Karl Theodor Reye (born 20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) was a German mathematician. He contributed to geometry, particularly projective geometry and synthetic geometry. He is best known for his introduction of configurations in the second edition of his book, Geometrie der Lage (Geometry of Position, 1876). The Reye configuration of 12 points, 12 planes, and 16 lines is named after him.
Reye also developed a novel solution to the following three-dimensional extension of the problem of Apollonius: Construct all possible spheres that are simultaneously tangent to four given spheres.
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