[Squeakland] Discovering Pi in Squeak

[subbukk]

At 12:21 PM 5/30/2007, Bert Freudenberg wrote:
>I bet if they are able to trace from the "turn by" tile into the
>method where pi is actually used directly, they are able to
>understand why this is not cheating. Besides, you could use radians
>directly for turning and then pi would not be involved directly.
The issue not about 'cheating', but in the equation:
 pi = perimeter/diameter where diameter = xmax - xmin
the rhs should not have used pi. degrees to radians conversion, sin and cos 
functions used in offset calculations all use pi.

>It's like your "blacksmith" argument - he doesn't actually need pi
>but could simply roll the wheel on the strip of metal to find the
>length. But that would be cheating because pi is built into the
>wheel, yes?
The purpose of the exercise is not to discover the length but that the ratio 
of perimeter to width is same for all circles and that this ratio is unique 
enough to deserve a separate name. The blacksmith who knows this ratio does 
not have to take the wheel off the cart to rim it :-).

Regards .. Subbu