Okay, last one for tonight… since I upset √2 with the previous formula, I thought I’d have a go using square roots, but didn’t find anything yet. Maybe another day.
But… I did find something using cube roots… in fact, the cube roots of 2, 3, 5, and something derived from 7 …. and the accuracy is the best yet, even if the formula is horribly complex. Beauty and the beast, I suppose.
Cubit in cubes…
I suppose we could write 10 as cube root of 1000 as well.
The comparison table now looks as follows:
| Method | Value | Difference from π/6 | Abs difference |
|---|---|---|---|
| π/6 | 0.52359877559830 | 0.00000000000000 | 0.00000000000000 |
| φ²/5 | 0.52360679774998 | 0.00000802215168 | 0.00000802215168 |
| Ave Year | 0.52360779708785 | 0.00000902148956 | 0.00000902148956 |
| π – φ² | 0.52355866483991 | -0.00004011075839 | 0.00004011075839 |
| 10²/φ²π²ⅇ² | 0.52376444099003 | 0.00016566539172 | 0.00016566539172 |
| cube roots | 0.52360035017194 | 0.00000157457365 | 0.00000157457365 |