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    Burkard's Publications – 2015

    Columns

  • Maths Masters (with M. Ross), A (semi-)regular weekly column that ran from July 2007 until November 2014 in the education section of the AGE newspaper in Melbourne, Australia. 255 articles.

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  • Mathsnacks (with M. Ross). A regular column that ran from 2004 to 2009 in Vinculum, the quarterly magazine for secondary teachers published by the Mathematical Association of Victoria. 26 articles.

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    Books

  • A Geometrical Picture Book

  • Universitext Series, Springer-Verlag, New York, 1998.
     
  • Geometries on Surfaces (with GF Steinke)

  • Encyclopedia of Mathematics and its Application 84, Cambridge University Press, 2001.
     
  • The Mathematics of Juggling

  • Springer-Verlag, New York, 2003.
     
  • Q.E.D.: Beauty in Mathematical Proof

  • Walker, New York, 2004.
     
  • Les ambigrammes: l'art de symetriser les mots

  • Editions Ecritextes, France, 2004.
     
  • The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your Shoes

  • The American Mathematical Society, Providence, 2006.
     
  • Eye Twisters: Ambigrams & Other Visual Puzzles to Amaze and Entertain

  • Constable & Robinson, London, 2007.
     
  • Math goes to the movies (with M. Ross)

  • Johns Hopkins University Press, Baltimore, 2012.
     

    Articles

  • The groups of projectivities of B-ovals

  • Geom. Dedicata 41, (1992), 337-359.
     
  • Topological ovals in 4-dimensional translation planes (with D. Betten)

  • Arch. Math. 63, (1994), 284-288.
     
  • Criteria for two-dimensional circle planes (with G. F. Steinke)

  • Beitr. Alg. Geom. 35 (1994), 181-191.
     
  • Elementary constructions of locally compact affine planes

  • Geom. Dedicata 56 (1995), 155-175.
     
  • Characterizations of analytic planar functions

  • J. Combin. Theory Ser A 71 (1995), 335-339.
     
  • Integrating and differentiating two-dimensional incidence structures

  • Arch. Math. 64 (1995), 75-85.
     
  • A sufficient condition for planar partition functions

  • Arch. Math. 65 (1995), 176-184.
     
  • Integrating completely unisolvent functions

  • J. Approx. Theory 82 (1995), 434-439.
     
  • Semi-biplanes on the cylinder

  • Geom. Ded. 58 (1995), 145-160.
     
  • Cut and paste in 2-dimensional projective planes and circle planes (with G. F. Steinke)

  • Canad. Math. Bull. 38 (1995), 469-480.
     
  • Maximal arcs in the complex projective plane

  • J. Geom. 54 (1995), 115-122.
     
  • Recycling circle planes

  • Bull. Austral. Math. Soc. 53 (1996), 325-340.
     
  • The piecewise projective group as group of projectivities

  • Results Math. 30 (1996), 122-135.
     
  • Continuous planar functions

  • Abh. Math. Sem. Univ. Hamburg 66 (1996), 113-129.
     
  • Abstract hyperovals and Hadamard designs

  • Australas. J. Comb. 16 (1997), 29-34.
     
  • Flat circle planes as integrals of flat affine planes

  • Geom. Dedicata 67 (1997), 149-163.
     
  • The inner and outer space of 2-dimensional Laguerre planes (with G. F. Steinke)

  • J. Austral. Math. Soc., Series A 62 (1997), 104-127.
     
  • Halbe Doppeldecker-Anschauliche Modelle von Semibiplanes (with A Schroth)

  • Überblicke Mathematik 1998, A Beutelspacher et al. eds., pp. 128-137, Vieweg, Braunschweig, 1997.
     
  • On the existence of topological ovals in flat projective planes (with N. Rosehr and G F Steinke)

  • Arch. Math. 68 (1997), 418-429.
     
  • Half-ovoidal flat Laguerre planes (with N. Rosehr and G. F. Steinke)

  • J. Geom. 60 (1997), 113-126.
     
  • Split Semi-Biplanes in Antiregular Generalized Quadrangles (with A. Schroth)

  • Bull. Belg. Math. Soc. 4 (1997), 625-637.
     
  • N-unisolvent sets and flat incidence structures

  • Trans. Amer. Math. Soc. 350 (1998), 1619-1641.
     
  • Invertible sharply n-transitive sets

  • J. Combin. Theory Ser. A 81 (1998), 231-254.
     
  • Toroidal circle planes that are not Minkowski planes

  • J. Geom. 63 (1998), 154-167.
     
  • Integrating n-unisolvent sets of functions

  • Arch. Math. 70 (1998), 313-318.
     
  • Plane models of semi-biplanes (with A. Schroth)

  • Beitr. Alg. Geom. 39 (1998), 135-153.
     
  • Semi-biplanes and antiregular generalized quadrangles (with A. Schroth)

  • Geom. Dedicata 69 (1998), 207-221.
     
  • Pretty pictures of geometries

  • Bull. Belg. Math. Soc. 5 (1998), 415-425.
     
  • Separating sets in interpolation and geometry

  • Aequationes Math. 56 (1998), 201-215.
     
