# Publications

*(Updated January 25, 2017)*

## Book

*Euler’s Gem: The Polyhedron Formula and the Birth of Topology*, Princeton University Press (2008) (Translations: Portuguese, Japanese, Korean, Chinese)

## Editorship

- I am the editor of
*Math Horizons*, the undergraduate magazine of the Mathematical Association of America (2014–18)

## Topology and Dynamical Systems

- “Entropy for symbolic dynamics with overlapping alphabets,”with Fabio Drucker (Dickinson ’11) and Jim Wiseman,
*Journal of Dynamics and Differential Equations***28**, Issue 2 (2016), pp. 301–315 - “Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces,” with Tarun Das, Keonhee Lee, and Jim Wiseman,
*Topology and its Applications***160**(2013), No. 1, pp. 149-158 - “Symbolic dynamics for nonhyperbolic systems,” with Jim Wiseman,
*Proceedings of the American Mathematical Society*,**138**(2010), 4373–4385 - “Itineraries of rigid rotations and diffeomorphisms of the circle,” with Paul Winkler (Dickinson ’07) and Jim Wiseman,
*Theoretical Computer Science*,**411**(2010), No. 1, pp. 259–265 - “Chain recurrence rates and topological entropy,” with Jim Wiseman,
*Topology and its Applications*,**156**(2008), No. 2, 251–261 - “Positively expansive dynamical systems,” with Jim Wiseman,
*Topology and its Applications***154**(2007), No. 3, 604–613 - “Equivalence of expanding properties,” with Jim Wiseman, in the problem section of
*Topology Proceedings*,**28**No. 1 (2004), 299–300 - “Topological helicity for framed links,” with Elizabeth Bouzarth (Dickinson ’03),
*Journal of Knot Theory and its Ramifications*,**13**(2004), No. 8, 1007–1019 - “Positively expansive homeomorphisms of compact spaces,” with Jim Wiseman,
*International Journal of Mathematics and Mathematical Sciences*,**54**(2004) 2907–2910 - “Bounded homeomorphisms of the open annulus,” with Jim Wiseman,
*New York Journal of Mathematics*,**9**(2003), 55–68 - “A fixed point theorem for bounded dynamical systems,” with Jim Wiseman,
*Illinois Journal of Mathematics*,**46**(Summer 2002), no. 2, 491–495, addendum, 48 (Fall 2004), No. 3, 1079–1080 - “Shift equivalence and the Conley index,” with John Franks,
*Transactions of the American Mathematical Society*,**352**(2000), No. 7, 3305–3322 - “Connection matrix pairs,” Conley Index Theory (Warsaw, 1997), 219–232,
*Banach Center Publications*,**47**, Polish Acad. Sci., Warsaw, 1999

## The History of Mathematics

- “Circular Reasoning: Who First Proved That
*C*Divided by*d*Is a Constant?”*The College Mathematics Journal*,**46**, No. 3 (May 2015), pp. 162–171 (This article will also appear in Princeton University Press’*The Best Writing on Mathematics 2016.)* - “The Japanese theorem for nonconvex polygons,”
*Convergence*, December 2013 - “The polyhedral formula,” In
*Leonhard Euler: Life, Work and Legacy*(R. Bradley and E. Sandifer, editors), volume 5 of the*Studies in the History and Philosophy of Mathematics*series. Elsevier, Amsterdam (2007) 421–439 - “The flaw in Euler’s proof of his polyhedral formula,” with Chris Francese,
*The American Mathematical Monthly*,**114**(April 2007) 286–296

