This is one of the best proofs of Ptolemy's Theorem ever.

@codebitcookie8053

2 жыл бұрын

Agreed

@Sciencedoneright

2 жыл бұрын

I agree lol

@modern_genghis_khan0393

Жыл бұрын

I agreed too

A beautiful presentation of a beautiful proof. I enjoyed it immensely. My one suggestion is that you may want to mention that it was first published (as far as I know) in 2012: William Derrick, James Hirstein, "Proof Without Words: Ptolemy’s Theorem", in The College Mathematics Journal, Vol. 43, No. 5 (November 2012), p. 386.

@MathyJaphy

2 жыл бұрын

Thank you! I'm glad you liked it, and I appreciate your letting me know the source of this proof. I have added a reference to the article in the video's description.

Dazzled me for a while! This channel & this video is so under-rated. More power to you!

The is literally the best proof I have ever seen of this theorem, like seriously this is pretty amazing

This video is very good, thank you. You deserve more views and likes.

@draganminic4928

2 жыл бұрын

Potpuno se slazhem, ali nema mnogo ljudi koji mogu da vide lepotu u dokazu neke teoreme.

Beautiful! I love the symmetry of this proof.

Your explanations are awesome!

Love the animation and explanation.

Your channel deserves million views my friend you are a good guy

👍Good stuff! Everything in this channel is very worthwhile.

Fantastic as always!

Thanks for this beautiful, articulate and intuitive proof 🤗

Wow! Amazing work!

I would love more videos from you. also some longer and more in depth!

This is the most beautiful prove for this theorem! thank you!

Finding this video when i was looking for ptolemy astronomy. Even this isnt what I looking for, I'm not disappointed and even thoroughly enjoying it 😊

One of the best background scores ever!

I prefer it with your voice, btw nice work! Keep going :)

Beautiful explanation of Ptolemy's Theorem, outstanding!

@MathyJaphy

5 ай бұрын

Thank you!

Can you please tell me what software you used for the presentation ? Thanks! Great idea btw

@MathyJaphy

Жыл бұрын

Thanks for watching! All my videos use Desmos Graphing Calculator plus screen capture, then iMovie to edit the screen capture video. For my first three videos, I controlled the animations by hand - starting sliders, turning expressions on and off, etc. Once the videos got too complicated for that, I wrote a javascript add-on that allows me to program these changes so they run automatically. Here's the Desmos Graph for this video: www.desmos.com/calculator/famrmmf7xs And my animation program is on GitHub: github.com/MathyJaphy/DesmosPlayer (it's got some bugs and quirks, but the instructions are all there if you want to try it).

I was the 667th upvote. I saved your video from darkness. You’re welcome.

Really great and helpful May I know which app is used for animation?

@MathyJaphy

Жыл бұрын

Thank you! I get that question a lot, so I put the answer in the description. I used Desmos Graphing Calculator to create the animations, and I wrote a plug-in for Chrome that lets me program the animations, which are otherwise controlled manually by moving sliders and displaying/undisplaying the various equations. See the description for links to the code on GitHub if you want to try it. The README file has a link to the Desmos graph I used for this video.

@LSMaths

Жыл бұрын

Thanks a lot sir

can’t believe he actually used the music. so good!

My god what the beautiful explanation ❤️❤️

@user-ke5id7ps8m

2 жыл бұрын

Good

Loved the way of describing

Beautiful theorem. The pioneering ancient Greeks!

Excellent video. Thanks a lot.

No.1 proof bro , I love it so much 🤟

very nice pictorial explanation

absolutely wonderful

Amazing,astonishing,unbelievable beautiful

Look at the triangle show, it's really easy to understand if we follow his teachings really great.

You are doing amazing great

I found an amazing Chanel, if only there were more videos to see..

Excellent proof ! Vow !!

Amazing video made with only four minutes!

Beautiful ❤️

This proof deserves handreds of thousands of likes.

Very Nice!

The animation is what helped me understand it most. How do you do it?

@MathyJaphy

9 ай бұрын

Hi, and thanks for the comment. I explain what I use to animate my videos in the description, along with links to the software if you want to try it yourself. Basically, it's Desmos Graphing Calculator turned into a programmable animation with a browser plug-in that I wrote which I call DesmosPlayer.

