Nonstandard Area Formula for a Right Triangle (proof without words)

In this video, we prove, wordlessly, that the area of a right triangle is the product of the two lengths on the hypotenuse lying on either side of the tangent point to the incircle.
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This animation is based on a visual proof by Roger B. Nelsen from the February 2007 issue of Mathematics Magazine (www.jstor.org/... ), page 45.
#manim #triangle #proofwithoutwords #math #mathvideo #righttriangle #incircle #area #geometry #visualmath #visualproof #pww #theorem
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Music in this video:
Instant Crush by Corbyn Kites

[@oddlyspecificmath]

This just makes me want to sit and remember how it was to experience things with the eyes of a child.

[@caspermadlener4191]

The formula can also be derived by finishing the ravi-substitution and doing some algebra with other formulas. Let z be the side of the square.
The standard formula's give
2A=(x+z)(y+z), and
A=rs=r(x+y+z), where r is the radius of the incircle, and s was the semiperimeter. In right triangles, r=z, so
A=(x+z)(y+z)-z(x+y+z)=xy.
I had to learn a lot of area formulas for triangles, mainly to solve geometric inequalities, but I never encountered A=xy. And the fact that the geometric derivation is more shorter that the most obvious algebraic derivation is also pretty cool.

[@lgooch]

Interesting, I’ve only encountered the Ravi Sub in inequalities.

[@Mutual_Information]

The music is so good! Makes a proof feel totally exciting

[@MathVisualProofs]

👍😀

[@carlkarl]

thanks sir , hope it will help in my jee advanced test on 4th June , love from India , I will go through all of ur content to grasp as much info relevant to me as possible thanks again

[@MathVisualProofs]

Good luck!

[@stage6fan475]

Very nice job. Love it! Never saw this one before and I have been reviewing geometry.

[@MathVisualProofs]

👍😀

[@Om-officepwgl]

Nice, please make more videos on geometry

[@MathOrient]

Amazing. Short and nice.

[@MathVisualProofs]

Thanks!

[@sereadavid7168]

Incredible 👍

[@philipp3761]

How do i get the x and y

[@zabitkhalifakuliyev2271]

Hi.can you prove that if a circle can be inscribed in a rectangular trapezoid, then the area of the trapezoid is equal to the product of the bases?

[@wedsonrodrigues6895]

Excelente professor. Poderia compartilhar o código? Suas animações são perfeitas

[@quay6292]

Try to do that with Herron formula

[@MathVisualProofs]

Heron’s formula does have related visual proof. It’s in the queue to work on. But it’s more involved

[@quay6292]

@@MathVisualProofs nice.
Thank you

[@user-sc6nv3dl6n]

Please make a vedio upon the divsion of two irrational numbers because its seem quite hard to visualise

[@MathVisualProofs]

I am not sure exactly how to do this... I am not aware of a good visual.

[@user-bi3wp9tz8v]

Hmmm

[@galaga16]

It is not wrong
But if I show my professor this he is going to call me an idiot

[@MathVisualProofs]

Why?

[@Grizzly01]

Is your professor not particularly good at maths?

[@galaga16]

Sarcastically he would tell me that
He would be able to acknowledge is works but he would laugh at how unorthodox it is