Solving Olympiad Level Geometry Problems with Complex Numbers

Описание: We thank Patrick Bauermann and Karl Fegert for their valuable feedback and for their permission to use the official logo of the Bundeswettbewerb Mathematik.

0:00 Introduction
1:32 Problem
2:20 Basics
5:42 Complex Plane
7:24 Addition and Subtraction
8:30 Scaling
9:30 Lines
11:10 Intersection of Lines
12:15 Absolute Value and Argument
13:10 Multiplication and Division
14:30 Rotation
15:43 Without Loss of Generality
19:33 Solution - Part 1
24:32 Solution - Part 2
28:06 Further Reading

Corrections:
9:20 the second -lambda should be replaced with +lambda
13:09 we meant to say: "The astute scholars amongst you may have noticed that we just looked at Cartesian geometry up to this point."
24:53 we meant to say: "We just know that D is somewhere on the line segment AC."

Resources from this video (including the proof): https://github.com/mathelehrer/geomet...
Resources from the Swiss Math Olympiad: https://mathematical.olympiad.ch/de/s...
Resources from the Bundeswettbewerb Mathematik: https://www.mathe-wettbewerbe.de/aufg...

This video is a submission for the Summer of Math Exposition 2:    • Summer of Math Exposition 2 Invitation  
It is a collaboration between Alexandru Duca (the domain expert) and me (the content producer).
You can find our original pitches on GitHub:
Alexandru Duca: https://github.com/leios/SoME_Topics/...
Number Cruncher: https://github.com/leios/SoME_Topics/...

While writing the script, Alexandru Duca drew inspiration from the following videos:
"The hardest problem on the hardest test" by 3Blue1Brown:    • The hardest problem on the hardest test  
"Vectors | Chapter 1, Essence of linear algebra" by 3Blue1Brown:    • Vectors | Chapter 1, Essence of linear alg...   ‪@3blue1brown‬
"String Theory Explained – What is The True Nature of Reality?" by Kurzgesagt:    • String Theory Explained – What is The True...   ‪@kurzgesagt‬

I learned to make some of the animations from the following videos:
Curtain:    • How to make REALISTIC CURTAIN in 3 ways - ...   ‪@QuyTran37‬
Sand Texture:    • Easy Procedural Sand Material -  Blender 2...   ‪@TR_MediaOfficial‬
Engraved Text:    • Engrave & Emboss Text Easily In Blender | ...   ‪@5MinutesBlender‬
Rope:    • Blender 3.1  Rigid Body And Cloth Simulati...   ‪@mk3dgraphics‬
Marble Texture:    • Procedural Marble Material (Blender Tutorial)   ‪@RyanKingArt‬
Gold Texture:    • Procedural Gold Material (Blender Tutorial)  
Explosions:    • VFX - Avengers Infinity War Dust Effect in...   ‪@3d-illusions‬
Flag:    • FLAGS (with blender)   ‪@CGMatter‬
Cell Fracture Explosion:    • Blender 2.8 Tutorial - Cell Fracture Explo...   ‪@blendermania3d‬

Music by Chris Zabriskie: http://chriszabriskie.com/
"Candlepower": http://chriszabriskie.com/divider/
"CGI Snake": http://chriszabriskie.com/divider/
"Divider": http://chriszabriskie.com/divider/
"I Am Running Down the Long Hallway of Viewmont Elementary": http://chriszabriskie.com/honor/
"We Always Thought the Future Would Be Kind of Fun": http://chriszabriskie.com/darkglow/
"What True Self, Feels Bogus, Let's Watch Jason X": http://chriszabriskie.com/reappear/
Licensed under Creative Commons Attribution 4.0: https://creativecommons.org/licenses/...