Linked Questions

20
votes
9answers
9k views

What is the simplest proof of the pythagorean theorem you know? [duplicate]

Maybe enough so to explain it to children.
-6
votes
1answer
235 views

How do we prove that the Pythagorean theorem holds for a right angled isoceles triangle with sides, $a,b,a$. [duplicate]

Possible Duplicate: What is the most elegant proof of the Pythagorean theorem? How do we prove that the Pythagorean theorem holds for a right angled isoceles triangle with sides, $a,b,a$. ...
1
vote
2answers
52 views

What is your favorite proof of the Pythagorean Theorem? Why? [duplicate]

My favorite is Euclid's original proof for two reasons: First, it requires minimal raw material. It only needs the result that the area of a triangle is half the area of a rectangle with the same ...
0
votes
1answer
74 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?
122
votes
14answers
19k views

What's the intuition behind Pythagoras' theorem?

Today we learned about Pythagoras' theorem. Sadly, I can't understand the logic behind it. $A^{2} + B^{2} = C^{2}$ $C^{2} = (5 \text{ cm})^2 + (7 \text{ cm})^2$ $C^{2} = 25 \text{ cm}^2 + 49 ...
15
votes
16answers
2k views

Beautiful, simple proofs worthy of writing on this beautiful glass door [closed]

What are some of the more beautiful proofs you know? I am measuring beauty in two dimensions -- first, how conceptually elegant is it and second, how aesthetically pleasing is it. Context: I work ...
32
votes
6answers
4k views

Pythagorean Theorem Proof Without Words (request for words)

I was intrigued by a book I saw called Proofs without Words. So I bought it, and discovered that the entire book doesn't have any words in it. I figured at least it would have some words explaining ...
13
votes
3answers
1k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...
6
votes
5answers
1k views

Are there any calculus/complex numbers/etc proofs of the pythagorean theorem?

I have been looking for proofs for the pythagorean theorem that don't use area calculation but calculus, complex numbers or any other interesting ways to proof it. I would love to see any interesting ...
6
votes
2answers
958 views

How to derive the law of cosines without the pythagorean theorem

To me, it seems that the Pythagorean theorem is a special case of the law of cosines. However, all derivations that I can find seem to use the Pythagorean theorem in the derivation. Are there any ...
13
votes
1answer
1k views

Is there a dissection proof of the Pythagorean Theorem for tetrahedra?

Of the many nice proofs of the Pythagorean theorem, one large class is the "dissection" proofs, where the sum of the areas of the squares on the two legs is shown to be the same as the area of the ...
8
votes
5answers
156 views

Naive approach to Pythagoras

The following has occupied me while learning about $a^2+b^2=c^2$, I then forgot about all that and recently (40yrs after) came across that again - and am still unable to understand. But today my next ...
3
votes
4answers
580 views

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle.

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle. First, I have never done a proof before, sorry I am so poor here. I have spent many hours but my actions have mostly used ...
9
votes
2answers
533 views

geometric meaning of a trigonometric identity

It follows from the law of cosines that if $a,b,c$ are the lengths of the sides of a triangle with respective opposite angles $\alpha,\beta,\gamma$, then $$ a^2+b^2+c^2 = 2ab\cos\gamma + 2ac\cos\beta ...

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