Area Proportional To Sums of Squares
All primitive triples with and with a odd can be generated as follows:
| Pythagorean triple | Semi-perimeter | Area | Incircle radius | Circumcircle radius |
|---|---|---|---|---|
| 1 + 2 + 3 | 1 | |||
| 1 + 2 + 3 + 4 + 5 | 2 | |||
| 1 + 2 + 3 + 4 + 5 + 6 + 7 | 3 | |||
| ....... | ....... | ....... | ....... | ....... |
| 1 + 2 + ... + a |
Read more about this topic: Formulas For Generating Pythagorean Triples
Famous quotes containing the words area, proportional, sums and/or squares:
“During the Civil War the area became a refuge for service- dodging Texans, and gangs of bushwhackers, as they were called, hid in its fastnesses. Conscript details of the Confederate Army hunted the fugitives and occasional skirmishes resulted.”
—Administration in the State of Texa, U.S. public relief program (1935-1943)
“The Humanity of men and women is inversely proportional to their Numbers. A Crowd is no more human than an Avalanche or a Whirlwind. A rabble of men and women stands lower in the scale of moral and intellectual being than a herd of Swine or of Jackals.”
—Aldous Huxley (1894–1963)
“At Timon’s villalet us pass a day,
Where all cry out,What sums are thrown away!’”
—Alexander Pope (1688–1744)
“And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.”
—Ezra Pound (1885–1972)