A Möbius-band chain pump. Al-Jazari, Book of Knowledge of Ingenious Mechanical Devices (1206)
Nonagonus secundi ordinis. Thomas Bradwardine, Geometria speculativa (c.1320)
The first maze. Giovanni Fontana, Bellicorum instrumentorum liber cum figuris (c.1420)
An unfolding of a snub cube. Albrecht Dürer, Underweysung der messung (1520)
A tree of forces in equilibrium. Simon Stevin, Byvough der Weeghconst [Supplement to The Art of Weighing] (1605)
Lifting the (punctured) disk to a helical screw. Henrik Stevin, Plaetboec vervangende de figuren of formen gehorig tottet Wisconstich filosofisch bedryf (1668)
Computing the area of a non-convex polygon. Albrecht Meister, Generalia de genesi figurarum planarum et inde pendentibus earum affectionibus (1770)
A simple closed curve. Bernard Bolzano, Die drey Probleme der Rectification, der Complanation und der Cubirung (1817)
Decomposing a non-simple curve into simple curves. Carl Friedrich Gauß, Zur Geometria situs (Nachlass) (c.1830)
Proving that every convex(!) polygon can be triangulated. Carl Friedrich Gauß, Zur Geometria situs (Nachlass) (c.1830)
A system of cycles and its dual system of arcs on a punctured torus. Bernhard Riemann, Theorie der Abel'schen Functionen (1857)
A pants decomposition. Johann Benedict Listing, Census Räumlicher Complexe (1862)
"Alexander" numbering of a nonsimple polygon. Johann Benedict Listing, Vorstudien von Topologie (1847)
Cutting a surface at non-critical heights. August Möbius, Theorie dr elementaren Verwandtschaft (1863)
A reciprocal pair of form/force diagrams. James Clerk Maxwell, On reciprocal figures and diagrams of forces (1864)
Flipping an edge in a triangulation. August Möbius, Ueber die Bestimmung des Inhalts eines Polyëders (1865)
The "Morse-Smale" complex of a smooth terrain. James Clerk Maxwell, On Hills and Dales (1870)
A planar map and its dual, specified by the same rotation system. Max Brückner, Vielecke und Vielflache: Theorie und Geschichte (1900)
Paul Klee, Pedagocial Sketchbook (1925), English translation by Sybil Moholy-Nagy (1953)
An untrangulatable polyhedron. Erich Schönhardt, “Über die Zerlegung von Dreieckspolyedern in Tetraeder" (1928)
Oscar Reutersvärd, Opus 1 (1934)
The "tree-onion figure" of a planar map. Max Dehn, Über kombinatorische Topologie (1936)
A squared rectangle. Leonard Brooks, Cedric Smith, Arthur Stone, and William Tutte, “The dissection of rectangles into squares” (1940)
Piet Hein's inspirations for the game "Polygon", now known as "Hex". Piet Hein, "Vil de lære Polygon?", Politiker (December 26, 1942)
An impossible pair of polyhedra. David Huffman, "Impossible Objects as Nonsense Sentences” (1971)
Elimination order for a regular grid. Alan George, "Nested Dissection of a Regular Finite Element Mesh” (1972)
Asteroids, developed by Lye Raine, Ed Logg, and Dominic Walsh (1979)