https://drawnmathematics.com/ Mathematics you can see, draw, and fold. en https://drawnmathematics.com/crease-patterns/a4-paper-size/https://drawnmathematics.com/crease-patterns/a4-paper-size/Mon, 26 Oct 2026 00:00:00 GMTA4 paper is 210 × 297 mm, a √2 rectangle to within a millimetre. Fold one sheet to see the ratio, then follow the proof that only √2 survives being halved. https://drawnmathematics.com/perspective/anamorphic-art/https://drawnmathematics.com/perspective/anamorphic-art/Mon, 26 Oct 2026 00:00:00 GMTThe smear in Holbein's The Ambassadors is a skull stretched along one slanting line. Unstretch it, find where to stand, and draw a stretched face of your own. https://drawnmathematics.com/fractals/coastline-paradox/https://drawnmathematics.com/fractals/coastline-paradox/Mon, 26 Oct 2026 00:00:00 GMTOn one 1:10m map, a 200 km ruler measures Great Britain's coast at 2,508 km and a 3.125 km ruler at 6,579 km. Walk it yourself and see where the rule stops. https://drawnmathematics.com/fractals/dragon-curve/https://drawnmathematics.com/fractals/dragon-curve/Mon, 26 Oct 2026 00:00:00 GMTFold a paper strip in half again and again, open every crease to 90°, and it traces a stage of the dragon curve. Checked to 16 folds: no edge used twice. https://drawnmathematics.com/puzzles/haberdashers-puzzle/https://drawnmathematics.com/puzzles/haberdashers-puzzle/Mon, 26 Oct 2026 00:00:00 GMTIn Dudeney's haberdasher's puzzle, four hinged pieces turn a triangle into a square. See the exact cuts, and why three straight-edged pieces fail if none flip. https://drawnmathematics.com/symmetry/islamic-geometric-patterns/https://drawnmathematics.com/symmetry/islamic-geometric-patterns/Mon, 26 Oct 2026 00:00:00 GMTDraw an eight-point star from one circle with a compass and straightedge, repeat it every 4 grid cells, and see why the pattern is p4m, or p4 once woven. https://drawnmathematics.com/symmetry/kaleidoscope/https://drawnmathematics.com/symmetry/kaleidoscope/Mon, 26 Oct 2026 00:00:00 GMTHow a kaleidoscope works: a lopsided drawing repeats with no seam only if the mirror angle is 180° divided by a whole number: 60° works, while 50° and 72° fail. https://drawnmathematics.com/crease-patterns/kawasakis-theorem/https://drawnmathematics.com/crease-patterns/kawasakis-theorem/Mon, 26 Oct 2026 00:00:00 GMTKawasaki's theorem: an inner point of a flat sheet folds flat only if alternate angles each total 180°. See a worked example, the ant-walk proof and the limits. https://drawnmathematics.com/puzzles/missing-square/https://drawnmathematics.com/puzzles/missing-square/Mon, 26 Oct 2026 00:00:00 GMTThe missing square puzzle's two 13-by-5 figures are not triangles. Each long edge bends by about 1.2°, and the thin gap between them is exactly one square. https://drawnmathematics.com/perspective/one-point-perspective/https://drawnmathematics.com/perspective/one-point-perspective/Mon, 26 Oct 2026 00:00:00 GMTDraw one-point perspective in ten steps: a horizon, one vanishing point, a cube sized with a distance point, a tiled floor, and a test on a Renaissance panel.