# Roger Alperin

*Professor Emeritus*roger.alperin@sjsu.edu

## Research Areas

- Algebra
- Number Theory
- Geometry

## In Memoriam

Roger Charles Alperin, a career mathematician, passed away peacefully on November 21, 2019 at his home in Carlsbad, California. He was 72.

Roger received a PhD in mathematics from Rice University in 1973. He went on to assistant professorships at Brown University (1973-1976), Haverford University (1976-1977), Washington University (1977-1978), and the University of Oklahoma (1978-1987), where he eventually became a full professor. He later took a full professorship at San Jose State University from 1987 to 2014, where he served as chairman from 2002 to 2004 and ultimately became Emeritus in 2015.

Roger leaves a substantial mathematical legacy. He published and presented extensively in the fields of group theory, algebra and number theory, and geometry and mathematical origami. He had a special passion for origami and devoted twenty years to developing foundational elements of the mathematical theory of origami constructions, folds, and numbers. Roger continued publishing and presenting in retirement and continued to work on math projects until his passing. In September of 2018, he presented three papers at the 7th International Meeting on Origami in Science, Mathematics and Education.

Roger will be remembered for his wonderful sense of humor, warm smile and commitment to family. His other interests included travelling, hiking, and beachcombing, especially for sea glass and seashells.

Roger was born on January 8, 1947 in Cambridge, Massachusetts. His late parents were Gladys (nee Swartz) and Melvin Alperin. His survivors include his beloved wife Gaye Lending Alperin; his sons from his first marriage, Howard (wife: Patricia) Alperin and Joshua (wife: Pilar) Alperin; and his granddaughter Alicea Alperin. He will be remembered as a loving stepfather to Marissa Holloway and Kara Solomon and an adoring grandfather to their children, Zoe Hormell, and Sophia and Mollie Solomon.

## Publications

### Group Theory

- Platonic Triangles of Groups, Experimental Mathematics, January 1999
- The Boundary of the Gieseking Tree in Hyperbolic Three-Space [pdf], Topology and Its Applications, May 1999
- Solvable Groups of Exponential Growth [pdf], Groups-Korea '98, De Gruyter, January 2000
- Uniform Exponential Growth of Polycyclic Groups [pdf], Geometria Dedicata 2002
- Schottky Lemma for Nonpositively Curved Singular Spaces [pdf], Geometria Dedicata 2002
- Uniform Exponential Growth, Actions on Trees and GL_2 [pdf], 2002, AMS Contemporary Math. 298
- Nonvanishing of entropy for lattices in Lie groups of rank one [pdf], Int. J. Alg. and Comp., Nov. 2005
- Splitting Theorem for Linear Polycyclic Groups , New York J. of Math., May 2009
- Undistorted Solvable Linear Groups [pdf], Trans. AMS, 363, 3185-3210, 2011

### Algebra and Number Theory

- Plimpton 322 [pdf] , March 2004
- Rationals and the Modular Group [pdf], MAA Monthly, 1999
- The Quartic Surface of Perfect Hexahedra [pdf], Rocky Mountain J., March 2001
- A Characterization of Finite Rings [pdf], March 2004
- The Modular Tree of Pythagoras [pdf], MAA Monthly, November 2005
- Remarks on a Problem of Eisenstein [pdf], JP Journal of Algebra and Number Theory, January 2007
- Golomb Rulers [pdf], Math. Mag. 84(1) Feb. 2011, 48-55
- Integral Cayley Graphs , E. J. Combinatorics, Feb. 2012, #44
- Integer Sequences generated by x[n+1]x[n-1]=x[n]x[n]+A [pdf], Fibonacci Quarterly, 49, 362-5, 2012
- Integral Sets and the Center of a Finite Group [pdf], Canadian Math. Bulletin, 2013
- Rational Subsets of Finite Groups [pdf], Int'l J. Group Theory, 2014

### Geometry and Mathematical Origami

- The Mathematics of Origami, New York Journal of Mathematics, July 2000
- Mathematical Origami and Alhazen's Problem & Origami Heptagon [pdf], 3rd International Meeting of Origami(3OSME), A. K. Peters, 2002
- Grand Tour of Pedals of Conics, Forum Geometricorum 2004
- Totally Real Pentagon [pdf], January 2004
- Trisections and Totally Real Origami [pdf], MAA Monthly 2005
- One-, Two- and Multifold Origami Axioms [pdf], (with Robert J. Lang) Proceedings of 4th OSME Conference-September 2006, AKPeters
- Totally Real Heptagon [pdf], Jan. 2007
- Cube Edge Colorings [pdf], July 2007
- Poncelet Pencil of Rectangular Hyperbolas, Forum Geometricorum 2010
- Origami Constructions in the Hyperbolic Plane [pdf], 5OSME, July 2010
- Solving Euler's Triangle Problems with Poncelet's Pencil, Forum Geometricorum 2011
- Constructions with Circle and Origami [pdf], March 2011
- Gauss-Newton Lines and Eleven Point Conics [pdf], Journal of Geometry and Graphics, 2012
- Folding the Hyperbolic Crane [pdf], Math. Intelligencer, Summer 2012, with Barry Hayes and Robert Lang