[IAEP] shape 31

[K. K. Subramaniam]

On Saturday 19 Sep 2009 8:27:45 am Bill Kerr wrote:
> <http://billkerr2.blogspot.com/2009/09/shape-31.html>"So, I realised this
> was a nice challenge in real maths and understanding of the application of
> variables, measurement, ratio, proportion and fractions"
>
> I see this as a good example of where constructionist methods
> are necessary and instructionist or conventional textbook methods
> could not work
Shape31 is essentially a 4-petal pattern using greek-T as a generator instead 
of petals. It can be drawn with a single trace.
  repeat 4 [ self tau: 75 ]
where 
 tau = [ :arm |
       self forward: arm//5.
       self amble: arm. self amble: arm*2//3. self amble: arm].
 amble = [ :dist | self forward: dist. self turn: 90 ].

A purely constructionist approach to patterns can be found in India 
(particularly in the south). Lookup Kolam in Google or Wikipedia. Kolams are 
intricate geometric patterns laid on the floor or board by running off rice flour 
thru the fingers. Large patterns require the artist to turn/move around in a 
way reminiscent of Papert's early experiments with children. Skills are 
acquired by observing, imitating elders and (lots of) practice. Beginners use 
a grid of dots to estimate magnitudes and proportions.

Traditional kolams used only pure rice flour as paste or powder (as offerings to 
hungry small insects and birds). These days, people also use color powders, 
much to the consternation of the elders :-).

Subbu