Mark 12 evenly-spaced dots around a circle. Connect every 5th one. A perfect five-pointed star appears — without measuring a single angle.
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.