Bezout solutions
A line of fixed slope is carried across the integer lattice, and at the offsets where it passes exactly through lattice points the solutions light up.
CSS
Numtheory
15 animationsChinese remainder
Two dials of three and five positions step together, each returning to its own zero often but the pair of readings only repeating after fifteen steps.
CSSCongruent residues
Two columns of different height give up whole groups of the modulus in turn until both are left holding the same remainder, tied across by a dashed rule.
CSSContinued fraction
A rectangle gives up the largest square it can hold, then the next, each term of the expansion taking the accent until the last two squares come out equal.
CSSConvergents
Successive convergents of a continued fraction overshoot then undershoot the target, the accent head stepping through them until the error is all but gone.
CSSEuclidean algorithm
Two measured bars take turns giving up a whole copy of the other, shrinking inside the ghosts of their original lengths until both stop on the greatest common divisor.
CSSEuler totient
A hand makes one turn of a twelve-position ring and every position that shares no factor with twelve swells as it passes, counting out the totient.
CSSModular clock
A hand adds ten hours at a time on a twelve-mark dial, wrapping past the zero notch on every step and coming to rest where it started.
CSSModular exponentiation
A raw power climbs away without limit while the same value taken modulo a ceiling folds back underneath it and carries on from the remainder.
CSSPositional base
Four binary places, each holding twice as long as the one to its right, counting down through every value the register can hold.
CSSPrime factor tree
A composite number is split again and again, each level peeling off a prime and handing the rest down until only prime leaves are left.
CSSResidue class
Fifteen integers on a rule, with each residue class modulo five lighting its three members and the brace that spans them before handing on to the next.
CSSSieve of Eratosthenes
A square grid of integers is struck out multiple by multiple, the twos then the threes then the fives, until only the primes are left standing.
CSSTrial division
A candidate length is tiled by one trial divisor after another, the tiles reaching the far stop cleanly when the division is exact and falling short by the remainder when it is not.
CSSTwin primes
A caliper of span two is carried along the integer ray and set down on each pair of primes two apart, latching on the tall prime ticks and passing over the rest.
CSS