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

Angles/Trigonometry
<spacer> Angles
Angle Sections
Inscribed Angles
Parallel line theorems
Trigonometry
Trig Identities
Trig Calculus
Parallax

Length / Area / Volume

Conics

Geometric Figures

The Taxicab Metric

Triangles

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<spacer> <spacer> Angles and Trigonometry > General Information

This section defines angles that are native to taxicab geometry and investigates their properties. Trigonometric functions and their identities are also explored.

  • Angles: Traditional taxicab geometry simply relied on Euclidean angles, but pure taxicab geometry has its own native angles and arc length based on the taxicab circle.

  • Angle Sections: Can't trisect a Euclidean angle? Step inside for a refreshing change of pace...

  • Inscribed Angles: A look at the Euclidean inscribed angle theorem in the framework of taxicab geometry.

  • Parallel line theorems: Many of the familiar theorems involving angles and parallel lines with transversals in Euclidean geometry carry over nicely to taxicab geometry.

  • Trigonometry: If we have angles, we must also have...TRIG!

  • Trig Identities: There are probably just as many trig identities in taxicab geometry as in Euclidean geometry.

  • Trig Calculus: Examination of the derivatives of taxicab trig functions.

  • Parallax: Parallax is the apparent shift of an object due to the motion of the observer. A commonly used approximation formula for parallax in Euclidean geometry turns out to be the exact formula in taxicab geometry - a rare simplification from Euclidean to taxicab geometry.
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