The converse of the theorem says that if, \({a^2} = {b^2} + {c^2}\) then you have a right-angled triangle and furthermore, the right angle is directly opposite \(a\) (the hypotenuse). We can therefore ...

This is a preview. Log in through your library . Abstract Let $A$ be a commutative local Noetherian ring with identity of Krull dimension $n, m$ its maximal ideal ...

This is a preview. Log in through your library . Abstract The following converse of the Hilbert Syzygy Theorem is proved. Suppose K is a noetherian commutative ring with identity that has finite ...

Pythagoras' theorem can also be used to solve 3D problems. You often need to use Pythagoras' theorem more than once in each problem as we create extra right-angled triangles in the 3D shapes. First ...