The Hidden Shape Inside the Multiplication Table

Put 200 dots on a circle and connect each number to its double. A perfect heart appears — and nobody drew it. This is the times table turned into geometry, and its curves hide in your coffee cup and in the Mandelbrot set. We start with clock arithmetic, draw times two and times three line by line, slide the multiplier smoothly through every value in between, and discover why straight lines create curves (envelopes and rolling circles). Then we bounce real light rays off a circular mirror, find the same cardioid inside the Mandelbrot set, and uncover strange coincidences — like why times 67 draws exactly the same picture as times 3. Chapters 0:00 A flower made of numbers 0:27 Numbers on a circle 1:29 Times two: the cardioid 2:15 Times three and beyond 2:58 The continuous morph 3:42 Why the curve appears 4:39 Light draws it too 5:50 Inside the Mandelbrot set 7:00 Hidden patterns Everything in this video — animations, simulations and music — was created from scratch with code. With 200 points, which multiplier draws exactly the same picture as ×7? A) ×143 B) ×193 C) ×107 Subscribe for more visual math and physics. #math #mathart #mathvisualization