Derivation of 1.77 


Where did the number 1.77 come from?  Yes, it is the square root of pi, but how was it derived?  Here is the explanation (taken directly from Usenet) from r.s.b.p.'s resident math wizard (since the legendary Mathgod has retired), Nate.

Subject:      Re: sqrt(Pi), redux
From: (nate)
Date:         1998/03/23
Message-ID:   <6f6j5m$>

although Mathgod is the one who came up with the derivation, he was able to pass along this much to me:

we are trying to solve the quantum dynamical fluctuations of the wave  equation of a basketball team (5 players).  he was able to show that the   ratio of shooting activity over the ratio of rebounding, passing, blocking,   stealing, and any other activity was collapsible into the ratio, when viewed   from directly above the court of the basket rim's internal area to the orthogonal cross-section made by two basketball trajectories.  this  othogonal cross-section area is D squared, where D is the diameter of the  ball.  the area inside the rim is the area of a circle twice the diameter  of a basketball, (pi)*D*D.   since the ratio is applicable to the team of 5  players (a dimensionsal metric of 2 when viewed from above, as in this case), to get the applicable ratio to an individual, you reduce the metric  to 1 dimension (for 1 player) by taking the square root.

for eras before they kept steals and blocks the equations were much more  formidible, as the modelling components added became unweildy to the layman.   you need to go back into the 5th Legendre polynomial (for 5 players).   the  best way to think of it is as a rotation away from orthogonality, reducing  the cross-section by tilting the square into a rhombus.  thus you get the  2.30... for those eras.

- nate

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