What's Behind the Parabola? (
Вставка
- Опубліковано 24 чер 2024
- Today we'll look at the amazing facts about a parabola
CONTENT
0:00 - Do straight lines form a curve?
0:28 - Parabola in 3D-space
1:01 - Gravity and trajectory
1:19 - Another envelope
1:44 - Geometric approach
2:29 - Optical property
2:44 - Parabola makes life better
3:28 - Graph of a quadratic function
4:24 - Conic sections and formulas
5:21 - Pascal's theorem
5:55 - Amazing fact!
6:30 - For real mathematicians
7:50 - Amazing connection!
8:28 - Geometry in pictures
9:32 - Fantastic fact!
10:20 - Divine animation
What facts did you know earlier, and which ones have you learned now?
Thanks for watching!
The fact that the 4 intersection points of those 2 parabolas lay on same circul amazes me
I was, am, and will always be captivated at the beauty of geometry!
This one is a great video! Really needed this as after retiring from Math Olympiad, I was having a hard time finding the beauty and fun I once found in mathematics. I'm really grateful to you for making such an amazing video!
Thank you for this story and the kind words!
I'm glad you appreciated the beauty of these facts
Great video! this is exactly how I imagined geometry back in highschool, just loved it. And good luck in the exposition!
Thank you for the kind words!
I start watching and immediately get suspicious, as the music is really familiar. I start listening carefully to the voice and I immediately recognise one of my favourite youtubers! Nice job, Wild, you have a really good accent. I'll be following you on your new channel. Best of luck!
whats his other channel?
@@laiton_, it's just local non-english videos. I'll keep working to make english versions here, if SoME3 helps me to get more interested viewers
Parabola gameplay: solve for x^2-4x+1
parabola lore:
As for 6:10 a projective geometric solution to the problem would be to look at desargue's involution using the four intersection points and the line at infinity, tge two parabolas are tangent to the line at infinity so the two perpendicular tangency points stay in place, since it is a projective involution that has fixed points A and B it will send C to D if and only if the cross ratio of (ABCD)=-1 now the statement that the 4 points are on a circle is equivalent to the statement that the conic section that goes through the 4 points and the point (1,i,0)=I on the line at infinity passes through (i,1,0)=J since all circles pass through these 2 points so if A,B are perpendicular on the line at infinity have the property (ABIJ)=-1 this is easily verifiable since the real rotation of all point on the line at infinity by 90 degrees is a projective involution that sends A to B and fixes I,J so as we showen earlier this means that (ABIJ)=-1 since there exists a projective involution that fixes I J and swaps A B
Brilliant, thank you!
I have never seen geometry be this beautiful... These animations and explanations must have taken so much time and effort
Thank you so much!!!
A month Back I thought of making geometry of conic sections treated geometrically but due to my jee preparation it got quite bothersome to manage to make a video (in the way I got started with manim though~), this was super thanks!
Beautiful animations and facts
This was epic. I just love it.
Is it WildMathing?)
Nope
Love it when math is basically art. Good video 👍
LEGENDARY video!!!
Presented in a very amazing and resonant way. Thank you!
It's pleasure to see so many kind-hearted comments here!
Amazing!❤
Amazing!
Gosh, this is so beautiful 😢😭
This is mindblowing
Very nice! What editor do you use to create these visuals?
Thank you!
I used ManimCE to create animations: docs.manim.community/en/stable/
That's why there is nothing special about montage
@@geometry_manim Thanks! Is it intuitive to learn?
@@NaviaryMusic, Manim is a Python library, so you need to go deeper into programming and OOP and it takes time. But if you like this way to make animations, then it would be fun to study
@@geometry_manim Thanks!
Попався, WildMathing 😎
amazing
At 5:05 it would be useful to put the formula for the discriminant in terms of the elliptic equation coefficients on screen.
Услышал знакомую мелодию
Take a look at Fortune’s Algorithm for finding the Voronoi tesselation of a set of points for a practical implementation of some of these ideas.
My man just hit me over the head with a tour de force of lines and curves
I like it
Wild math думал, что мы не узнаем легенду, скрывающуюся за таинственным псевдонимом "geometry"
Nifty !
2:17 I was given this definition in school, we had a whole chapter on locus of points
That's great! I'm glad to know that
Hi, I just started learning manim. Do you have a repository where I could view the code for your video?
Hey! To make more videos, I plan to start Patreon in the future and share useful code snippets there. That's why I can't post them now.
But I've made a prototype with reflective property: discord.com/channels/581738731934056449/1051722064781901874/1051767835719909417
Useful code for animations and lessons can be found here: ua-cam.com/users/TheoremofBeethovenvideos
And here are nice tutorials from dev: www.youtube.com/@behackl
thanks a lot@@geometry_manim
This why I love geometry ❤❤❤
Какие-то подозрительно знакомые музыка и голос))
6:10 let the first parabola be ay^2 + by + c - x = 0, the second dx^2 + ex + f - y = 0, if those four (x, y) points satisfy both equations they satisfy d(ay^2 + by + c - x) + a(dx^2 + ex + f - y) = 0 which is an equation of a circle as it has no xy term and coefficients for x^2 and y^2 are equal
And here is the winner!
Can I ask what animating program you use? Manim perhaps?
Yes, this is ManimCE: www.manim.community
@6:00 : you asked about why the concyclicity...be my guest : "two conics intersect in four concyclic points iff their axes are parallel". One proof is given using google to find the Simonic's january 2013 paper "On a problem concerning two conics" ...an easy deduction from Theorem 1.
Many thanks! To be honest I know how to prove the fact 6:00, but it's always interesting to read something new. That's why I really appreciate your comment!
*Wild Mathing?*
Wild mathing?😂
8:18
These are my text problem visual view
Ellipse??? Wdym its a parabola right
I'm just amazed at how absurd peer review has gotten. They write something that nobody can understand. I take a few minutes to try and figure out what it is they are saying, only to find out it is trivial. Why did this over educated clown waste my time? Then there is you. This whole competition really. You say wonderful stuff and it is all perfectly understandable. The funny thing is, I bet those guys doing peer review would look confused and say your work is not well defined.
Hey, thanks for sharing this! I would be interested to know what comments people write on my video (even if they are unfair). And in any case, I am very grateful to 3B1B for this competition, because it brought new views and subscribers. A lot of new good videos have appeared on UA-cam, this is very cool!
@@geometry_manim in case there was a misunderstanding, I'll make this very clear. I love your work.
@@thomasolson2823, I've got it, thank you!