Laws of Rational Trigonometry
Wildberger states that there are five basic laws in rational trigonometry. He also states, correctly, that these laws can be verified using high-school level mathematics. Some are equivalent to standard trigonometrical formulae with the variables expressed as quadrance and spread.
In the following five formulas, we have a triangle made of three points A1, A2, A3, . The spreads of the angles at those points are s1, s2, s3, and Q1, Q2, Q3, are the quadrances of the triangle sides opposite A1, A2, and A3, respectively. As in classical trigonometry, if we know three of the six elements s1, s2, s3, Q1, Q2, Q3, and these three are not the three s, then we can compute the other three.
Read more about this topic: Rational Trigonometry
Famous quotes containing the words laws of, laws and/or rational:
“If ... we admit a divinity, why not divine worship? and if worship, why not religion to teach this worship? and if a religion, why not the Christian, if a better cannot be assigned, and it be already established by the laws of our country, and handed down to us from our forefathers?”
—George Berkeley (16851753)
“In time of war the laws are silent.”
—Marcus Tullius Cicero (10643 B.C.)
“If we did not have rational souls, we would not be able to believe.”
—St. Augustine (354430)