Think Twice
Mathematics in motion.
Generating Conic Sections with Circles | Part 3. The Hyperbola
Generating Conic Sections with Circles | Part 2. The Parabola
Generating Conic Sections with Circles | Part 1. The Ellipse
Euler's Formula V - E + F = 2 | Proof
Every Polygon can be Triangulated Into Exactly n-2 Triangles | Proof by Induction
Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle
The Fermat Point of a Triangle | Geometric construction + Proof |
A fun probability puzzle with a neat geometric solution.
Constructing a Square of Equal Area to a given Polygon
Alternating series #2 | Visual solution |
Visual Calculus: Derivative of sin(θ) is cos(θ)
What is the area under an arc of a cycloid curve?
Napoleon's theorem | Proof |
Cavalieri's Principle in 3D | Volume of a sphere |
Alternating series #1 | Visual solution |
Pythagorean theorem | 3 Visual Proofs |
Approximating Pi ( Monte Carlo integration ) | animation
Finding the general formula for nth octagonal number | Visual proof |
Arithmetic mean vs Geometric mean | inequality among means | visual proof
Infinite Sums | Geometric Series | Explained Visually
Geometry of Binomial Theorem | Visual Representation | 2 examples
Four squares with constant area | Visual Proof | Squaring the segments |
Geometry: Viviani's theorem | Visualization + Proof |
Fitting a Cube Through a Copy of Itself | Rupert's Cube |
Chaos Game | Fractals emerging from chaos | Computer simulation |
Unfolding The Dragon | Fractal Curve |
Двойной маятник | Хаос | Эффект бабочки | Компьютерная симуляция
Cutting a Möbius strip in half (and more) | Animated Topology |
Area of dodecagon | Beautiful geometry | Visual mathematics