Alan Schoen
Alan Schoen | |
---|---|
Born | Alan Hugh Schoen December 11, 1924 Mount Vernon, New York, U.S. |
Died | July 26, 2023 Carbondale, Illinois. U.S. | (aged 98)
Nationality | American |
Alma mater | Yale University, University of Illinois Urbana-Champaign |
Known for | Gyroid, Rombix |
Scientific career | |
Fields | Physicist |
Institutions | NASA, Southern Illinois University Carbondale |
Thesis | Self-diffusion in alpha solid solutions of silver-cadmium and silver-indium (1958) |
Doctoral advisor | David Lazarus |
Alan Hugh Schoen (December 11, 1924 – July 26, 2023) was an American physicist and computer scientist best known for his discovery of the gyroid, an infinitely connected triply periodic minimal surface.
Professional career
Alan Schoen received his B.S. degree in physics from
After retiring from academia he continued his work on numerous infinite families of minimal surfaces and on inventing geometric puzzles and images.[5] He was active in the early days of the recreational math conference called Gathering 4 Gardner.
Contributions
Alan Schoen is best known for discovering (while working at NASA) a minimal surface that he named the gyroid.[6][7][8] 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.[9] The gyroid has become popular among scientists as more and more new occurrences of it in nature are being discovered.[10][11][12] Earlier in his career, while conducting his doctoral research on atomic diffusion 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.[13] His finding was soon confirmed algebraically by Tharmalingam and Lidiard.[14] Schoen's preoccupation with this subject eventually led him to an interest in minimal surfaces and the discovery of the gyroid.[15]
Schoen also published scientific papers on families of minimal surfaces, and books on geometric images and puzzles.[16] In the early 1990s, Schoen designed Rombix[17] — a combinatorial dissection puzzle, which uses multicolored tiles that are composites of 8-zonogons, to create various designs.[18] He also developed The Geometry Garret, a website full of different families of geometric structures (considered "cool stuff" by Alan's academic colleagues).[15][19] Alan Schoen held U.S. patents (see below) for six of his inventions.
Death
Alan Schoen died in Carbondale, Illinois, on July 26, 2023, at the age of 98.[20]
Selected works
Schoen, Alan H. (1970) "Infinite periodic minimal surfaces without self-intersections." NASA Tech. Note No. D-5541. Washington, DC.[6]
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).[21]
Ed Pegg, Alan H. Schoen, and
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.[22]
Patents
Listing of U.S. patents issued to Alan H. Schoen:
- 1972 U.S. patent 3,663,346 Honeycomb core structures of minimal surface tubule sections
- 1972 U.S. patent 3,663,347 Honeycomb panels formed of minimal surface periodic tubule layers
- 1973 U.S. patent 3,757,476 Expandable space-frames
- 1994 U.S. patent 4,223,890 Set of tiles for covering a surface
- 1994 U.S. patent 5,314,183 Set of tiles for covering a surface
- 2001 U.S. patent 20,010,035,606 Set of blocks for packing a cube
See also
References
- ^ a b "Alan Schoen geometry". schoengeometry.com. Retrieved 2023-08-11.
- ^ hdl:2142/76317.
- ^ NASA Tech Brief. January 1975. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740000252.pdf
- ^ "People - SIU - Department of Design". siudesign.org. Retrieved 2023-08-11.
- ^ SIU Dept. of Mathematics. Alan Schoen - Gyroid. http://math.siu.edu/faculty-staff/about-us/gyroid.php Archived 2017-10-29 at the Wayback Machine
- ^ a b Schoen, Alan H. (1970). "Infinite periodic minimal surfaces without self-intersections." https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19700020472_1970020472.pdf Archived May 27, 2010, at the Wayback Machine
- ^ Schoen, A.H.: Infinite Regular Warped Polyhedra and Infinite Periodic Minimal Surfaces. Not. Amer. Math. Soc., vol. 15, 1968, p. 727.
- ^ Schoen, A.H.: A Fifth Intersection-Free Infinite Periodic Minimal Surface of Cubic Symmetry. Not. Amer. Math. Soc., vol. 16, 1969, p. 519.
- ^ James A. Dolan, Bodo D. Wilts, Silvia Vignolini, Jeremy J. Baumberg, Ullrich Steiner, and Timothy D. Wilkinson. Optical Properties of Gyroid Structured Materials: From Photonic Crystals to Metamaterials. Adv. Optical Mater. 2014, DOI: 10.1002/adom.201400333 https://www.np.phy.cam.ac.uk/uploads/2014-uploads/AdvOptMat14_gyroidreview.pdf
- ^ "Home | Cornell Chronicle". news.cornell.edu. Retrieved 2023-08-11.
- ^ "week225". math.ucr.edu. Retrieved 2023-08-11.
- ISSN 1059-1028. Retrieved 2023-08-11.
- ^ "Physical Review Letters - Volume 1 Issue 4". journals.aps.org. Retrieved 2023-08-11.
- ^ K. Tharmalingam and A.B. Lidiard. Isotope effect in vacancy diffusion. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics Series 8, Volume 4, 1959 - Issue 44. http://www.tandfonline.com/doi/abs/10.1080/14786435908238264?needAccess=true&journalCode=tphm19&
- ^ a b "Alan Schoen geometry". schoengeometry.com. Retrieved 2023-08-11.
- ^ "Kadon Enterprises, Inc., Alan Schoen profile". www.gamepuzzles.com. Retrieved 2023-08-11.
- ^ Rombix. Illustrated Booklet. http://schoengeometry.com/b-fintil-media/little_red_book.pdf
- ^ "isbn:9810247028 - Google Search". www.google.com. Retrieved 2023-08-11.
- ^ Alan Schoen. Infiite Tilings. http://schoengeometry.com/c-infintil.html
- ^ "Dr. Alan Hugh Schoen". Legacy. Retrieved 29 July 2023.
- .
- PMID 24098851.
External links
- The Geometry Garret
- Works by or about Alan Schoen in libraries (WorldCat catalog)[1]
- Gyroid at MathWorld