Reciprocal Pythagorean Theorem

This is a short, animated visual proof of the reciprocal Pythagorean theorem, which relates the reciprocals of the side lengths and the reciprocal of the altitude of a right triangle.

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[Drestanto]

at the start: "oh, it's just h = ab/sqrt(a²+b²)"
at the end: "whoa, that's beautiful"

[neologicalgamer]

Holy fuckin' shit, so you can use that as a shortcut to find the h of any right triangle that you can use pythagorus on. That shit's wild bro

[tyronekim]

That is a bad ass fact. I learned something new today. Thank you.

[Sprkd_GD]

Why is the youtube algorithm trying to teach me math.. is this a sign?

[vladimirrodriguez]

Great visual proof and reinterpretation of the Pythagorean theorem, all the content posted is appreciated👍👏😊

[RandyKing]

that’s pretty awesome…too bad my geo students take their exam tomorrow…. i’ll just have to put that in my back pocket till the fall semester👍👍👍

[lillii]

You can also say that a² - h² = d² and b² - h² = e², with d + e = c. Now add them as such: a² - 2h² + b² = d² + e², and add 2de on both sides to get a² - 2h² + b² + 2de = c², we know that a² + b² = c² therefore 2(de - h²) = 0, hence de - h² = 0, so we conclude that h² = de. This shows that the length of the height can be found from its position on the hypotenuse.

[hithere]

This is the most beautiful thing i have ever learnt in mathematics

[cuitaro]

Just discovered a proof for this yesterday involving a whole bunch of side steps. But I must say, this one is so beautiful and elegant! I shall tell my professor about it. :)

[ericworm]

This visual proof could come in handy, thanks for posting! Relearning calculus, quantum mechanics, etc for mental exercise and fun. (30 plus years from undergrad chem degree :) )

[asparkdeity]

Wow, u really redid the video after one of my older comments! Thank you for the great content

[FurryNonsense]

Okay, but how does this help me do anything in life?

[wr]

i learnt this in school but didn't understand why, now i'm mind blown

[alfadog]

I'll be thinking about this all day now. h = ab/(sqrt(a^2+b^2))

[patum]

I learned about it a few moths ago, it helped me in some math problems

[ahmadb.e.k]

I was searching that and you gave it to me thank you a lot

[Sloop_Jonz_B]

This all went over my head…but I’m happy to be here.

[wafikiri_]

This relationship between sum of inverses now makes my engineering mind race across similar sums of inverses found in lots of formulas. The first thing to be related is ellipses. I'll have to dig in deeper.

[shayanemdadi]

That's right, in the 11th grade, our teacher had given us a question and the only relation that could be used to solve it in high school was this relation, and I had obtained this relation from the inscribed circles of a triangle

[E_E_KE]

Its nice that i see this after a math test where i really could have used this formula. Would have saved me alot of time