| 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
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