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Taxicab Geometry
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Kevin's Corner
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- Unpublished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- Unpublished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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