Question

BEST GETS BRAINLIEST Proof for Pythagoras Theorem (I’ll take multiple different approaches) Please make it logical/satisfying.

Answer 1

Answer:

Proofs for Pythagoras Theorem usually use visual/geometry approaches. I don't post pictures in my answers, so I will present a linear algebra approach. You can see it in the blog posted by Professor Terence Tao.

Note that there are several elegant proofs using animations and drawings, but this is just personal.

I've seen this some time ago, it is really interesting proof.

It states that $a^2+b^2=c^2$ is equivalent to the statement that the matrices

$%\begin{pmatrix}a & b \\ -b & a%\end{pmatrix}%$    $\begin{pmatrix}a& b \\-b & a\\\end{pmatrix}$ and $\begin{pmatrix}c & 0\\0 & c \\\end{pmatrix}$ have the same determinant.

The determinant of the first matrix is $a^2+b^2$

The determinant of the second matrix is $c^2$

Once the linear transformations associated with these matrices differ by rotation, we claim that

$a^2+b^2=c^2$