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
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?
The result of the substitutions 314 and 100 into the two procedures produce the same circles.
This can be confirmed by rearranging the formula: $C=\pi d$.
Experimentation with this relationship through investigating
the two procedures and creating circles which touch and/or which
are related by particular enlargements all support familiarity with
the relationship between the diameter and circumference of any
circle.