Intersecting Chords Theorem (visual proof)

Рет қаралды 20,716

Жыл бұрын

This is a short, animated visual proof demonstrating and proving the intersecting chords theorem from geometry. #manim #math #mathshorts #mathvideo #intersectingchords #geometry #chords #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #inequality
This animation is based on a visual proof from Hubert Shutrick that appears on the beautiful math website Cut-the-knot (www.cut-the-knot.org/Curricul...)
To learn more about animating with manim, check out:
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Пікірлер: 54

@mayormccheese819 Жыл бұрын

This channel is seriously underrated. I've always loved showing visual proofs when tutoring math, as I think it illustrates how beautiful math can be and can make things a lot more intuitive and clear up a lot of confusion that comes with dense notation and jargon. Thanks for another great video.

@MathVisualProofs Жыл бұрын

Thanks for watching! I agree that it can't hurt to have a visual representation to go along with "formal" ideas :)

@SuperYoonHo Жыл бұрын

@@MathVisualProofs I agree that "Mayor McCheese is a fun name

@puneetkumarsingh1484 Жыл бұрын

Mind blown away. The idea of scaling and attaching the triangles together was fresh one to me. I would have never thought of that

@MathVisualProofs Жыл бұрын

:) Glad you liked it!

@RandyKing314 Жыл бұрын

agreed, that was pretty sweet.

@MathVisualProofs Жыл бұрын

@@RandyKing314 thanks :)

@mathflipped Жыл бұрын

Great proof, and a nice visualization.

@MathVisualProofs Жыл бұрын

Thanks as always! :)

@MathCuriousity 10 ай бұрын

Hey so I did some thinking: firstly - I stumbled on a proof that didn’t need scaling and just uses setting the ratio of sides of one triangle to ratio of sides of another to finish proof without ever needing scaling. That being said - I am still uneasy and untrusting of the idea of “scaling” to use the proof you did. I can’t explain WHY it makes me uneasy but can you help me feel I can trust your scaling idea? Thank you and again - love you channel!

@gabedarrett1301 Жыл бұрын

I used to hate proofs. Your channel changed my mind, and that's saying a lot!

@MathVisualProofs Жыл бұрын

😀

@두룸깨 7 ай бұрын

Thanks to you, I can understand it👍

@SuperYoonHo Жыл бұрын

Thank you!!!

@MathVisualProofs Жыл бұрын

Welcome!

@SuperYoonHo Жыл бұрын

@@MathVisualProofs Nice animations! I knew this theorem but just had to watch again because you made it so well;)

@katiatzo 8 ай бұрын

excellent!!!

@MathVisualProofs 8 ай бұрын

Thank you! Appreciate it.

@MathCuriousity 10 ай бұрын

What a gorgeous video and great channel! Thank you so much for helping those with Aphantasia who want to grasp geometry!

@MathVisualProofs 10 ай бұрын

Glad it helps!

@MathCuriousity 10 ай бұрын

@@MathVisualProofs would you please perhaps use a different approach to explain to me why I can trust the scaling method? I saw another method proving interesting chiefs theorem using ratio of sides of similar triangles set equal to one another and no scaling used. Please help me trust scaling as legitimate. I want to open my eyes to your truth.

@MathVisualProofs 10 ай бұрын

@@MathCuriousity If you are using similarity of triangles, you are essentially using the scaling argument. The ratio of sides being equal is essentially saying you can scale one triangle to the other. In this visual argument, we use scaling so we can create the parallelogram. So we scale both triangles independently to similar triangles that then fit together along a diagonal.

@MathCuriousity 10 ай бұрын

@@MathVisualProofsI didn’t think of the similar triangles also z using scaling. Very interesting. Let me reapproach your solution with that and then get back to you. Thank u so much!❤

@adelgouda3450 Жыл бұрын

Excellent

@MathVisualProofs Жыл бұрын

Thanks!

@gauravrathor902 8 ай бұрын

Amazing

@MathVisualProofs 8 ай бұрын

Thanks!

@denelson83 Жыл бұрын

How about a proof that uses Ptolemy's theorem?

@johneonas6628 Жыл бұрын

Thank you for the video.

