[Squeakland] Discovering Pi in Squeak

Alan Kay alan.kay at squeakland.org
Wed May 30 05:05:09 PDT 2007


Hi --

Bert points out that it is easy to use forward by, turn by to make 
pologons whose diameters can be measured.

For example, you can make a big circle with a turn by 1 and sum the 
forwards, and also remember max y and min y to get the diameter. This 
will give you a pretty good value for Pi.

You didn't mention the ages of your children.

But it is always good to get them to do some reasoning about measures 
of various kinds and areas. I think that the manipulation of the 
strings, etc.,  might be too awkward (but see the discussion in the 
"Powerful Ideas" book about measurement).

I would just give them squares of different sizes and see if they can 
work out how a side might relate to the perimeter, and if so, why 
something like that would also work for a diagonal. The idea that the 
relationship is the same regardless of scale is a biggie for 
children. Discovering the relation for the area is even bigger.

Before that I would use rulers with different scales to make similar 
figures (starting with triangles), and get them to see that nature 
doesn't care how our rulers are laid out (a measurement taken with 
one ruler can be used to make a similar figure of a different scale 
using a different ruler). This is a very good way to show how and why 
proportions work (and many studies have shown that proportions and 
the normalizations associated with them are not learned well by most children).

Cheers,

Alan

At 10:41 PM 5/29/2007, 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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