Thomas Fincke (January 6, 1561–April 24, 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years.

Fincke was born in Flensburg, Schleswig and died in Copenhagen. His lasting achievement is found in his book Geometria rotundi (1583), in which he introduced the trigonometric functions tangent and secant.

His son in law was the great Danish physician and natural historian, Ole Worm, who married his daughter, Dorothea.

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