@anuamba

9 ай бұрын

@@MathyJaphyBut the player plugin is deleted from github. Can you share it?

@anuamba

9 ай бұрын

@@MathyJaphy Holy Fuuk you replied to 2 year old video. so can you share the link to the desmos player plugin cause it is removed from Github and thanks

@MathyJaphy

9 ай бұрын

I'm still making videos for the channel, so I notice comments on any of them, new or old! :-). I tested the link in the description before replying, and as far as I can tell, the repository is still there. I see my instructions and my javascript file. I'm not a GitHub expert so I don't know why you can't see it (assuming you entered the link correctly). If you have any idea, let me know and I'll investigate.

@MathyJaphy

9 ай бұрын

@anuamba I may have found the reason that you couldn't get to my GitHub. It looks like a KZread bug. When you click on the link in the description, it includes the close-parentheses in the URL! I fixed it by removing the period after the close-parentheses. Could you try it now and see if the link works for you?

This is really interesting proof. I do have concern on "scaling A" as you can't scale a segment with a factor of another length of segment this with only compass and straightedge. A*B is only interpretable as area, not length. Is there any way to circumvent this issue?

@warmpianist

2 жыл бұрын

Ok so I looked at the animation again and we can actually scale by "F/A" for second triangle and "B/A" for third triangle instead, we get C+DB/A = EF/A. And some small algebra should lead to the same Ptolemy's theorem.

@MathyJaphy

2 жыл бұрын

Granted, but there's nothing that prevents scaling a triangle by a unitless quantity that happens to be equivalent to one of the side lengths.

@nighteyemonroe8057

2 жыл бұрын

if you admit that (1,1) and (0,0) can be constructed A*B can also be constructed.

@QuantumHistorian

2 жыл бұрын

No, even the Greeks knew how to draw a line segment whose length was equal to the product of the length of any other two line segments. It's the *lengths* of the lines being multiplied, so there's no dimensional problem. Coming from a physics background, I had the same confusion as you for ages.

@warmpianist

2 жыл бұрын

@@QuantumHistorian if you are given a unit length, then yes. Is it possible without using unit length?

Hermosa demostración.

Nice!!

Thank you ❤️

Subscribed!

It was hard to believe that it could be this easy...

v cool! (but could small letters be used instead?)

@MathyJaphy

2 жыл бұрын

That was my problem when I first posted this video (LOL): kzread.info/dash/bejne/ao2jj9ird7TVoaw.html. But seriously, I assume you mean that upper case letters usually represent vertices, not side lengths. I wasn’t thinking about that when I set up the animation. I guess I preferred the aesthetics of capitals. I’ll be more careful about following convention in the future.

Very nice!

@rivkahlevi6117

2 жыл бұрын

PS love the outro.

@shlomi8307

Жыл бұрын

Ketiva v chatima tova sister. I also found a good channel of a friend called bethalgebra just new

It was awesome!

Which software you use for animation

@MathyJaphy

2 жыл бұрын

Desmos graphing calculator.

Thanks sir

Just wow!

Very cool.

I would have used small letters a, b, c, d, e, f for the measures of the line segments. Capital letters are conventionally used to denominate points.

@MathyJaphy

2 жыл бұрын

You're right. It didn't occur to me until after posting the video that I was not following the usual conventions. I leaned towards capitals for legibility on small screens, but I probably could have made it work with lower case.

Hey I'm looking for a nice Introductory geometry book with many exercises. I'm starting my major next year and I have been focusing mainly on calc, proofs and linear algebra but I'd like to refresh my knowledge in geometry

@MathyJaphy

Жыл бұрын

Thanks for asking, but I don't have anything to suggest, as I'm not a math professional. I'm sure you can find recommendations on reddit, r/geometry. Good luck with your major! See you in #SoME3, perhaps?

Indeed beautiful. 🤗

Such a circle is known as Circumcircle. It's a circle that passes through all vertices (corner points) of a polygon.

@MathyJaphy

2 жыл бұрын

I know. I chose to avoid using that technical term in my script. It sounds just a little bit funny. :-). Thanks anyway for the comment!

Any convex quadrilateral whose opposite angles add up to 180° is a cyclic quadrilateral, right?? I mean, I have no doubt that for any cyclic quadrilateral, opposite angles add up to 180°. But is the reciprocal true?, i.e. is it true that any convex quadrilateral whose opposite angles add up to 180° is a cyclic quadrilateral?? (i.e. there is a circle passing through each of the four vertices). How can you prove it?

