| Silver means | ||
| 0: | ½ (0 + √4) | 1 |
| 1: | ½ (1 + √5) | 1.618033989 |
| 2: | ½ (2 + √8) | 2.414213562 |
| 3: | ½ (3 + √13) | 3.302775638 |
| 4: | ½ (4 + √20) | 4.236067978 |
| 5: | ½ (5 + √29) | 5.192582404 |
| 6: | ½ (6 + √40) | 6.162277660 |
| 7: | ½ (7 + √53) | 7.140054945 |
| 8: | ½ (8 + √68) | 8.123105626 |
| 9: | ½ (9 + √85) | 9.109772229 |
| ... | ||
| n: | ½ {n + √(n^2 + 4)} | |
The more general simple continued fraction expressions
are known as the silver means or metallic means of the successive natural numbers. The golden ratio is the silver mean between 1 and 2, while the silver ratio is the silver mean between 2 and 3. The term "bronze ratio", or terms using other names of metals, are occasionally used to name subsequent silver means. The values of the first ten silver means are shown at right. Notice that each silver mean is a root of the simple quadratic equation
where n is any positive natural number.
Read more about this topic: Silver Ratio
Famous quotes containing the words silver and/or means:
“no thread
Of cloudy silver sprinkles in your gown
Its venom of renown, and on your head
No crown is simpler than the simple hair.”
—Wallace Stevens (1879–1955)
“I wish to reiterate all the reasons which [my predecessor] has presented in favor of the policy of maintaining a strong navy as the best conservator of our peace with other nations and the best means of securing respect for the assertion of our rights of the defense of our interests, and the exercise of our influence in international matters.”
—William Howard Taft (1857–1930)