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:
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
—Jean Baudrillard (b. 1929)
“I think she means to tangle my eyes too!”
—William Shakespeare (1564–1616)
“My mother dandled me and sang,
“How young it is, how young!”
And made a golden cradle
That on a willow swung.
“He went away,” my mother sang,
“When I was brought to bed....””
—William Butler Yeats (1865–1939)
“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)