Is there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.

Janessa Olson
2022-07-07
Answered

Non-geometric Proof of Pythagorean Theorem

Is there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.

Is there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.

You can still ask an expert for help

asked 2022-09-01

For each of the following, can the measures represent sides ofa right triangle? Explain your answers.a. 3 m, 4 m, 5 mb. $\sqrt{2cm},\sqrt{3cm},\sqrt{5cm}$

asked 2022-07-11

pythagorean theorem extensions

are there for a given integer N solutions to the equations

$\sum _{n=1}^{N}{x}_{i}^{2}={z}^{2}$

for integers ${x}_{i}$ and zan easier equation given an integer number 'a' can be there solutions to the equation

$\sum _{n=1}^{N}{x}_{i}^{2}={a}^{2}$

for N=2 this is pythagorean theorem

are there for a given integer N solutions to the equations

$\sum _{n=1}^{N}{x}_{i}^{2}={z}^{2}$

for integers ${x}_{i}$ and zan easier equation given an integer number 'a' can be there solutions to the equation

$\sum _{n=1}^{N}{x}_{i}^{2}={a}^{2}$

for N=2 this is pythagorean theorem

asked 2022-06-04

Deduce the Pythagorean Theorem [duplicate]

Let V be an inner product space,and suppose that x and y are orthogonal vectors in V.We also know ${\Vert x+y\Vert}^{2}={\Vert x\Vert}^{2}+{\Vert y\Vert}^{2}$.My question is how can we deduce the pythagorean theorem in ${\mathbb{R}}^{2}$ from it.If possible give geometrical views.

Any help will be greatly appreciated.

thanks!! in advance.

Let V be an inner product space,and suppose that x and y are orthogonal vectors in V.We also know ${\Vert x+y\Vert}^{2}={\Vert x\Vert}^{2}+{\Vert y\Vert}^{2}$.My question is how can we deduce the pythagorean theorem in ${\mathbb{R}}^{2}$ from it.If possible give geometrical views.

Any help will be greatly appreciated.

thanks!! in advance.

asked 2022-05-28

How does the attached figure prove the Pythagorean theorem?

asked 2022-06-13

Can the Pythagorean Theorem be extended like this?

What is the significance, if any, of the fact that

${3}^{3}$ + ${4}^{3}$ + ${5}^{3}$ = ${6}^{3}$

?

How curious this is. This would be like the Pythagorean Theorem exploding into a higher dimension, on steroids.

What is the significance, if any, of the fact that

${3}^{3}$ + ${4}^{3}$ + ${5}^{3}$ = ${6}^{3}$

?

How curious this is. This would be like the Pythagorean Theorem exploding into a higher dimension, on steroids.

asked 2021-01-15

An airplane starting from airport A flies 300 km east, then 350 km at 30 degrees west of north and then 150 km north to arrive finally at airport B. The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight? How far willthe pilot travel in the flight? Assume there is no wind during either flight.

asked 2022-05-03

Pythagorean theorem does require the Cauchy-Schwarz inequality?

In Wikipedia I found a proof of Schwarz inequality making use of the Pythagorean Theorem. Anyway I'm wondering... isn't that a petitio principii? Isn't the Pythagorean Theorem in Hilbert spaces proved by the Cauchy-Schwarz inequality? Or effectively is the Pythagorean Theorem a stronger if not equivalent notion?

In Wikipedia I found a proof of Schwarz inequality making use of the Pythagorean Theorem. Anyway I'm wondering... isn't that a petitio principii? Isn't the Pythagorean Theorem in Hilbert spaces proved by the Cauchy-Schwarz inequality? Or effectively is the Pythagorean Theorem a stronger if not equivalent notion?