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 and/or rational:
“The main foundations of every state, new states as well as ancient or composite ones, are good laws and good arms ... you cannot have good laws without good arms, and where there are good arms, good laws inevitably follow.”
—Niccolò Machiavelli (1469–1527)
“We fetch fire and water, run about all day among the shops and markets, and get our clothes and shoes made and mended, and are the victims of these details, and once in a fortnight we arrive perhaps at a rational moment.”
—Ralph Waldo Emerson (1803–1882)