Phi^10-by-Phi^10 Rectangle and Progressive Difference

(phi^20) - (1 + phi + (phi^3) + (phi^5) + (phi^7) + (phi^9) + (phi^11) + (phi^13) + (phi^15) + (phi^17) + (phi^19)) = 0 *1 *2 shows how I am going to theorize my "Phi-by-Phi (Golden) Rectangle" with Excel Trigonometry.

Excel, Google and websites like Virtual Library of Useful URLs - Fibonacci Numbers and the Pascal Triangle, which will be referred to from time to time, will help beginners like myself further explore the golden ratio and Fibonacci Numbers.

*1 06/11/18
((phi + 1)^10) - (1 + (phi^10) + ((10 * phi) * ((phi^8) + 1)) + ((45 * (phi^2)) * ((phi^6) + 1)) + ((120 * (phi^3)) * ((phi^4) + 1)) + ((210 * (phi^4)) * ((phi^2) + 1)) + (252 * (phi^5))) = 0

*2 06/11/26
the golden ratio^20 = 15 126.9999

(phi^20) - ((1 + phi)^10) = 0

(phi^10) - sqrt((1 + phi)^10) = 0

the golden ratio^10 = 122.991869

the golden ratio^5 = 11.0901699


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