LOGO Challenge 11 - More on Circles

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates this relationship.
Age
11 to 16
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



A reminder:

$C = \pi \times d$ or $C = 2 \times\pi \times r$

Where C is the circumference of a circle and $\pi$(pi) is equal to 3.14159...


In terms of LOGO it means that circles of any diameter, radius or circumference can be drawn. Consider the following procedure:

TO CIRC :C
REPEAT 360 [ FD :C/360 RT 1]
END


What do you think this is about?

Once decided, trace the procedure through in your mind's eye.

If you can, talk to others about what you think is happening. If in doubt out check your thoughts by typing in the procedure and testing what it does. N.B. Pi is a primitive approximately equal to 3.14159.

Try CIRC 314

For now experiment by changing:

The number of times you repeat the instruction (360) Or the length of the circumference (:C) Or the amount of turn done after each forward movement (1 degree)

Alternatively you might like to consider the next procedure:

TO CIR :D
REPEAT 360 [FD :D*PI/360 RT 1]
END
Try the following CIR 100


What do you notice now?