Number every point round a circle and join each one to its double. Every line you draw is straight, and yet a heart-shaped curve appears — then a different one at three, and again at five, and it never stops. Numa is a lab for that sort of thing: the patterns hiding inside ordinary arithmetic, and the reasons behind them.
Five rooms: Paint (tap a rule and a hundred-square chart answers — count by three and five and the twice-painted squares are the fifteens; count by two, three, five and seven and what stays blank are the primes, made rather than announced; tapping a square carries it into Learn), Patterns (a times-table wheel drawing curves out of straight chords, an Ulam spiral where primes fall onto unexplained diagonals, runs of numbers with a rule to find, and an atlas including the 1089 trick and Kaprekar's 6174, both run step by step), Quests (twenty experiments with stars, plus one that generates a new question every time), Learn (twenty-two ideas from what a number line is and what sits left of zero, through divisors, primes, Euclid's algorithm and Euler's totient, to two problems nobody has solved — every example worked out for the number you are holding, and every entry readable plainly or in full), and Settings (English, 日本語, 中文).
Free, installable, works offline. No ads, no accounts, no tracking. Part of Zoey's Lab, with Huely (a colour lab), Ditty (a Morse code lab) and Tessa (a shape lab).