Hi,
I am trying to create an experiment to help children my kids discover numbers like Pi. I don't want Pi to be introduced to kids as an "irrational" number. It is a real number that exists in curved shapes. While countables can be understood with beads or pebbles and fractions with slices, numbers like Pi will need continuous things like sticks and strings[1].
The kids start the play by placing two sticks in a V-shape and use a string to span the other ends. Add another stick to the mix and spread the sticks out radially. Extend the string to the tip of the new stick and back again to the starting point to form a triangle. Keep increasing the number of sticks and use the string to form squares, pentagons and so on. Soon a circle takes shape and the string converges to its perimeter. Now get the child to mark this length and express it in terms of stick units (fractions allowed). Repeat with different lengths of sticks. Let the child discover that some measures are not countable or even expressible easily as a fraction. Now the name 'Pi' can be introduced and the perimeter could be expressed as 2*Pi. Pictures of village blacksmith trying to cut a strip of iron to rim a bullock cart wheel set the tone for the exercise.
As a parent of two young kids, I worry about kids hurting themselves with the sticks. Squeak is a lot safer for such experiments. The nearest object that I could use in Squeak is the Star. But the number of sticks (vertices count) or stick length (distance between center and vertex) or the string segment length (distance between adjacent vertices) are not computable from the properties visible in the viewer.
Did I miss something or is there a better way to do this in Squeak?
Thanks in advance .. Subbu [1] Sutra in Sanskrit. The humble string is so useful in conveying complex concepts that the term Sutra also gets applied for formulae (e.g. E=mc^2) and theory, theses etc.