  • Four-dimensional compact projective planes of orbit type (1,1) (with D. Betten)

  • Results Math. 36 (1999), 208-236.
     
  • Yea why try her raw wet hat: a tour of the smallest projective space

  • Math. Intelligencer 2 (1999), 38-43.
     
  • A family of 2-dimensional Laguerre planes of generalised shear type (with G.F. Steinke)

  • Bull. Austral. Math. Soc. 61 (2000), 69-83.
     
  • Squaring the triangle.

  • Geom. Dedicata 83 (2000), 229-243.
     
  • Mathemagical Ambigrams

  • Proceedings of the Mathematics and Art Conference 2000, Bond University, 10-12 December 2000, pp. 21-32.
     
  • A collection of ambigrams of mathematicians' names

  • Math. Intelligencer, 22 (2000), 37.
     
  • Topological homology semi-biplanes (with A. Schroth)

  • Monatsh. Math. 132 (2001), 67-84.
     
  • Ambigrams-one of Escher's blind spots

  • Proceedings of the 3rd International Conference on Mathematics and Design 2001, Deakin University Geelong, 3-5 July 2001, pp. 323-331.
     
  • Some constructions of small generalized polygons (with H. Van Maldeghem)

  • J. Combin. Theory Ser. A. 96 (2001), 162-179.
     
  • Generalized Flatland (with H. Van Maldeghem and A. Schroth)

  • Math. Intelligencer 23 (2001), 33-47.
     
  • Centering small generalized polygons-projective pottery at work

  • Discrete Math., 254 (2002), 373-386.
     
  • What is the best way to lace your shoes?

  • Nature, 420 (2002), 470.
     
  • Variations on a theme in paper folding

  • Amer. Math. Monthly, 111 (2004), 39-47.
     
  • On the Kleinewillinghöfer types of flat Laguerre planes (with G. F. Steinke)

  • Results Math., 46 (2004), 103-122.
     
  • Linear geometries on the Möbius strip: a theorem of Skornyakov type (with R. Löwen)

  • Bull. Austral. Math. Soc., 72 (2005), 17-30.
     
  • Turning the tables: feasting from a mathsnack (with M. Ross)

  • Vinculum, 42 (2005), 6-9
     
  • Mathematical table turning revisited (with B. Baritompa, R. Löwen and M. Ross)

  • Math. Intelligencer, 29 (2007), 49-58.
     
  • Virtual points and separating sets in spherical circle planes (with G.F. Steinke)

  • Beitr. Alg. Geom. 48 (2007), 443-467.
     
  • Review of John Stillwell's book "Yearning for the impossible"

  • Australian Mathematical Gazette, (2007), 224-225.
     
  • Juggling, Maths and a Beautiful Mind

  • Plus+ magazine, September 2009.
     
  • Ringing the changes (with M. Ross)

  • Plus+ magazine, December 2009.
     
  • Mathematical Rugby (with M. Ross)

  • Math. Gazette, 94 (2010), 450-463.
     
  • On what day of the week were you born? (with M. Ross)

  • Plus+ magazine, March 2010.
     
  • How to make a perfect plane (with M. Ross)

  • Plus+ magazine, August 2010.
     
  • New maths curriculum a feeble tool calculated to bore (with M. Ross)

  • Opinion piece. The Age, 4.3.2010.
     
  • Minimizing the footprint of your laptop (on your bedside table)

  • Math. Intelligencer, 33 (2011), 33-35.
     
  • The Mathematics of Juggling, in La Matematica, volume 3 "L'intreccio con le scienze", Einaudi, Torino, Italy, 2011. (The linked in article is the English version of this article that appeared in Italian).
     
  • A case of infinite hangover (with M. Ross and David Treeby)

  • Amer. Math. Monthly, 119 (2012), 122-139.
     
  • Book Review of Essential Mathematical Methods 3&4 CAS Enhanced TI-N/CP Versions (2012) Cambridge University Press (with M. Ross and D. Treeby)

  • Vinculum, 49 (2012), 8.
     
  • The movies have your number (with M. Ross)

  • Vinculum, 50 (2013), 4-8.
     
  • Write Your Own Recipe for Rubik's Cube

  • Math Horizons, April 2013, 23-25.
     
  • TracTricks

  • Math Horizons, April 2014, 18-19.
     
  • Tony Abbott is a liar: It's a mathematical truth (with M. Ross)

  • Opinion piece. The Age, 29.5.2014.
     
  • Kenichi Miura's water wheel, or the dance of the shapes of constant width

  • Math. Intelligencer, 36 (2014), 30-36.
     
      This article will also appear in the collection "The Best Writing on Mathematics 2015" edited by Mircea Pitici, Princeton University Press.
     
  • Viviani à la Kawasaki: Take Two

  • Math. Magazine, 87 (2014), 280-283.
     
  • Fibonacci or fairy tale? (with M. Ross)

  • Math Horizons, February 2015, 16-17.
     
  • The intersection game

  • Math Horizons, April 2015, 8-11.
     
  • Stacking wine bottles revisited

  • Math. Intelligencer, the Springer online first version appeared 12 March 2015.
     

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