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Academic Research
Interest and academic research in taxicab geometry has been increasing in recent years. Below is a list of known articles, papers, and general research in taxicab geometry and related applications. To report additional books, research, or articles, please email. Algebra The Taxicab Group ^ (Abstract)  Doris J. Schattschneider  The American Mathematical Monthly, Vol. 91, No. 7 (AugSep 1984), pp. 423428 Angles and Trigonometry Taxicab Trigonometry (Abstract / PDF)  Ruth Brisbin and Paul Artola  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 8, No. 2 (Spring 1985), pp. 8995 On the Taxicab Trigonometry (PDF)  Ziya Akça and Rüstem Kaya  Journal of Institute Of Mathematics and Computer Sciences, Vol. 10, No. 3, pp. 151159 Taxicab Angles and Trigonometry (Abstract / PDF / HTML  secondary: PDF / HTML)  Kevin Thompson and Tevian Dray (1997)  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 11, No. 2 (Spring 2000), pp. 8796 Crackpot Angle Bisectors! (PDF / Mirror)  Robert J. MacG. Dawson  Mathematics Magazine, Vol. 80, No. 1 (Feb 2007), pp. 5964 On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane (PDF / Mirror)  Ayşe Bayar, Süheyla Ekmekçi, and Münevver Özcan  International Electronic Journal of Geometry, Vol. 2, No. 1 (2009), pp. 1724  Summary: Law of Sines and Law of Cosines for taxicab geometry Arbitrary Sectioning of Angles in Taxicab Geometry (PDF)  Kevin P. Thompson (2010)  Unpublished Taxicab Calculus: Trig Derivatives (PDF)  Kevin P. Thompson (2012)  Unpublished Area and Volume Area of a Taxicab Triangle in Terms of the Taxicab Distance (PDF / Mirror)  Münevver Özcan and Rüstem Kaya  Missouri Journal of Mathematical Sciences, Vol. 15, No. 3 (Fall 2003)  Summary: Gives an equivalent of Heron's Formula in Taxicab Geometry. Area Formula for Taxicab Triangles (Abstract / PDF)  Rüstem Kaya  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 12, No. 4 (Spring 2006), pp. 219220 Volume of a Tetrahedron in the Taxicab Space (PDF / Mirror)  Harun Bariş Çolakoğlu and Rüstem Kaya  Missouri Journal of Mathematical Sciences, Vol. 21, No. 1 (Winter 2009), pp. 2127 The Nature of Length, Area, and Volume in Taxicab Geometry (PDF Mirror)  Kevin P. Thompson  International Electronic Journal of Geometry, Vol. 4, No. 2 (2011), pp. 193207 Conic Sections Pyramidal Sections in Taxicab Geometry (PDF)  Richard Laatsch  Mathematics Magazine, Vol. 55, No. 4 (Sep 1982), pp. 205212 Lines and Parabolas in Taxicab Geometry (Abstract / PDF)  Joseph M. Moser and Fred Kramer  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 7, No. 7 (Fall 1982), pp. 441448 Taxicab Geometry: Another Look at Conic Sections (Abstract / PDF)  David Iny  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 7, No. 10 (Spring 1984), pp. 645647 Parabolas in Taxicab Geometry (PS / PDF)  Y. Phoebe Ho and Yan Liu  Missouri Journal of Mathematical Sciences, Vol. 8, No. 2 (Spring 1996) General Equation for Taxicab Conics and Their Classification (PDF)  Rüstem Kaya, Ziya Akça, I. Günalti, and Münevver Özcan  Mitt. Math. Ges. Hamburg, 19 (2000), pp. 135148 Differential Geometry Connections and Minimizing Geodesics of Taxicab Geometry (PDF)  Kocayusufoğlu, Ismail and Ertuğrul Özdamar  Mathematical and Computational Applications, Vol. 5, No. 3 (2000), pp. 191200 Higher Dimensions / On Surfaces On the Norm in Higher Dimensional Taxicab Spaces (PDF)  Ziya Akça and Rüstem Kaya  Hadronic Journal Supplement, Vol. 19 (2004), pp. 491502 On the Distance Formulae in Three Dimensional Taxicab Space (PDF)  Ziya Akça and Rüstem Kaya  Hadronic Journal, Vol. 27, No. 5 (2004), pp. 521532 On the Taxicab Distance on a Sphere (PS / PDF)  Ayşe Bayar and Rüstem Kaya  Missouri Journal of Mathematical Sciences, Vol. 17, No. 1 (Winter 2005). Geometric Figures Concerning Circles in Taxicab Geometry ^  Songlin Tiana, ShingSeung Soa, and Guanghui Chen  International Journal of Mathematical Education in Science and Technology, Vol. 28 (1997), pp. 727733 A Synthetic Approach to the Taxicab Circles (ZIP / PDF)  Harun Bariş Çolakoğlu and Rüstem Kaya  Applied Sciences (Balkan Society of Geometers), Vol. 9 (2007), pp. 6777 Regular Polygons in the Taxicab Plane (PDF)  Harun Bariş Çolakoğlu and Rüstem Kaya  Scientific and Professional Journal of the Croatian Society for Geometry and Graphics, Vol. 12 (2008), pp. 2733 Regular Polygons in Some Models