Casey Mann is an American mathematician, specializing in

discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory *Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit *Discrete group, a ...

and computational geometry, in particular

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ge ...

and

knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

. He is Professor of Mathematics at

University of Washington Bothell The University of Washington Bothell (UW Bothell) is a branch campus of University of Washington in Bothell, Washington. It was founded in 1989 and is located just northwest of the junction of Interstate 405 and State Route 522, and it shares a ...

, and received the PhD at the

University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a public land-grant research university in Fayetteville, Arkansas. It is the flagship campus of the University of Arkansas System and the largest university in the state. Founded as Arkansas ...

in 2001. He is known for his 2015 discovery, with Jennifer McLoud-Mann and undergraduate student David Von Derau, of the 15th and last class of

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

pentagon In geometry, a pentagon (from the Greek language, Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is ...

s to tile the plane. Mann is also known for his work on

Heesch's problem 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 Hei ...

, to which he contributed a polygon with ''Heesch number'' 5. This problem is closely related to the

einstein problem In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an "einst ...

, of whether there exists a shape that can tessellate space, but only in a non-periodic way.

Education and career

Mann received his B.S. in Mathematics at

East Central University East Central University (ECU or East Central) is a public university in Ada, Oklahoma. It is part of Oklahoma's Regional University System. Beyond its flagship campus in Ada, the university has courses available in McAlester, Shawnee, and Duran ...

Ada, Oklahoma Ada is a city in and the county seat of Pontotoc County, Oklahoma, United States. The population was 16,481 at the 2020 United States Census. The city was named for Ada Reed, the daughter of an early settler, and was incorporated in 1901. Ada is ...

, and completed his Ph.D. in 2001 from the

. His dissertation in

discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic ge ...

, supervised by

Chaim Goodman-Strauss Chaim Goodman-Strauss (born June 22, 1967 in Austin TX) 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 Sy ...

, was ''Heesch's Problem and Other Tiling Problems''. Upon completing his doctorate, Mann joined the

University of Texas at Tyler The University of Texas at Tyler (UT Tyler) is a public research university in Tyler, Texas. Founded in 1971, it is a part of the University of Texas System. UT Tyler consists of five professional colleges and one traditional college of arts and ...

faculty for eleven years.. He joined the faculty of University of Washington Bothell in 2013, where he is active in engaging undergraduate students in research.

References

External links

Casey Mann's website
Living people University of Arkansas alumni University of Texas at Tyler faculty University of Washington Bothell faculty Year of birth missing (living people) {{US-mathematician-stub