Alan Hugh Schoen (born December 11, 1924) is an American physicist and computer scientist best known for his discovery of the

gyroid A gyroid is an infinitely connected Triply periodic minimal surface, triply periodic minimal surface discovered by Alan Schoen in 1970. History and properties The gyroid is the unique non-trivial embedded member of the associate family of the ...

, an infinitely connected triply periodic

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

Professional career

Alan Schoen received his B.S. degree in physics from

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

in 1945 and his Ph.D. in physics from

University of Illinois The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

at Urbana-Champaign in 1958.Alan Schoen. 2017. Personal email communication with J. Kocik His doctoral dissertation was entitled “Self-Diffusion in Alpha Solid Solutions of Silver-Cadmium and Silver-Indium.” After completing graduate work he was employed (between 1957 and 1967) as a research physicist by aerospace companies in California, and also worked as a free-lance solid-state physics consultant. In 1967, he took the position of senior scientist at NASA's Electronics Research Center (ERC) in Cambridge, Massachusetts,Alan H. Schoen. Triply-periodic minimal surfaces. http://schoengeometry.com/e-tpms.html where he did geometry research and served as the Chief of the Office of Geometrical Applications. While at NASA, he also worked on expandable space frames. In 1970, Schoen accepted a position at

California Institute of the Arts The California Institute of the Arts (CalArts) is a private art university in Santa Clarita, California. It was incorporated in 1961 as the first degree-granting institution of higher learning in the US created specifically for students of both ...

, where he taught calculus and computer graphics. In 1973, he accepted a teaching position in the Department of Design at

Southern Illinois University Carbondale Southern Illinois University (SIU or SIUC) is a public research university in Carbondale, Illinois. Founded in 1869, SIU is the oldest and flagship campus of the Southern Illinois University system. The university enrolls students from all 50 s ...

(SIUC), where he taught computer graphics, algebra, and analytic geometry to design students. This was a former home department of

Buckminster Fuller Richard Buckminster Fuller (; July 12, 1895 – July 1, 1983) was an American architect, systems theorist, writer, designer, inventor, philosopher, and futurist. He styled his name as R. Buckminster Fuller in his writings, publishing more t ...

- an American designer and inventor who popularized the

geodesic dome A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure, making geodesic dom ...

. In 1982, Schoen accepted a joint appointment in the Department of Mathematics and Department of Computer Science at SIUC. In August 1985, he moved to the SIUC campus in Nakajo, Japan, where he taught a course in computer science and also helped to teach English at a local Japanese junior high school. Upon his return to Carbondale in 1988, he taught FORTRAN and Digital Design in the Electrical Engineering Department at SIUC until his retirement in 1995. After retiring from academia he continued his work on numerous infinite families of minimal surfaces and on inventing geometric puzzles and images. Gyroid unit cell stereo image

Contributions

Alan Schoen is best known for discovering (while working at NASA) a minimal surface that he named the

. The name stems from the impression in the gyroid's structure that each continuous channel in the array, along different principal crystallographic axes, has connections to additional intersecting channels, which “gyrate” along the channel length. The gyroid has become popular among scientists as more and more new occurrences of it in nature are being discovered. Earlier in his career, while conducting his doctoral research on

atomic diffusion Atomic may refer to: * Of or relating to the atom, the smallest particle of a chemical element that retains its chemical properties * Atomic physics, the study of the atom * Atomic Age, also known as the "Atomic Era" * Atomic scale, distances comp ...

in solids (1957), Schoen discovered that for self-diffusion in crystalline solids, there is a simple relation between the Bardeen-Hering correlation factor and the isotope effect that makes it possible to distinguish between ''vacancy'' and ''interstitial'' diffusion mechanisms. He later found evidence from a FORTRAN program that his equation is exact in all close-packed cubic structures. His finding was soon confirmed algebraically by Tharmalingam and Lidiard. Schoen's preoccupation with this subject eventually led him to an interest in minimal surfaces and the discovery of the gyroid. Alan Schoen has also published scientific papers on families of minimal surfaces, and books on geometric images and puzzles. In the early 1990s, Schoen designed Rombix — a combinatorial dissection puzzle, which uses multicolored tiles that are composites of 8-zonogons, to create various designs. He also developed The Geometry Garret, a website full of different families of geometric structures (considered "cool stuff" by Alan's academic colleagues). Alan Schoen holds U.S. patents (see below) for six of his inventions.

Selected works

Schoen, Alan H. (1970) "Infinite periodic minimal surfaces without self-intersections." NASA Tech. Note No. D-5541. Washington, DC. McSorley, John and Schoen, Alan. (2013) "Rhombic tilings of (n,k)-Ovals, (n,k,λ)-cyclic difference sets, and related topics." ''Discrete Mathematics'' 313, No. 1 (Jan 2013). Ed Pegg, Alan H. Schoen, and Tom M. Rodgers. (2008) Homage to a pied puzzler. hardback — 325 pages, CRC Press/ Taylor and Francis Group. . Ed Pegg, Alan H. Schoen, and Tom Rodgers (2009) Mathematical wizardry for a Gardner hardback — 220 pages, A K Peters Schoen, Alan H. (2012) Reflections concerning triply-periodic minimal surfaces. ''Interface Focus'' 30 May 2012.

Patents

Listing of U.S. patents issued to Alan H. Schoen: *1972 Honeycomb core structures of minimal surface tubule sections *1972 Honeycomb panels formed of minimal surface periodic tubule layers *1973 Expandable space-frames *1994 Set of tiles for covering a surface *1994 Set of tiles for covering a surface *2001 Set of blocks for packing a cube

References

External links