Linked Questions

0
votes
1answer
111 views

why a^2 + b^2 = c^2 in right-angled triangle [duplicate]

a^2 + b^2 = c^2 what is the demonstration of this rule with triangle which has 90 deg? can be proofed using geometry?
89
votes
17answers
57k views

What is the most elegant proof of the Pythagorean theorem? [closed]

The Pythagorean Theorem is one of the most popular to prove by mathematicians, and there are many proofs available (including one from James Garfield). What's the most elegant proof? My favorite ...
13
votes
17answers
3k views

Irrational numbers in reality

I have a square tile which measures 1 metre by 1 metre, by the Pythagorean identity the diagonal from one corner to another will be $\sqrt 2$ metres. However $\sqrt 2$ is an irrational number, could ...
21
votes
3answers
2k views

For x < 5 what is the greatest value of x

It can't be $5$. And it can't be $4.\overline{9}$ because that equals $5$. It looks like there is no solution... but surely there must be?
8
votes
5answers
3k views

which axiom(s) are behind the Pythagorean Theorem

There are many elementary proofs for the Pythagorean Theorem, but no matter they use areas, similarities, even algebraic proofs, it is not straightforward to tell why it is true tracing back to the (...
9
votes
2answers
1k views

Non-geometric Proof of Pythagorean Theorem [closed]

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 ...
12
votes
3answers
8k views

Proving the area of a square and the required axioms

I recently realized the area formula of all polygons, and most basic figures can be proven from the areas of square and rectangle. For example if we know the area of rectangle, we can the area formula ...
5
votes
4answers
534 views

The validity of the proofs of the Pythagorean Theorem and the concept of area

this might be a very elemental question but it has been bothering me for a while. Must of the proofs I've seen of the Pythagorean Theorem involve showing that the areas of the squares with side length ...
6
votes
3answers
381 views

Is Pythagoras' theorem about distances or areas?

In $\mathbb{R}^2$ with the 1-norm or $\infty$-norm, Pythagoras' theorem is false for lengths of sides of a "right-angled'' triangle, but it is true for areas of shapes on the sides. For example, given ...
6
votes
0answers
88 views

What is the epistemological status of the usual proof(s) of Pythagoras' theorem?

Pythagoras' theorem has a variety of geometric proofs, such as: I want to teach at least one of these proofs to my high school students, because it shows that the formula $\|(x,y)\| = \sqrt{x^2 + y^2}...