**Lincos** is a constructed language first described in 1960 by Dr. Hans Freudenthal in his book *Lincos: Design of a Language for Cosmic Intercourse, Part 1*. It is a language designed to be understandable by any possible intelligent extraterrestrial life form, for use in interstellar radio transmissions. Freudenthal considered that such a language should be easily understood by beings not acquainted with any Earthling syntax or language. Lincos was designed to be capable of encapsulating "the whole bulk of our knowledge."

**Hans Freudenthal** was a Jewish-German-born Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.

In geometry, a **honeycomb** is a *space filling* or *close packing* of polyhedral or higher-dimensional *cells*, so that there are no gaps. It is an example of the more general mathematical *tiling* or *tessellation* in any number of dimensions. Its dimension can be clarified as *n*-honeycomb for a honeycomb of *n*-dimensional space.

**Astrolinguistics** is a field of linguistics connected with the search for extraterrestrial intelligence (SETI).

In mathematics, the **Freudenthal magic square** is a construction relating several Lie algebras. It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras *A*, *B*. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in *A* and *B*, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction.

**Rostislav Ivanovich Grigorchuk** is a Soviet and Russian mathematician working in the area of group theory. He holds the rank of Distinguished Professor in the Mathematics Department of Texas A&M University. Grigorchuk is particularly well known for having constructed, in a 1984 paper, **the first example of a finitely generated group of intermediate growth**, thus answering an important problem posed by John Milnor in 1968. This group is now known as the Grigorchuk group and it is one of the important objects studied in geometric group theory, particularly in the study of branch groups, automata groups and iterated monodromy groups.

**John Robert Stallings Jr.** was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.

**James W. Cannon** is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He was an Orson Pratt Professor of Mathematics at Brigham Young University.

In the mathematical field of graph theory, the **Goldner–Harary graph** is a simple undirected graph with 11 vertices and 27 edges. It is named after A. Goldner and Frank Harary, who proved in 1975 that it was the smallest non-Hamiltonian maximal planar graph. The same graph had already been given as an example of a non-Hamiltonian simplicial polyhedron by Branko Grünbaum in 1967.

**Thomas Zaslavsky** is an American mathematician specializing in combinatorics.

**Luis Radford** is professor at the School of Education Sciences at Laurentian University in Sudbury, Ontario, Canada. His research interests cover both theoretical and practical aspects of mathematics thinking, teaching, and learning. His current research draws on Lev Vygotsky's historical-cultural school of thought, as well as Evald Ilyenkov's epistemology, in a conceptual framework influenced by Emmanuel Levinas and Mikhail Bakhtin, leading to a non-utilitarian and a non-instrumentalist conception of the classroom and education.

In mathematics, the **Freudenthal spectral theorem** is a result in Riesz space theory proved by Hans Freudenthal in 1936. It roughly states that any element dominated by a positive element in a Riesz space with the principal projection property can in a sense be approximated uniformly by simple functions.

In computational geometry, a **power diagram**, also called a **Laguerre–Voronoi diagram**, **Dirichlet cell complex**, **radical Voronoi tesselation** or a **sectional Dirichlet tesselation**, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for a given circle *C* consists of all the points for which the power distance to *C* is smaller than the power distance to the other circles. The power diagram is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii.

**Dănuţ Marcu** is a Romanian mathematician and computer scientist, who received his Ph.D. from the University of Bucharest in 1981. He claimed to have authored more than 400 scientific papers.

In algebra, **Freudenthal algebras** are certain Jordan algebras constructed from composition algebras.

In geometry and crystallography, a **stereohedron** is a convex polyhedron that fills space isohedrally, meaning that the symmetries of the tiling take any copy of the stereohedron to any other copy.

**Pham Huu Tiep** is a Vietnamese American mathematician specializing in group theory and Lie theory. He is currently a Joshua Barlaz Distinguished Professor of Mathematics at Rutgers University.

**Ascher Otto Wagner** was an Austrian and British mathematician, specializing in the theory of finite groups and finite projective planes. He is known for the Dembowski–Wagner theorem.

In geometry, a **Reinhardt polygon** is an equilateral polygon inscribed in a Reuleaux polygon. As in the regular polygons, each vertex of a Reinhardt polygon participates in at least one defining pair of the diameter of the polygon. Reinhardt polygons with sides exist, often with multiple forms, whenever is not a power of two. Among all polygons with sides, the Reinhardt polygons have the largest possible perimeter for their diameter, the largest possible width for their diameter, and the largest possible width for their perimeter. They are named after Karl Reinhardt, who studied them in 1922.

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