Shapes

Curves that never finish, solids from Euclid to the fourth dimension, surfaces with one side or none, plane curves from the cycloid to Cassini’s ovals, and knots tied in space. Your browser computes each one from its equations while you watch. Open a shape to turn it by hand and change its settings; its record says who found it and links to its entry on mathcurve.

113 shapes · 22 fractals · 8 polyhedra and polytopes · 27 surfaces · 53 curves · 3 space curves and knots

Names and order follow mathcurve.com, Robert Ferréol’s encyclopedia of remarkable curves, surfaces, fractals and polyhedra.

Fractals

Shapes that repeat at every scale: curves of infinite length around finite areas, dusts and sponges, and the attractors of chaotic motion. The mathcurve index

Polyhedra and polytopes

Solids with flat faces, from Euclid’s five through Kepler’s stars to the six regular solids of four-dimensional space. The mathcurve index

Surfaces

One-sided bands, bottles with no inside, soap films, string models, and algebraic surfaces cut from a block. The mathcurve index

Curves

Curves in the plane, traced by a point riding a wheel or a turning rod, or found as the line where an equation in x and y takes one value. The mathcurve index

Space curves and knots

Curves that leave the plane, such as the line where a sphere meets a cylinder, and knots: closed loops in space that cannot be undone without cutting. The mathcurve index

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