A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.
Marjorie Rice was an American amateur mathematician most famous for her discoveries in geometry. Rice was born February 16, 1923 in St. Petersburg, Florida, and died July 2, 2017 in San Diego, California, where she was living with her son and his wife.
William Mark Goldman is a professor of mathematics at the University of Maryland, College Park. He received a B.A. in mathematics from Princeton University in 1977, and a Ph.D. in mathematics from the University of California, Berkeley in 1980.
In geometry, the Heesch number of a shape is the maximum number of layers of copies of the same shape that can surround it. Heesch's problem is the problem of determining the set of numbers that can be Heesch numbers. Both are named for geometer Heinrich Heesch, who found a tile with Heesch number 1 and proposed the more general problem.
Branko Grünbaum was a Yugoslavian-born mathematician of Jewish descent and a professor emeritus at the University of Washington in Seattle. He received his Ph.D. in 1957 from Hebrew University of Jerusalem in Israel.
László Fejes Tóth was a Hungarian mathematician who specialized in geometry. He proved that a lattice pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane. He also investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced to a finite case analysis and, later, that the problem might be solved using a computer.
The "happy ending problem" is the following statement:
In geometry, a Cairo pentagonal tiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of the plane by hexagons and named for its use as a paving design in Cairo. It is also called MacMahon's net after Percy Alexander MacMahon, who depicted it in his 1921 publication New Mathematical Pastimes. John Horton Conway called it a 4-fold pentille.
In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon.
Victor L. Klee, Jr. was a mathematician specialising in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics. He spent almost his entire career at the University of Washington in Seattle.
In geometry, a shape is said to be anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that shape there are two tiles that are not equivalent under any symmetry of the tiling. A tiling by an anisohedral tile is referred to as an anisohedral tiling.
Heiko Harborth is Professor of Mathematics at Braunschweig University of Technology, 1975–present, and author of more than 188 mathematical publications. His work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory.
Károly Bezdek is a Hungarian-Canadian mathematician. He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada. Also he is a professor of mathematics at the University of Pannonia in Veszprém, Hungary. His main research interests are in geometry in particular, in combinatorial, computational, convex, and discrete geometry. He has authored 3 books and more than 130 research papers. He is a founding Editor-in-Chief of the e-journal Contributions to Discrete Mathematics (CDM).
Ileana Streinu is a Romanian-American computer scientist and mathematician, the Charles N. Clark Professor of Computer Science and Mathematics at Smith College in Massachusetts. She is known for her research in computational geometry, and in particular for her work on kinematics and structural rigidity.
Stanley Wagon is a Canadian-American mathematician, a professor of mathematics at Macalester College in Minnesota. He is the author of multiple books on number theory, geometry, and computational mathematics, and is also known for his snow sculpture.
Karl August Reinhardt was a German mathematician whose research concerned geometry, including polygons and tessellations. He solved one of the parts of Hilbert's eighteenth problem, and is the namesake of the Reinhardt polygons.
Doris J. Schattschneider is an American mathematician, a retired professor of mathematics at Moravian College. She is known for writing about tessellations and about the art of M. C. Escher, for helping Martin Gardner validate and popularize the pentagon tiling discoveries of amateur mathematician Marjorie Rice, and for co-directing with Eugene Klotz the project that developed The Geometer's Sketchpad.
Chaim Goodman-Strauss is an American mathematician who works in convex geometry, especially aperiodic tiling. He is on the faculty of the University of Arkansas and is a co-author with John H. Conway of The Symmetries of Things, a comprehensive book surveying the mathematical theory of patterns.
Jennifer McLoud-Mann is an American mathematician known for her 2015 discovery, with Casey Mann and undergraduate student David Von Derau, of the 15th and last class of convex pentagons to tile the plane. She is a professor of mathematics at the University of Washington Bothell, where she is currently the Vice Dean of Curriculum & Instruction of the School of STEM. Beyond tiling, her research interests include knot theory and combinatorics.
James A. Morrow is an American mathematician and professor emeritus of mathematics at the University of Washington in Seattle, Washington. His research interests shifted from several complex variables and differential geometry to discrete inverse problems in the middle of his career.
