Explore a comprehensive video series delving into intriguing mathematical concepts and problems. Dive deep into topics such as symmetry in classic problems, David Wilson's divisibility graph, surprising algebra in geometry, and complex numbers in high dimensions. Discover the Triatic Formula, understand the Gauss-Bonnet Theorem, and unravel math mysteries for young mathematicians. Investigate Catalan Numbers through dots in circles and parentheses, explore the peculiarities of fractions on the number line, and learn about bee numbers and honeycomb patterns. Examine favorite number trees, Hemachandra Numbers, Theon's Ladder, and squangular numbers. Study sums of powers formulas, lattice points in circles, and partially-filled Latin squares. Delve into card pile mathematics, Archimedes' Law of Lever, the Golden Ratio, and the volume of a sphere. Explore Euler's famous formula, cube roundness, tie folding, gender balance puzzles, and the Citardauq Formula. Conclude with an in-depth look at the classic egg-dropping puzzle, offering over 12 hours of engaging mathematical content for curious minds.
Overview
Syllabus
Using Symmetry to Your Advantage: Some Classic Problems in New Light.
David Wilson's Curious Divisibility Graph -- and more!.
Surprising Algebra in Geometry.
Are Complex Numbers Forced Upon Us? Multiplication in High Dimensions.
The Triatic Formula: Having Quirky Fun making things Quadratic, Triangular.
Not-so-Curvy Curves on Not-so-Curvy Surfaces: Understanding the Gauss-Bonnet Theorem.
A Math Mystery for Young Mathematicians.
Dots in a Circle and Parentheses Numbers: A Sneaky Way into the Catalan Numbers.
Fractions Take Up No Space on the Number Line (Whoa!).
Bee Numbers and the Power of Honeycomb! (via Seven Puzzles).
My Favourite Number Tree (and the sqrt(2) and weird binary, and more!).
An Astonishing Property of the Hemachandra Numbers (and the primes, and the non-squares, and more!).
Theon's Ladder, Squangular Numbers, International Paper, and more!.
Sums of Powers Formulas.
Sums of Powers: Part II. Proving the Whacky Integration Technique from part I (if you are game!).
Lattice Points in Circles: A curious puzzle.
Partially-Filled Latin Squares and Semi-Magic Squares: A Follow-Up Video.
Card Pile Mathematics and Semi-Magic Squares.
Archimedes' Law of Lever.
A Golden Ratio Surprise.
How Archimedes First Deduced the Volume of a Sphere.
A Surprising Appearance of Euler's Famous Formula: V- E + F = 2.
How Round is a Cube? (Answer: Just as round as a sphere!).
Tie Folding and a link to Artin's Conjecture.
Gender Balance Puzzle.
The Citardauq Formula.
Egg Dropping: Going beyond just solving the classic puzzle.
Taught by
James Tanton
