Taxicab Angles and Trigonometry
نویسندگان
چکیده
A natural analogue to angles and trigonometry is developed in taxicab geometry. This structure is then analyzed to see which, if any, similar triangle relations hold. A nice application involving the use of parallax to determine the exact (taxicab) distance to an object is also discussed.
منابع مشابه
The Combinatorial Structure of Trigonometry
The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles. When applied to the sum of an infinite number of infinitesimal angles, these identities lead to the power series expansions of the trigonometric ...
متن کاملZiggy: very interactive trigonometry
In this paper we describe a highly interactive touch-based application to teach the basics of trigonometry to secondary school students. The application, called Ziggy, lets students “touch” and “push” triangles, dynamically modifying the shape and size, and observe the effect on the angles, sides and the trigonometric ratios. We describe the pedagogical rationale behind Ziggy, the user interfac...
متن کامل00 6 Elementary Notions of Lattice Trigonometry
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some tri...
متن کاملOf Lattice Trigonometry
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some tri...
متن کاملNotions of Lattice Trigonometry
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some tri...
متن کامل