the theorem that irrational lengths may be constructed -- see Pythagorean Spiral. If we use that consequence to construct the spiral, what's the difference whether we call that spiral a use or a consequence of the theorem?

 

[Perlita]

Is your question a matter of semantics?

For example, it's a consequence of the theorem that irrational lengths may be constructed -- see Pythagorean Spiral. If we use that consequence to construct the spiral, what's the difference whether we call that spiral a use or a consequence of the theorem?

A consequence should be a definition or relation "derived" from the theorem. This is how I see it.