Euclid's algorithm as squares in a rectangle
A 48 by 18 rectangle is filled with the largest possible squares in stages: two 18-squares leave a 12 by 18 strip, one 12-square leaves a 12 by 6 strip, and two 6-squares complete the tiling exactly. Each tiling stage corresponds to one division step in Euclid's algorithm, and the final square size, 6, is the greatest common divisor. Useful for students learning why the algorithm works geometrically, not just as arithmetic steps.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
To find gcd(48, 18), tile a 48 by 18 rectangle with the largest squares possible. Two 18-squares leave a 12 by 18 strip; one 12-square leaves a 12 by 6 strip; two 6-squares finish it exactly. Each step is one line of Euclid's algorithm, and the last square, 6, is the gcd.
Make the next one in this series
- Show gcd(1071, 462) with the same square-tiling method and count the steps
- Animate the algorithm as repeated subtraction instead of division to compare speeds
- Connect square tiling to continued fractions using the same rectangle example
