I knew that the ratio between successive items in the Fibonacci sequence converged on the golden ratio φ, but I only recently discovered that it doesn't matter where you start (including wild starting points, too); if it follows the Fibonacci form, you'll always get to φ:

• 1, 2, 3, 5, 8, 13, 21, 34, 55, 89: 89/55 = 1.618182
• 1, 100, 101, 201, 302, 503, 805, 1308, 2113, 3421: 3421/2113 = 1.619025
• -1, -2, -3, -5, -8, -13, -21, -34, -55, -89: -89/-55 = 1.618182
• 152, -5, 147, 142, 289, 431, 720, 1151, 1871, 3022: 3022/1871 = 1.615179
• 1e-06, 42, 42.000001, 84.000001, 126.000002, 210.000003, 336.000005, 546.000008, 882.000013, 1428.000021: 1428/882 = 1.619048
• 0.01, 1, 1.01, 2.01, 3.02, 5.03, 8.05, 13.08, 21.13, 34.21: 34/21 = 1.619025

¶ 1470 Posted at 04.00 PM ⇒ No Comments ( neat | fyi )