Extraordinary Conics: The Most Difficult Math Problem I Ever Solved

This is a real math problem I faced, and the process I went through to solve it. Despite being a difficult problem, I tried to focus on the beautiful visuals and interesting discoveries I made about conic sections that I doubt anyone knows about. While this isn't my typical style of video, there was a ton of coding that went into this (all open source) and an interactive app of this entire video. Check them out below!

Chapters:
0:00 Introduction
0:23 5 Elements
3:47 Duality
5:49 Skew Axes
7:39 My Hardest Problem (Part 1)
10:14 My Hardest Problem (Part 2)
13:59 My Hardest Problem (Part 3)

In Homage To:
Definitely subscribe to these channels if you like this video!

Six Umbrellas - The Psychedelic And (CC BY-SA 4.0)
Six Umbrellas - Monument (CC BY-SA 4.0)

Meydän - The Beauty of Maths (CC BY 4.0)

Yakov Golman - Dance (CC BY 4.0)

[feynman]

"I'm not 3b1b"

He said it to hide the truth.

[Yogfan]

i didn't understand like 90% of this video but yeah shapes are cool.

[abigailmcdowell]

I now really REALLY want 3b1b to prove all the assumptions in this video 😅

[dumbeh]

me having no idea what any of this means.
“ah yes of course... the... matrix.”

[sireevictineerivero]

"There is a conic that passes through any 5 points."
Yeah.

"Parabolas are halfway between an ellipse and a hyperbola."
Mhmm...

"The equation can be simplified by this matrix."
Uh...Right. Sure.

"AcosTheta +
...I guess?

"Frobenius product."
Now you're just making up words.

[Jellylamps]

My favorite thing in math is “oh you can just do this simple and seemingly unrelated thing to figure out the problem and it always works”

[johnerickson]

A mathmatician: Aw yes a very satisfying math problem
Me: Whoa look at the cool lines on the screen

[Vit-Pokorny]

programmers be like: "Just knowing it works was good enough for me"

[Nasrul]

Math with text: **boring**

Math visually: *_"let's get funky!"_*

[Otori]

I know enough to know I don't know enough to fully appreciate this

hehe pretty lines and shapes

[John-hzxy]

He makes Desmos look like a children's toy.

[jakehate]

"you might have seen a comic section represented like this before"
Me: hmmmm yes go on

[skj]

Kids today are lucky to have these kinds of visualizations for geometry. This type of stuff works wonders for the young mind in developing a very valuable sense of intuition for mathematics. This is really great work. Keep it up!

[kebman]

I think you'll _love_ POV-Ray. It's an old raytracer. You have to program the inputs. Modellers exist for it, but the true joy of using this program is wading through the pleasurably well-made documentation, and the complicated yet fully logical mathematical models used to trace the forms. You can make some very complex forms with it, including quartic objects, and objects modelled with various forms of "noise" algorithms, and of course fractals. I don't know any other raytracer that is so comprehensive, and yet logically set up. It might be old, but it still has it's uses.

[DeveloperDesmond]

CodeParade! This video is amazing!

Here's my criticism:

- When you have variables on screen, like A, B, or R1, it's really hard to keep track of *what* the variable represents. Salman Khan does a really good job in his videos of alleviating this problem in two ways: 1.) He keeps the diagram on screen when doing algebra. 2.) He color codes the variables to the diagram. If x represents a distance, he'll draw the distance in blue, and then use the same color blue whenever he writes x. If you pause your video at 10:34 or 10:25, you'll notice a block of text and a diagram, but no way for the viewer to quickly relate the diagram to the text.

- You introduced the problem statement at 8:00, which is probably too late. I also don't think you explained the *why* well enough for this problem. 3Blue1Brown's video, "This problem seems hard, then it doesn't, but it really is
, " is an example of Grant Sanderson's effort to tell an engaging narrative, even when the problem being solved isn't important.

[columbusmyhw]

15:30: "And negative areas are hyperbolas." Correction: this is area squared, so negative 'area squared', or imaginary areas, are hyperbolas.

[adamschultz]

"iT tUrNs OuT yOu JuSt InVeRt ThE mAtRiX" like that means anything in the world to anyone but Lawrence fishburn

[abd.]

9:00
The mid points lie on a line is called "Gauss line of a complete quadrilateral". Whose existence in proved in the Gauss Bodenmiller Theorem

[joaogabrielneto]

I'm a lawyer, why am i seeing this and why its so interesting?

[lock_ray]

After taking a more advanced linear algebra course I came back to this video and actually understood it this time! Thanks for the motivation CodeParade!