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Play, download and edit the free video The Fabricius-Bjerre Formula.

A charming drawing of a closed curve may hide a beautiful mathematical equation: the Fabricius-Bjerre formula.

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3Blue1Brown Summer of Math Exposition

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References:

Fabricius-Bjerre, Fr.
On the double tangents of plane closed curves.
Math. Scand. 11, 113-116 (1962).

Halpern, B.
Global theorems for closed plane curves.
Bull. Am. Math. Soc. 76, 96-100 (1970).

Fabricius-Bjerre, Fr.
A relation between the numbers of singular points and singular lines of a plane closed curve.
Math. Scand. 40, 20-24 (1977).

Weiner, Joel L.
Global properties of spherical curves.
J. Differ. Geom. 12, 425-434 (1977).

Pignoni, Roberto.
Integral relations for pointed curves in a real projective plane.
Geom. Dedicata 45, No. 3, 263-287 (1993).

Ferrand, Emmanuel.
On the Bennequin invariant and the geometry of wave fronts.
Geom. Dedicata 65, No. 2, 219-245 (1997).

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