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Information and research about the geometry invented by Herman Minkowski
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Taxicab Geometry

Angles / Trigonometry

Length / Area / Volume

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The Taxicab Metric

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<spacer> <spacer> 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 (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- Unpublished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- Unpublished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)

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. 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

The Behavior of Midsets When Repeatedly Taking the Midset of Two Lines in l1 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. 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)

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* Contains questionable methods, approaches, or conclusions.
^ Sadly, these articles are not freely available online.
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