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Taxicab Geometry Angles / Trigonometry Length / Area / Volume Conics Geometric Figures The Taxicab Metric Triangles ![]() Research Other Resources Links News / Updates ![]() Kevin's Corner |
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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 . Algebra The Taxicab Group ^ (Abstract) - Doris J. Schattschneider - The American Mathematical Monthly, Vol. 91, No. 7 (Aug-Sep 1984), pp. 423-428 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. 89-95 On the Taxicab Trigonometry (PDF) - Ziya Akça and Rüstem Kaya - Journal of Institute Of Mathematics and Computer Sciences, Vol. 10, No. 3, pp. 151-159 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. 87-96 Crackpot Angle Bisectors! (PDF / Mirror) - Robert J. MacG. Dawson - Mathematics Magazine, Vol. 80, No. 1 (Feb 2007), pp. 59-64 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. 17-24 - 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of Cosines for taxicab geometry Arbitrary Sectioning of Angles in Taxicab Geometry (PDF) - Kevin P. Thompson (2010) - Unpublished Taxicab Calculus: Trig Derivatives (PDF) - Kevin P. Thompson (2012) - Unpublished Area and Volume Area of a Taxicab Triangle in Terms of the Taxicab Distance (PDF / Mirror) - Münevver Özcan and Rüstem Kaya - Missouri Journal of Mathematical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. 219-220 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. 21-27 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. 193-207 Conic Sections Pyramidal Sections in Taxicab Geometry (PDF) - Richard Laatsch - Mathematics Magazine, Vol. 55, No. 4 (Sep 1982), pp. 205-212 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. 441-448 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. 645-647 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. 135-148 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. 191-200 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. 491-502 On the Distance Formulae in Three Dimensional Taxicab Space (PDF) - Ziya Akça and Rüstem Kaya - Hadronic Journal, Vol. 27, No. 5 (2004), pp. 521-532 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, Shing-Seung Soa, and Guanghui Chen - International Journal of Mathematical Education in Science and Technology, Vol. 28 (1997), pp. 727-733 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. 67-77 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. 27-33 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. 76-87 On Euler's Quadrilateral Theorem in the Taxicab Plane ^ (Abstract) - Nilgün Sönmez - Ukranian Mathematical Congress, 2009. (abstract only) History Karl Menger and Taxicab Geometry (PDF) - Louise Golland - Mathematics Magazine, Vol. 63, No. 5 (Dec 1990), pp. 326-327 Taxi Cab Geometry: History and Applications! (PDF / Mirror) - Chip Reinhardt - The Montana Mathematics Enthusiast, Vol. 2, No. 1 (Apr 2005), pp. 38-64 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. 115-127 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. 295-308 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. 381-384 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. 535-539 The Taxicab Space Group (PDF) - Ö. Gelişgen and Rüstem Kaya - Acta Mathematica Hungarica, Vol. 122, No. 1-2 (2009), pp. 187-200 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. 69-81 A Taxicab Version of the Erdös-Mordell Theorem (PDF / Mirror) - Nilgün Sönmez - Kragujevac Journal of Mathematics, Issue 32 (2009), pp. 157-164 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 well-known distances and related isometries (PDF / Mirror) - Harun Bariş Çolakoğlu and Rüstem Kaya - Mathematical Communications, Volume 12 (2011), pp. 21-35. 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. 77-88 Taxicab Geometry - A New Slant (PDF) - Katye O. Sowell - Mathematics Magazine, Vol. 62, No. 4 (Oct 1989), pp. 238-248 The πs Go Full Circle (PDF) - Russell Euler and Jawad Sadek - Mathematics Magazine, Vol. 72, No. 1 (Feb 1999), pp. 59-63 The inner-product of Iso-Taxicab Geometry (ZIP / PDF) - Ismail Kocayusufoğlu - Applied Sciences (Electronic Journal), Balkan Society of Geometers, Vol. 7 (2005), pp. 107-111 On the Iso-Taxicab Trigonometry (ZIP / PDF) - Ismail Kocayusufoğlu and Tuba Ada - Applied Sciences (Electronic Journal), Balkan Society of Geometers, Vol. 8 (2006), pp. 101-111 Taxicab Geometry: some problems and solutions for square grid-based 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 Posing-Solving 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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