#3**+10 **

Sorry, rosala...I should have explained more....Phi is the irrational number (1 + √5) / 2 ≈ 1.61803398874989485

If you have regular pentagon of side length = 1, then the length of one of its diagonals turns out to be "Phi"

Also....if you're familiar with the Fibonacci Series.......as the series grows larger, the ratio between a successive term and its preceding term tends towards Phi....!!

Athough you probably have enough studying to do in school....here's a whole website devoted to Phi....http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html

(You may find it interesting to just look at a little of it at a time...!!!)

CPhill
Dec 30, 2014

#1**+5 **

1.61803398874989485^4 = 6.85410196624968457504

We could have also found this by summing ..... 1.61803398874989485^2 +1.61803398874989485^3........since Phi has the interesting property that Phi^n + Phi^(n + 1) = Phi^(n + 2)......!!!!

CPhill
Dec 30, 2014

#3**+10 **

Best Answer

Sorry, rosala...I should have explained more....Phi is the irrational number (1 + √5) / 2 ≈ 1.61803398874989485

If you have regular pentagon of side length = 1, then the length of one of its diagonals turns out to be "Phi"

Also....if you're familiar with the Fibonacci Series.......as the series grows larger, the ratio between a successive term and its preceding term tends towards Phi....!!

Athough you probably have enough studying to do in school....here's a whole website devoted to Phi....http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html

(You may find it interesting to just look at a little of it at a time...!!!)

CPhill
Dec 30, 2014

#7**0 **

Of course Chpill took the more detailed version but both statements are correct.

NotTheBestMathMaster
Dec 30, 2014

#8**+5 **

I am sorry **NotTheBestMathMaster** but your answer is not correct.

phi to the power of 4 is phi^4

this is different from phi multiplied by 4 which is phi*4

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I shall show you on some more every day numbers.

3^4 = 3*3*3*3 = 81

where as

3*4 = 3+3+3+3 = 12

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Melody
Dec 31, 2014