@MathyJaphy

2 жыл бұрын

Excellent question. Yes, the reciprocal is true. By way of contradiction, assume you have a convex, non-cyclic quadrilateral ABCD where angle ABC and angle ADC are supplementary. Draw the circumcircle of triangle ABC, and note that D is not on that circle. If D is outside the circle, find the point on line AD that intersects the circle, and call it E. If D is inside the circle, extend AD until it intersects the circle, and call that point E. Since ABCE is a cyclic quadrilateral, angle AEC is supplementary to angle ABC and must therefore be equal to angle ADC. That's impossible.

@antoniopedrofalcaolopesmor6095

2 жыл бұрын

@@MathyJaphy Wow, nice! Thank you! *You meant: " If D is outside the circle, find the point on line AD that intersects the circle, and call it E."

@MathyJaphy

2 жыл бұрын

Thanks for pointing out my typo. I’ve corrected it.

Proud to be the 69th subscriber

@draganminic4928

2 жыл бұрын

Your joke is in a bad taste.

@alencherian1739

2 жыл бұрын

NICE

Wow, que satisfactorio es entender algo

subbed

Hey, where are new videos? It's good content, keep work

Insanely tought. Dictionary is licked to thank you😷

@MathyJaphy

Жыл бұрын

Thanks for the comment! I don't understand it, but I'll take it as a compliment. :-)

The video is great but would be better with voice over in the second part

Can you explain me how can you solve the factor of 'A','B' or 'F'..

@MathyJaphy

4 ай бұрын

I would be happy to, but I don't understand the question. What do you mean by "solve the factor of..."?

@SabrinaHoq

4 ай бұрын

@@MathyJaphy it would be helpful for my project if you could provide the measurement of the sides of the triangle..

@MathyJaphy

4 ай бұрын

​@@SabrinaHoq Yes, you're referring to the part where I scale each triangle by different factors. But I don't know what you mean by "solve". Some commenters have questioned whether it's okay to multiply a length by a length because the units become squared. But I'm not multiplying by a length, just a value that happens to be the same as the length of one of the other sides. You can always scale the sides of a triangle by a constant value without changing its angles. Does that answer your question?

@SabrinaHoq

4 ай бұрын

@@MathyJaphy Can I use the same constant value every time,??

@MathyJaphy

4 ай бұрын

@@SabrinaHoq The lengths of the triangles' sides (A, B, C, D, E and F) are defined by the quadrilateral you start with. A, B, C and D are the lengths of the quadrilateral's sides. E and F are the lengths of the diagonals. For the quadrilateral that I used as a demo in the video, the lengths are approximately (A=1.49, B=1.11, C=3.34, D=1.66, E=1.98, F=1.94). Is this helpful?

LETS SHOUT FOR PTOLEMY!

I thought you were saying it's a sick quadrilateral, I was like maybe corona.

@draganminic4928

2 жыл бұрын

So, did you disinfect your hands? 😆

I know the answer to the last question (3:54): VERY!

So…. I’m seeing a pattern of video content just leaving my sight into the edges of my screen.

Post more

@MathyJaphy

2 жыл бұрын

Soon… 😃

best 😉😉😉😉

I am from 🇮🇳India.

@alencherian1739

2 жыл бұрын

🤨

Using technology makes math more fun!!😎

I cannot believe that you are not a mathematician.

Boing! ???

@MathyJaphy

2 жыл бұрын

Translation…? :-)

@ruxleec

2 жыл бұрын

@@MathyJaphy The "Boing!" at the end's missing? 🙃

@MathyJaphy

2 жыл бұрын

Ah, got it. Yeah, that silliness was only for the joke video. I didn’t think I’d use the song again either, but I needed something for the end screen in this particular case.

Yup, your welcome :)

@MathyJaphy

Жыл бұрын

Thanks, I'm a big fan! Got any other theorems for me to animate? :-)

One peculiar thing is if all the opposite sides are equal then you'll get the Pythagorean Theorem.

@MathyJaphy

8 ай бұрын

Yes, indeed! That's what the first 30 seconds of the video is about, only in reverse. I start with Pythagoras, then generalize to the case where opposite sides are _not_ equal. :-)