Karl August Reinhardt (27 January 1895 – 27 April 1941) was a German mathematician whose research concerned geometry, including polygons and tessellations.
His dissertation, Über die Zerlegung der Ebene in Polygone, concerned tessellations of the plane, and was supervised by Ludwig Bieberbach.
In 1924, Reinhardt moved to the University of Greifswald as an extraordinary professor, under the leadership of Johann Radon; this gave him an income sufficient to support himself without a second job, and afforded him more time for research.
In a 1928 paper, Zur Zerlegung der euklidischen Räume in kongeuente Polytope[7] Reinhardt solved this part by finding an example of such a tessellation.
[8] Another of his works, Über die dichteste gitterförmige Lagerung kongruenter Bereiche in der Ebene und eine besondere Art konvexer Kurven from 1934, constructed the smoothed octagon and conjectured that, among all centrally-symmetric convex shapes in the plane, it is the one with the lowest maximum packing density.