Pythagorean theorem from a (semi) circle!
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- Опубликовано: 23 июн 2024
- 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/10.2307/2686255).
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Thanks!
For other proofs of this same fact check out the following playlist:
• Pythagorean Theorem
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![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
The fact that theres like 600 proofs of the Pythagorean theorem baffles me
Must be SUPER true then😁
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).
But we still don't know why the Pythagoreans were afraid of beans.
Dude had a cult following…
@@thomasholden500nighttime gas
This is one of many Pythagorean proofs that I can understand rapidly!
I’ve actually thought about if Thale’s theorem and the Pythagorean theorem had a connection for a while. Nice!
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
Wow even though I don't really use this anymore I had always wondered how they came to find that equation, interesting!
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 original proof was even more simpler one. A proof anyone can discover just by playing with some triangles.
wow this is actually very digestible
You be square. Too cool for school.
Nice. Great animation as well.
I hadn't seen this proof!
Wow I didn't expect that you can find the Pythagorean theorem using a circle but at least it's something to know
Za mene je ovo mnogo komplikovano, nista ne razumem. Svaka cast vama koji razumete!
Genius ! 👏 👏 👏
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
0:12 if you type it like this, we can click
That was what my geometry hw was tryna explain to me 😂 never got that…
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.
This sounds like alien talk to me bro
I always wonder what a geometrical proof of hyperbolic or spherical Pythagorean theorem would look like...
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.
Nice, but why is the right angle triqngle actually not precisely right angle? It's like 92-93° from the drawing
what proves that the two triangle's similar?
Why not c+a/b =c-a/b (complimentary side of two similar triangle ) ??
It but just me or was I completely lost
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. RUclips shorts is not the format to learn math.
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 !
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
@@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.
i did not understand anything you just said. i failed math and this is why