Relation To Various Means and The Golden Ratio
Let H, G, and A be the harmonic mean, the geometric mean, and the arithmetic mean of two positive numbers a and b with a > b. If a right triangle has legs H and G and hypotenuse A, then
and
where is the golden ratio
Read more about this topic: Right Triangle
Famous quotes containing the words relation to, relation, means, golden and/or ratio:
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)
“You can discover what your enemy fears most by observing the means he uses to frighten you.”
—Eric Hoffer (1902–1983)
“Venerandam,
In the Cretan’s phrase, with the golden crown, Aphrodite,
Cypri munimenta sortita est, mirthful, oricalchi, with golden
Girdles and breast bands, thou with dark eyelids
Bearing the golden bough of Argicida.”
—Ezra Pound (1885–1972)
“People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.”
—Samuel Butler (1835–1902)