Rational Trigonometry Using Maple

2021 ◽  
pp. 365-375
Author(s):  
Thomas Schramm
Keyword(s):  
Rational Trigonometry

scholarly journals Rational Trigonometry in Higher Dimensions and a Diagonal Rule for $2$-planes in Four-dimensional Space

KoG ◽  
2017 ◽  
pp. 47-54
Author(s):  
Norman Wildberger
Keyword(s):  
Dimensional Space ◽  
Higher Dimensions ◽  
Natural Generalization ◽  
Principal Angles ◽  
Rational Trigonometry ◽  
Pythagoras Theorem ◽  
The Cross

We extend rational trigonometry to higher dimensions by introducing rational invariants between $k$-subspaces of $n$-dimensional space to give an alternative to the canonical or principal angles studied by Jordan and many others, and their angular variants. We study in particular the cross, spread and det-cross of $2$-subspaces of four-dimensional space, and show that Pythagoras theorem, or the Diagonal Rule, has a natural generalization forsuch $2$-subspaces.

scholarly journals The Feuerbach Theorem and Cyclography in Universal Geometry

KoG ◽  
2020 ◽  
pp. 47-58
Author(s):  
William Beare ◽  
Norman Wildberger
Keyword(s):  
Finite Field ◽  
Unit Circle ◽  
Finite Fields ◽  
Algebraic Approach ◽  
Rational Points ◽  
Field Case ◽  
Rational Trigonometry ◽  
Universal Geometry ◽  
Simplified Form

We have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequent formulas involve the three parameters that define them. Tangency of incircles is treated in the oriented setting via a simplified form of cyclography. Some interesting features of the finite field case are discussed.

scholarly journals GARIS DI LAPANGAN HIMPUNAN BILANGAN BULAT MODULO 17

2013 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Denni Hariati Sinaga ◽  
Idha Sihwaningrum ◽  
Ari Wardayani
Keyword(s):  
Unique Property ◽  
Rational Trigonometry

n this paper we discuss rational trigonometry in the field F17 ,in particular point, lines and their properties. A unique property in this field is given by the null lines.

scholarly journals The Universal Parabola

KoG ◽  
2018 ◽  
pp. 24-40
Author(s):  
Si Chun Choi ◽  
Norman Wildberger
Keyword(s):  
General Framework ◽  
Rational Trigonometry

We develop classical properties, as well as some novel facts, for the parabola using the more general framework of rational trigonometry. This extends the study of this conic to general fields.

Efficient FPGA Hardware Implementation for Robot Manipulator Kinematic Modeling Using Rational Trigonometry

2019 ◽  
Vol 17 (09) ◽  
pp. 1524-1536
Author(s):  
Rogelio Martinez Peralta ◽  
Erik Zamora Gomez ◽  
Juan Humberto Sossa Azuela
Keyword(s):  
Hardware Implementation ◽  
Robot Manipulator ◽  
Kinematic Modeling ◽  
Rational Trigonometry
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