Pythagorean theorem from a (semi) circle!

Рет қаралды 67,691

Күн бұрын

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the semicircle and Thales triangle theorem. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths.
This animation is based on a proof due to Michael Hardy from the November, 1986 issue of The College Math Journal (doi.org/10.230....
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Thanks!
For other proofs of this same fact check out the following playlist:
• Pythagorean Theorem
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Пікірлер: 60

@6D-Hexagon 3 ай бұрын

The fact that theres like 600 proofs of the Pythagorean theorem baffles me

@GusBatista03 3 ай бұрын

Must be SUPER true then😁

@FootLettuce 3 ай бұрын

Here's a more baffling fact: the theorem of Quadratic Reciprocity in number theory is much more complicated than this, yet it is the second most proven after Pythagorean with (196 proofs).

@thomasholden500 3 ай бұрын

But we still don't know why the Pythagoreans were afraid of beans.

@kkupsky6321 3 ай бұрын

Dude had a cult following…

@dougr.2398 2 ай бұрын

@@thomasholden500nighttime gas

@77rauldhino 3 ай бұрын

This is one of many Pythagorean proofs that I can understand rapidly!

@Cheungoldsix Ай бұрын

I dont understand😢 why does c-a/b=b/c+a

@JustAnIdiot6969 26 күн бұрын

@@Cheungoldsix if two triangles are similar then the ratio of their sides are equal

@error_6o6 3 ай бұрын

I’ve actually thought about if Thale’s theorem and the Pythagorean theorem had a connection for a while. Nice!

@jasonrubik 3 ай бұрын

You would like the video about Ptolemy's Theorem and it's relationship to the Golden Ratio via Inversion. Numberphile did a great video on the topic with Dr. Stankova

@Sk8Tank 3 ай бұрын

Wow even though I don't really use this anymore I had always wondered how they came to find that equation, interesting!

@Biagio_0 3 ай бұрын

This is just a proof of the Theorem, not the original one. Furthermore the first person to find out about this theorem wasn't actually Pythagora since it was knows centuries earlier in Babylon and India.

@the-boy-who-lived 3 ай бұрын

The original proof was even more simpler one. A proof anyone can discover just by playing with some triangles.

@oafgeek Ай бұрын

Never saw this proof before, might be my new favorite

@mauschen_gaming 3 ай бұрын

Wow I didn't expect that you can find the Pythagorean theorem using a circle but at least it's something to know

@BonkoTheFat 3 ай бұрын

wow this is actually very digestible

@kkupsky6321 3 ай бұрын

You be square. Too cool for school.

@reecec626 3 ай бұрын

I hadn't seen this proof!

@andrashorvath2411 3 ай бұрын

Nice. Great animation as well.

@luckytrinh333 2 ай бұрын

Wow Really neat proof!

@nikhilbarod1896 3 ай бұрын

Why not c+a/b =c-a/b (complimentary side of two similar triangle ) ??

@aza-jo9ru Ай бұрын

This proof is very more important than it looks. Indeed, it shows that you can demonstrate the famous Pythagoras theorem by using Thales theorem (or called also intercept theorem). The question here is "where is this Thales theorem?",as an answer the unicity of tan() for both triangles, the blue and the red one. Just think for it 😅. Here is a good question can we now demonstrate Thales theorem by the pythagorian one.

@aza-jo9ru Ай бұрын

@mathvisualproofs What do you think Sir am right?

@aza-jo9ru Ай бұрын

What do you think Sir am I right?

@rcb3921 3 ай бұрын

draw the circle and label the lengths as shown at the 0:12 second mark. Now, reflect the tringle horizontally over the diameter of the circle. From the power cord theorem: (c + a) * (c - a) = b² c² - a² = b² c² = a² + b²

@milanstevic8424 3 ай бұрын

0:12 if you type it like this, we can click

@waldoarriagada3180 Ай бұрын

you did not prove anything. What you displayed is Euclide's Theorem.

@toferg.8264 2 ай бұрын

It’s! Beautiful!

@uguree 2 ай бұрын

Nice, but why is the right angle triqngle actually not precisely right angle? It's like 92-93° from the drawing

@CONQUERER09776 2 ай бұрын

If in the left triangle you did base/purpendicular then why why you did purpendicular/base in right triangle?

@HolidayArt 2 ай бұрын

So cool!!!!

@Jcom3030 2 ай бұрын

👌🏻

@rajkotalovic9784 3 ай бұрын

Za mene je ovo mnogo komplikovano, nista ne razumem. Svaka cast vama koji razumete!

@orterves 3 ай бұрын

Thale's theorem, courtesy of Wikipedia: One way of formulating Thales's theorem is: if the center of a triangle's circumcircle lies on the triangle then the triangle is right, and the center of its circumcircle lies on its hypotenuse.

@eileenguan3634 2 ай бұрын

what proves that the two triangle's similar?

@WWEMikano Ай бұрын

Ok, but how do you know that the inscribed triangle is a right triangle without already knowing Pythagoras' Theorem is true?

@MathVisualProofs Ай бұрын

That’s Thales triangle theorem. You can prove that just using inscribed angle theorem - you don’t need Pythagoras

@WWEMikano Ай бұрын

@@MathVisualProofs Nevermind, for some reason I thought you needed Pythagoras for the inscribed angle theorem lol. Should have looked up a proof before commenting

@MathVisualProofs Ай бұрын

@@WWEMikano No worries! It is interesting because the Pythagorean theorem is equivalent to the parallel postulate, so in theory, you can use the Pythagorean theorem to prove the inscribed angle theorem... It all starts to feel circular for sure :)

@theoremus 3 ай бұрын

Would you also consider this a trigonometric proof? The ratio of sides is called the tangent of an angle. Similar triangles have same angles, hence the ratio is equal for both.

@spoocewok 3 ай бұрын

It but just me or was I completely lost

@bfboobie 3 ай бұрын

He went pretty fast. Unlike a classroom setting. Ive never seen this proof and would have to rewatch it a few times and sit down with pencil and paper and write it out to absorb it, so don't feel bad. KZbin shorts is not the format to learn math.

@tim_exp 23 күн бұрын

+1🧠✨️ pathagratheram

@mehdimabed4125 3 ай бұрын

I always wonder what a geometrical proof of hyperbolic or spherical Pythagorean theorem would look like...

@augryan7518 2 ай бұрын

Wow❤

@sbrinkley1022 2 ай бұрын

@babyelian77 3 ай бұрын

Genius ! 👏 👏 👏

@brotundwasser 2 ай бұрын

Cac-a

@laurenfaulk4637 2 ай бұрын

That was what my geometry hw was tryna explain to me 😂 never got that…

@BombsBug 3 ай бұрын

i did not understand anything you just said. i failed math and this is why

@sajadeshahidpour2008 3 ай бұрын

Greetings, could anyone kindly explain 0:22 the "top angles are complementary" which justifies that the right angled triangles (cyan and magenta) are similar ? Thanks !

@Zuun74 3 ай бұрын

To be similar a two triangles must share at least 2 of the same angles. Since the angles of both of the triangles equal 90 each triangles angle should equal 45 they also share a 90 degree angle at the bottom of the line connecting them

@sajadeshahidpour2008 3 ай бұрын

@@Zuun74thank you I think I understand. Both cyan and magenta triangles are similar to the "bigger" inscribed triangle because : 1) they all share a right angle 2) magenta also shares one angle 3) cyan also shares another angle 3) in other words, cyan and magenta each share two angles with the inscribed triangle 4) thus, cyan, magenta and inscribed triangle are all similar.