## Undergraduate Mathematics and Miscellaneous Publications

- “I [heart] Math,“ to appear in
*Chalkdust* - “Game, SET, Math,” to appear in
*Math Horizons* - “Building a Professional Network with Twitter,” to appear in
*MAA FOCUS* - “Measuring Tapes for Circles and Spheres,” to appear in
*The College Mathematics Journal* - “A Trisectrix from a Carpenter’s Square,” to appear in
*Mathematics Magazine* - “Sugihara’s Impossible Cylinder,”
*Math Horizons**,***24**(September 2016) No. 1, 18–19 - “A Conversation with Timothy Gowers,”
*Math Horizons**,***23**(September 2015) No. 1, 10–14 - “Proof without words: The maximum sum of inradii,”
*The College Mathematics Journal***46**(January 2015) No. 1, 23 - “Gabriel’s paper horn,” Gathering 4 Gardner 11 gift exchange
- “Letters of recommendation,”
*XRDS (Crossroads: the ACM Magazine for Students)*,**17**(Spring 2011) No. 3, 6 - “A π-less Buffon’s needle problem,”
*Mathematics Magazine*,**79**(December 2006) No. 5, 385–389 - “Centers of the United States,”
*The College Mathematics Journal*,**36**(November 2005) No. 5, 366–373 - “An illuminating example of the Gauss map,”
*The College Mathematics Journal*,**35**(January 2004) No. 1, 14 - “Math goes pop: The American public succumbs to the allure of a formerly ‘uncool’ discipline,” with Cotten Seiler,
*Dickinson Magazine*,**80**, No. 4, Spring 2003 - I was “blurbed” on the dust jacket of
*The Universe in Zero Words: The Story of Mathematics as Told Through Equations*, by Dana Mackenzie, Princeton University Press, 2012 - I was “blurbed” on the dust jacket of
*Mathematicians: An Outer View of an Inner World*, by Mariana Cook, Princeton University Press, 2009 - I was “blurbed” on the dust jacket of
*How Round is Your Circle? Where Engineering and Mathematics Meet*, by John Bryant and Chris Sangwin, Princeton University Press, 2008

## Book Reviews

- Review of
*Journey Through Genius,*by William Dunham,*Math Horizons,*April 2014 - Review of
*The Survival of a Mathematician: From Tenure Track to Emeritus**,*by Steven G. Krantz, American Mathematical Society, 2009, for MAA Reviews, (March 30, 2009) - Review of
*Five-Minute Mathematics*, by Ehrhard Behrends, American Mathematical Society, 2008, for MAA Reviews, (July 6, 2008) - Review of
*Hesiod’s Anvil: Falling and Spinning Through Heaven and Earth*, by Andrew J. Simoson, The Mathematical Association of America, Washington D.C., 2006, for Read This! The MAA Online Book Review Column, (February 18, 2008) - Review of
*Topology and its Applications*, by William F. Basener, Wiley, 2006, for MAA Reviews, (January 12, 2007) - Review of
*Topology Now!*, by Robert Messer and Philip Straffin, The Mathematical Association of America, Washington D.C., 2006, for Read This! The MAA Online Book Review Column, (April 8, 2006)

## Translations

- “Solution of a geometric problem about lunes formed from circles,” 2013 translation (w/ Chris Francese and Travis Ramsey (Dickinson ‘13)) of Leonhard Euler’s paper “Solutio Problematis geometrici circa lunulas a circulis formatas,”
*Commentarii academiae scientiarum Petropolitanae***9**(1744) 207–221 (available online at the Euler Archive) - “On
*n*-gons,*n*-sided figures, and polyhedra,” 2006 translation (w/Anne Maiale) of pages 20–22 of Karl Georg Christian von Staudt’s book*Geometrie der Lage*, Nürnberg, 1847 - “Addition to Euler’s Polyhedral Theorem,” 2006 translation (w/Anne Maiale) of J. F. Hessel’s paper “Nachtrag zu dem Euler’schen Lehrsatz von Polyedern,”
*Journal für die Reine und Angewandte mathematik***8**(1832), 13–20 - “Easier proof of a stereometric theorem of Euler,” 2006 translation (w/Anne Maiale) of Jacob Steiner’s paper, “Leichter Beweis eines stereometrischen Satzes von Euler,”
*Journal für die reine und angewandte Mathematik*1 (1826), 364–367 - “Proof of some notable properties with which solids enclosed by plane faces are endowed,” 2004 translation (w/ Chris Francese) of Leonhard Euler’s paper “Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita,” Novi Commentarii Academiae Scientiarum Petropolitanae,
**4**(1752), 94–108 (available online at the Euler Archive)