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:
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”
—Albert Einstein (1879–1955)
“Laws and customs may be creative of vice; and should be therefore perpetually under process of observation and correction: but laws and customs cannot be creative of virtue: they may encourage and help to preserve it; but they cannot originate it.”
—Harriet Martineau (1802–1876)
“Nature has not placed us in an inferior rank to men, no more than the females of other animals, where we see no distinction of capacity, though I am persuaded if there was a commonwealth of rational horses ... it would be an established maxim amongst them that a mare could not be taught to pace.”
—Mary Wortley, Lady Montagu (1689–1762)