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math.MG2020
The complete characterization of tangram pentagons
Sarah Sophie Pohl, Christian Richter
The old Chinese puzzle tangram gives rise to serious mathematical problems when one asks for all tangram figures that satisfy particular geometric properties. All convex tangr…
math.MG2020
Incongruent equipartitions of the plane into quadrangles of equal perimeter
Dirk Frettlöh, Christian Richter
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. A…
math.MG2020
On the monotonicity of the isoperimetric quotient for parallel bodies
Christian Richter, Eugenia Saorín Gómez
The isoperimetric quotient of the whole family of inner and outer parallel bodies of a convex body is shown to be decreasing in the parameter of definition of parallel bodies, alon…