Pythagorean Theorem: The Spiral of Roots

hypoteneuse--»h
n--»number of triangles

i think If we know the hypoteneuse we can calculate the number of triangles we've drawed to get to the actual triangle... but i'm not shure... by the expression:

h=[root]n+1


Am I right?

Thanks!!! Eres el amo!!

It's simple just expand an remember a proof.
i.e 2sinthetacostheta=sin2theta.

i will be making some videos on A LEVEL maths that might be helpful to you

I'm a student. can you help me solve this problem. It involves trigonometric identities.

Q. Show that: sinθ(1+2cosθ)= sinθ+sin2θ?
Plot the curves for sinθ and sin2θ and hence calculate the area enclosed by the two curves between θ=0 & π/6

thanks

math, is art

splendid as always.

thanks for a great video, have a nice week :)

This was fun to watch. Thanks Mr. MathTV.

The triangle exists just as you see it. The implication is that not all numbers can be written as fractions or decimals. In fact, there are an infinite number of these numbers that cannot be written as fractions or decimals.

Does the first example imply that a triangle with two sides of 1 and hypoteneuse of 2 is an impossible shape in reality?

This is absolutely mind blowing. I <3 Math :)

I agree. That is a beautiful piece of math art.

I also like the way you can use the seperate line segments to quickly construct a triangle with a hypotenuse of irrational length.

sqrt(3), sqrt(2), sqrt(5)

Only with the Pythagorean Theorem is anyone allowed to make that association above.

I always thought that was a pretty spiral.