[Squeakland] Discovering Pi in Squeak

[Bert Freudenberg]

Using "forward by, turn by" you can draw a circle of known  
circumference, similar to how kids can measure the circumference of a  
large circle in the sand by counting footsteps. Measuring the  
diameter is easy - take the ratio and you're done.

So "turn by 120" three times makes your "three stick" version. You  
can go up to 360 sticks by using 1 degree turns ...

There also is a project for discovering pi (using real-world  
materials) in the "Powerful Ideas" book.

- Bert -


On May 30, 2007, at 7:41 , subbukk wrote:

> 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.
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