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Nonstandard Area Formula for a Right Triangle (proof without words)
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- Опубликовано: 28 май 2023
- 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
This just makes me want to sit and remember how it was to experience things with the eyes of a child.
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.
Interesting, I’ve only encountered the Ravi Sub in inequalities.
The music is so good! Makes a proof feel totally exciting
👍😀
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
Good luck!
Very nice job. Love it! Never saw this one before and I have been reviewing geometry.
👍😀
Nice, please make more videos on geometry
Amazing. Short and nice.
Thanks!
Incredible 👍
How do i get the x and y
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?
Excelente professor. Poderia compartilhar o código? Suas animações são perfeitas
Try to do that with Herron formula
Heron’s formula does have related visual proof. It’s in the queue to work on. But it’s more involved
@@MathVisualProofs nice.
Thank you
Please make a vedio upon the divsion of two irrational numbers because its seem quite hard to visualise
I am not sure exactly how to do this... I am not aware of a good visual.
Hmmm
It is not wrong
But if I show my professor this he is going to call me an idiot
Why?
Is your professor not particularly good at maths?
Sarcastically he would tell me that
He would be able to acknowledge is works but he would laugh at how unorthodox it is