Mark 12 evenly-spaced dots around a circle. Connect every 5th one. A perfect five-pointed star appears — without measuring a single angle.
108.0°
72.0°
540°
5
Skips on 12 dots
Mark 12 evenly-spaced dots round a circle, then connect every k-th dot. Skip 5 → five-pointed star (pentagram). Skip 4 → triangle. Skip 3 → square. Skip 7 → pentagram the other way. Skip 6 → just a line, then nothing new.
With 12 dots, why does 'skip 3' draw a square instead of a 12-pointed star?
Skip-counting around a circle (mod n) is the doorway to modular arithmetic — the same maths behind internet encryption.
Try other skips
12 dots, skip 4 → triangle. Skip 3 → square. Skip 5 → pentagram. Skip 7 → another pentagram, going the other way. Skip 6 → six dots and a vertical line, then nothing.
Skip-counting modulo a number is the door to modular arithmetic — the same maths that powers internet encryption.