@MathVisualProofs Жыл бұрын

Thanks for watching

@MathCuriousity 10 ай бұрын

Hey question: firstly love your channel and love these proofs, however - the moment we scale a triangle up, aren’t we changing the triangles and thus providing a faulty proof? Could you help me understand why your scaling of both was “legal” and sort of preserved the integrity of the proof?

@MathVisualProofs 10 ай бұрын

As long as you scale each side by the same value the triangles maintain their angles and that’s what’s important for the proof. The angles fit together so that we have a parallelogram.

@MathVisualProofs 10 ай бұрын

And thanks!

@MathCuriousity 10 ай бұрын

@@MathVisualProofs I think I see. Thank you kindly!

@pavelkoprivec8840 4 ай бұрын

Angle Side Side theorem says that if two triangles have the same corresponding angle and and same corresponding two sides. In this case this is true we have congruent triangles. Flipping the upper left triangle up and translating across a line ab coresponds to cd. Thats why ab = cd

@pavelkoprivec8840 4 ай бұрын

Two trianles are simmilar. So ratios of b/d = c/a, multipying both sides by a*d, you get a * b = c * d

@amirk6290 Жыл бұрын

Excellent ❤️👍

@MathVisualProofs Жыл бұрын

Thanks!

@simpleman283 Жыл бұрын

I went to hit the like thumb, but noticed that I already had. Too bad I can't do it again.

@MathVisualProofs Жыл бұрын

Hah! Thanks. I appreciate it regardless 👍😀

@camper2908 5 ай бұрын

So could anyone explain? I draw a circle 10cm diametre. Then a line from circle to the center with 7 cm length. Now a line perpendicular the free extreme 4,5cm length. So I want to know what's the diameter. axb=dxc, so 7b=4,5x4,5, 7b=20,25; b=20,25/7= 2,89cm. But I know it's 3cm. 😮

@klaplays8853 4 ай бұрын

Yoo who else gotta do this in class

@jpopelish Жыл бұрын

Now, show that all angles subtended by and arc must be equal.

@GreylanderTV Жыл бұрын

While clearly proven true, I find this unsatisfying as a visual proof. First(and most importantly), it hinges entirely on the subtending angle theorem, which is not intuitive and should also be visually proven as a lemma, or at least reference to a separate visual-proof video for that fact. Second, the "scale each triangle by a length from the other" step isn't really visualized. Instead we just see them scaled to the same size arbitrarily(see below**). Third the parallelogram was unnecessary. It doesn't hurt, per se, but is a bit of a distraction. Simply the fact that the triangles are similar is enough to say all scaled sides are equal -- you might as well super-impose them. The way the parallelogram is presented makes it seem important/essential to the proof, which it isn't. **On the arbitrary scaling: Depending on the size of the circle, scaling could shrink both, or one could become larger while the other becomes smaller. Just resizing two similar triangles to the same size doesn't really "visualize" the scaling by these factors, so the important fact that they rescale to the same size, is merely asserted, and not demonstrated visually. The assertion is visualized by an arbitrary choice of size, but the assertion itself, is not proven visually. A case could be made this step is so obvious it does not need to be visualized, but I'd say if you can't visualize the multiplication of lengths of two line segments, you need to at least mention that scaled sizes are unknown and show smoothly varying possibilities by putting actual length values, varying those, and showing the two scaled triangles always the same size from both being tiny, to one larger and one smaller, to both being larger.

@MathVisualProofs Жыл бұрын

Interesting thoughts. Thanks for sharing. I agree that this relies on another theorem, but I am fine stating that one and leaving people to look it up if they are interested (is how to learn best). As to the parallelogram argument, I like it that way - and I was staying true to the cited visual proof: www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/HubertIntersectingChords.shtml :)

@ojas3464 Жыл бұрын

** "hinges entirely on the subtending angle theorem" ** I only ½ agree with this. For one pair of equal angles, vertically opposite angles can be used, and equality 2 angles of triangles imply their similarity.

@GreylanderTV Жыл бұрын

@@ojas3464 Can be used, but wasn't. 😜 And you still _need_ the chord theorem.

@shanaiashanesicat4108 5 ай бұрын

May exam check

@Moses_VII 6 ай бұрын

I had to watch twice to understand how you scale one triangle by b and the other by c. Explain it on more detail for the other viewers who may not understand as well as I did.