LOGO Challenge 10 - Circles
In LOGO circles can be described in terms of polygons with an
infinite (in this case large number) of sides - investigate this
definition further.
Age
11 to 16
Challenge level
These challenges arose from conversations and ideas during a Royal Institution Saturday morning Maths Workshop. Consider the procedure:
TO POLY :X :Y
REPEAT :Y [FD :X LT 360/:Y]
END
where :X and :Y are variables, that can be changed as you experiment and try to understand what is happening.
Think about, try to imagine, then experiment with:
POLY 50 7
POLY 20 16
POLY 20 30
etc..
What happens as the value for :Y increases yet further? (i.e. considering the limitations with your monitor's powers of resolution.)
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BUT
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What is the most elegant way of coding the drawing of a circle of radius 60 screen units in the centre of your screen?
[Hint: use the primitive HOME to return turtle.]
Naturally, geometric designs have long been embellished with circles.
You might like to consider re-creating the following designs this month.
Image
Image
Image
It is not easy to create concentric circles and quite alot of
work is needed in calculating the diameters of circles based on the
length of the side of your many sided polygon.
A step size of 1 unit and a turn of 1 degree produces a circle
of circumference 360 units.
A step size of 2 units and a turn of 1 degree produces a
circle with a circumference of 720 units.
From these you can work out the diameter as
$C = \pi d$.
That should help you work out where you need to start the next
circle.
Some LOGO programs, like MSWLogo understand "PI" and will do
calculations which include it. For example: PI * 2 will give a
decimal answer.