Explore a comprehensive geometry course covering a wide range of topics from ancient Japanese temple problems to modern mathematical olympiad challenges. Delve into fascinating geometric concepts including inscribed shapes, circle properties, area calculations, and proportionality theorems. Tackle engaging problems involving hexagons, parabolas, ellipses, and polyhedra. Learn about historical contributions to geometry, such as the Lunes of Alhazen and Thales' Proportionality Theorem. Discover the golden ratio in art and examine unique geometric properties. Practice solving complex problems using various methods, including applications of calculus and complex plane geometry. Encounter intriguing concepts like Bretschneider's formula and Sangaku (Japanese temple geometry). Enhance your problem-solving skills with olympiad-level questions and teacher examination problems from different countries, providing a global perspective on geometric reasoning and applications.
Overview
Syllabus
A Japanese Temple Geometry Problem from 1800..
A relaxing geometry problem..
A geometry quickie!.
An inscribed tower of squares..
Portuguese Math Olympiad | 2019.
What is the radius of the large circle?.
A simple geometry problem with a nice generalization..
A quick geometry problem..
Hexagon, meet parabola..
Maximize the area of one ellipse!.
What is the area of the shaded region??.
A quick geometry problem..
What is the shaded area??.
What is the radius of ??.
What is the shaded area?.
Find the missing radius!.
Find the shaded area!!.
How big is the square?.
The Lunes of Alhazen.
A viewer suggested geometry problem..
How big can y be?.
A nice geometry trick!.
What is the radius of ?.
Proposed by a 15 year-old in 1812!!!.
Half of a deathly area....
Thales Proportionality Theorem.
What a big twist!.
From my favorite geometry book..
What is the radius of ?.
a look at the future....
Challenge: Solve this without Calculus!.
Did I make this too hard?.
a 2500 year old geometry problem..
What are the side lengths of this triangle??.
Can you solve this with a different method??.
An interesting geometry competition problem..
A really cool property of polyhedra!.
A tricky geometry problem!.
What happens when you stack circles on each other?.
Can you find the area of this triangle??.
An artist's discovery of the golden ratio..
Does this red region have a name?? Let's find its area!.
What is the radius of ? -- A fun geometry puzzle..
a nice geometry problem in the complex plane..
a nordic geometry problem.
an absurdist geometry problem.
What is Bretschneider's formula??.
An example of classic Japanese geometry -- Sangaku.
Geometry from an exam for teachers..
A nice Iranian geometry problem.
Taught by
Michael Penn