of Protractor Geometry (PDF / Mirror)  Harun Bariş Çolakoğlu and Rüstem Kaya  International Electronic Journal of Geometry, Vol. 2, No. 2 (2009), pp. 7687 On Euler's Quadrilateral Theorem in the Taxicab Plane ^ (Abstract)  Nilgün Sönmez  Ukranian Mathematical Congress, 2009. (abstract only) Taxicab Butterflies (PDF)  Kevin P. Thompson  Unpublished History Karl Menger and Taxicab Geometry (PDF)  Louise Golland  Mathematics Magazine, Vol. 63, No. 5 (Dec 1990), pp. 326327 Taxi Cab Geometry: History and Applications! (PDF / Mirror)  Chip Reinhardt  The Montana Mathematics Enthusiast, Vol. 2, No. 1 (Apr 2005), pp. 3864 Erratum: An Improvement on the article Taxi Cab Geometry: History and Applications! (PDF / Mirror)  Benjamin Urland  The Montana Mathematics Enthusiast, Vol. 4, No. 1, pp. 115127 Integral Geometry Integral geometry for the taxicab metric (at arXiv)  Tom Leinster  Unpublished The Taxicab Metric The Norm in Taxicab Geometry (PDF / Mirror)  Cumali Ekici, Ismail Kocayusufoğlu, and Ziya Akça  Turkish Journal of Mathematics, Vol. 22, No. 3 (1998), pp. 295308 On the Ratio of Directed Lengths in the Taxicab Plane and Related Properties (PDF / Mirror)  Münevver Özcan and Rüstem Kaya  Missouri Journal of Mathematical Sciences, Vol. 14, No. 2 (Spring 2002) Summary: Validates Ceva's Theorem in Taxicab Geometry A Note on the Variation of Taxicab Lengths Under Rotations (Abstract / PDF)  Münevver Özcan, Süheyla Ekmekçi, and Ayşe Bayar  Pi Mu Epsilon Journal, Worcester, MA. Vol. 11, No. 7 (Fall 2002), pp. 381384 Taxicab Versions of the Pythagorean Theorem (Abstract / PDF)  Harun Bariş Çolakoğlu and Rüstem Kaya  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 12, No. 9 (Fall 2008), pp. 535539 The Taxicab Space Group (PDF)  Ö. Gelişgen and Rüstem Kaya  Acta Mathematica Hungarica, Vol. 122, No. 12 (2009), pp. 187200 The Behavior of Midsets When Repeatedly Taking the Midset of Two Lines in l_{1} Geometry (PDF / Mirror)  Joshua M. Fitzhugh and David L. Farnsworth  International Journal of Mathematics and Mathematical Sciences, Volume 2014 (2014), Article ID 832647 Triangles Taxicab Versions of Some Euclidean Theorems (PDF)  Harun Bariş Çolakoğlu and Rüstem Kaya  International Electronic Journal of Pure and Applied Mathematics, Vol. 26, No. 1 (2006), pp. 6981 A Taxicab Version of the ErdösMordell Theorem (PDF / Mirror)  Nilgün Sönmez  Kragujevac Journal of Mathematics, Issue 32 (2009), pp. 157164 Taxicab Triangle Incircles and Circumcircles (PDF)  Kevin P. Thompson (2010)  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 13, No. 5 (Fall 2011) Generalizations of the Taxicab Metric A generalization of some wellknown distances and related isometries (PDF / Mirror)  Harun Bariş Çolakoğlu and Rüstem Kaya  Mathematical Communications, Volume 12 (2011), pp. 2135. General Interest / Applications / Related Topics Taxi! (HTML)  Joe Malkevitch  American Mathematical Society Feature Column (undated) Taxicab Geometry (Abstract / PDF)  Barbara E. Reynolds  The Pi Mu Epsilon Journal, Worcester, MA. Vol. 7, No. 2 (Spring 1980), pp. 7788 Taxicab Geometry  A New Slant (PDF)  Katye O. Sowell  Mathematics Magazine, Vol. 62, No. 4 (Oct 1989), pp. 238248 The πs Go Full Circle (PDF)  Russell Euler and Jawad Sadek  Mathematics Magazine, Vol. 72, No. 1 (Feb 1999), pp. 5963 The innerproduct of IsoTaxicab Geometry (ZIP / PDF)  Ismail Kocayusufoğlu  Applied Sciences (Electronic Journal), Balkan Society of Geometers, Vol. 7 (2005), pp. 107111 On the IsoTaxicab Trigonometry (ZIP / PDF)  Ismail Kocayusufoğlu and Tuba Ada  Applied Sciences (Electronic Journal), Balkan Society of Geometers, Vol. 8 (2006), pp. 101111 Taxicab Geometry: some problems and solutions for square gridbased fire spread simulation (PDF / Mirror)  David Caballero  V International Conference on Forest Fire Research, D. X. Viegas (ed.), 2006 Taxicab Geometry: Not the Shortest Ride Around Town * (PDF / Mirror)  Christina Janssen  Dissertation (unpublished), Iowa State University, Jul 2007 A Study on Problem PosingSolving in the Taxicab Geometry and Applying Simcity Computer Game (PDF / Mirror)  Tuba Ada and Aytaç Kurtuluş  The Mathematics Education into the 21st Century Project, Proceedings of the 10th International Conference (2009) * Contains questionable methods, approaches, or conclusions. ^ Sadly, these articles are not freely available online. 

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