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:
“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”
—Thomas Jefferson (1743–1826)
“There is something servile in the habit of seeking after a law which we may obey. We may study the laws of matter at and for our convenience, but a successful life knows no law.”
—Henry David Thoreau (1817–1862)
“It is not to be forgotten that what we call rational grounds for our beliefs are often extremely irrational attempts to justify our instincts.”
—Thomas Henry Huxley (1825–95)