Why slicing a cone gives an ellipse (beautiful proof)

Dandelin spheres, conic sections, and a view of genius in math.
An equally valuable form of support is to simply share some of the videos.

Thoughts on the recent change to be sponsor-free:

I originally saw the proof of this video when I was reading Paul Lockhart's "Measurement", which I highly recommend to all math learners, young and old.

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

Music by Vincent Rubinetti:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------

Various social media stuffs:

[rickeyward]

"You can often view glimpses of ingeniousness not as inexplicable miracles, but as the residue of experience. And when you do, the idea of genius goes from being mesmerizing to instead being actively inspirational" -Grant Sanderson (3blue1brown)
phenomenal quote.

[Fermion.]

Me: Just going about my daily life.
3Blue1Brown: Ever wondered why slicing a cone gives an ellipse?
Me: I wonder why slicing a cone gives an ellipse.

[Chicabaduk]

No, I've never wondered why slicing a cone gives an ellipse.
But surely was wonderful to see why.

[bimalpandey]

0:04 "Suppose you love math ..." I clicked on a 12 min video about an ellipse, come on dude.

[m_riatik]

regular mathematician: QED
3Blue1Brown: *BADA-BOOM BADA-BING*

[AustiuNoMatterWho]

Idk why I love squishification so much as a word

[JackFlashTech]

I like what you said about genius being a product of experience. Many people look at Einstein's Relativity, for example, as being an idea out of nowhere, but in its day, and for those in the field, it was not as strange as you would think. Einstein didn't just see something that no one was looking for; there were known inconsistencies between the theories of Maxwell's equations of how electromagnetism worked, and Newton's equations an how people thought electromagnetism SHOULD work. Einstein was trying to figure that out, and the Theory of Relativity was the result.

[qtheplatypus]

“Let’s focus our attention” well played sir.

[shoebmoin]

I don't know what's the magic in your voice that i cant close the video until i watch it completely.

[Papa]

10:22 Henri Poincaré said : "Mathematics is the art of giving the same name to different things."

(La mathématique est l'art de donner le même nom à des choses différentes.)

[MrShmazoo]

Just returned to this video and was reminded of what a wonderful production it is. You are a gem, 3b1b. You have an absolute knack for mathematical communication, and I admire you passion for making the art more accessible. I’ve shown this video to many friends who ask me “why do you think pure math is beautiful?” or “Why should I care if it doesn’t have an application?” and I think you answer those questions better than anyone else I’ve ever seen. Bravo!

[TioiraMusic]

I chose to study arts, languages and history just to getaway from Math due to a horrible teacher I had in high school. That is the way the education system works is Spain regretfully. You are forced to make a choice on branches of study when you are anything more than a teenager. Now I'm 37 and Math has been ever since growing on me. I found this video so beautiful I almost cried. Thanks a mill!

[kishanthakkar]

The concluding idea was interesting too...

“You can often view glimpses of ingeniousness not as inexplicable miracles, but as the residue of experience.... And when you do, the idea of genius goes from being mesmerizing to instead being actively inspirational...”

[laradimello]

While watching your videos I often wonder how can a teacher teach these topics without the softwares and animations you use. Like this videos are truly a form of art!

[jamespotter]

Congrats! U got a 6th grader who knows essentially nothing about stuff like spheres, cones, and ellipses to understand the concept

[ItsJJOLO]

On the other hand, the animation quality is well explained and simplified in a mesmerizing way; and not only the animation but your voice. Very comforting and makes what ever topic you talk about comforting.

[drone_better]

12:20 Only you would make sure the hands of a clock that spends 3 seconds on the screen are perfectly synchronised.

[AustinGarrett]

Hi, physics major here. If you turn the cone upside down, and imagine it to be a graph of force as a function of (x, y) position, what you have are two decoupled simple harmonic oscillators. Thus any free trajectory along the surface of the cone has two components that oscillate with simple harmonic motion, which we know describes an ellipse.

More insights into math from physics!

[jfbarbosaboro]

The genius is who explain things like this in such an EASY way for everyone!! Congratulations!! You are an AMAZING teacher!!

[xKuukkelix]

I have a latin test in 2 hours and im watching this for some reason