LOGO Challenge 10 - Circles

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.