7.1 I LOVE Pi & Phi
PI & PHI
Love, love is strange
A lot of people take it for a game
Once you get it, you're in an awful fix
After you've had it, you'll never want to quit
Many people , don't understand
They think loving is money in the hand
Your sweet loving is better than a kiss
When you leave me sweet kisses I miss
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In 2010 I created this pi sliding puzzle.
The game contains 7 discs: 3 blue, 3 gray and 1 white.
The aim of the game is to switch places
between the 3 blue and 3 gray ones.
The game was never commercialized.
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The value of PHI & PI
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Can you prove it for n = 1, 2 en 3?
There is a general proof involving complex analysis!
My PIPHI-problem.
Let M be the center of the upper face of a cube whose edges have length 1.
This cube is tilted so that it rolls without sliding.
After tilting four times, the point M is on top again.
Show that the total length of the traject of M equals
HINT. The picture on the left shows you
half of the traject of the point M.
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