Here n means the factorial of n which means the product ofall the whole numbers from 1 to n

For example, 4! means 1x2x3x4 which is 24.

So, using the particular angles above in sin (pi/10) and cos(pi/5) we have formulae for phi (4>) and Phi (■£>) in terms of powers of pi (0):-

25 7,500 5,625,000 7,875,000,000 In the upper formula, going to up to the pi9 term only will give phi to 9 decimal places whereas stopping at the pi8 term in the lower formula will give Phi to 7 decimal places.

These two formula easily lend themselves as an iterative method for a computer program (i.e. using a loop) to compute Phi and phi. To compute the next term from the previous one, multiply it by (pi/5)2 [or (pi/10)2 for phi] and divide by two integers to update the factorial on the bottom, remembering to add the next term if the previous one was subtracted and vice versa. Finally multiply your number by 2.

You will need and an accurate value of Pi. Here is Pi to 102 decimal places:

3. 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82..

With thanks to John R Goering for suggesting this connection between Phi and pi.

1-61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 . .More. . l^fFI

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