The Dragon Curve.

Quadratic Multiplication with Area Models.

1/4 1/16 1/64 1/256 . . . = 1/3

There are only five Platonic solids in Euclidean geometry Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron.

Viviani’s Theorem, named after the Italian mathematician Vincenzo Viviani, states that for any point inside an equilateral triangle, the sum of the perpendicular distances from the point to the three sides is always equal to the altitude (height) of the triangle.

Geometry of the Sum of Squares.

The property that makes the π rule the whole of mathematics.

(a b)³ = a³ b³ 3a²b 3ab²

Seventeen Equations that changed the world.🌐

This mind-bending animation is based on the Haberdasher’s Puzzle, discovered in 1902 by Ernest Henry Dudeney, one of Britain’s greatest recreational mathematicians. He first published it in the Daily Mail, framing it as a whimsical story: a haberdasher (a dealer in sewing goods) is given a piece of valuable cloth shaped like an equilateral triangle. He needs to cut it into a perfect square for a customer using the fewest cuts possible and without wasting a single thread. Dudeney shocked the mathematical world by proving it could be done in just four pieces. Even more amazingly, he proved the pieces could be hinged together at their corners, forming a continuous chain that opens as a triangle and closes into a square.

Constructing a perpendicular to a line through a point.

Geometric Series Proof via Concentric Pentagon Dissection.

The Fibonacci's Elephant.

Ever wondered how 3D objects spin smoothly in games, animations, or even real-world robotics? This is the magic behind it! Meet the rotation matrices that control how things twist around the X, Y, and Z axes. From video games to spacecraft navigation, these rotations power the invisible math that makes our digital world feel real.

In 1963, mathematician Stanislaw Ulam was stuck in a long, tedious presentation. To pass the time, he started doodling. He wrote the number 1, then spiraled 2, 3, 4, and so on outward in a grid. Then, he highlighted only the prime numbers. Instead of random static, a hidden structure emerged from the chaos. Distinct, striking diagonal lines of primes shot across the page. It’s known as the Ulam Spiral, and it visually proves one of the most beautiful mysteries in mathematics: the "atoms" of our number system aren't as random as they seem. There is order in the chaos.

Anatomy of a Definite Integral.

The Anatomy of Bayes’ Theorem.

Thomas Bayes, an 18th-century English mathematician, developed Bayes' Theorem, a method for determining the likelihood of an event based on new information. It's like updating your guess when you learn more. After his death, one of his friends published it based on Bayes' essay.

“We must believe that we are gifted for something, and that this thing, at whatever cost, must be attained.” ― Marie Curie