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 will need 5 copies of this script.
To duplicate a script, right-click (or control-click) on its
TOPMOST block. (In this case, the REPEAT block.)
You will see a menu of options. Choose "duplicate."
Move the copy where you want it..1.1i114.1.1TIF A. Getting this just right is very subtle. The note on 5.5 just above explains how to write a block that draws a circle of a given radius. If the side of the square is 100, then the diameter of the circle should also be 100, and so the radius should be 50. And the circle has to start at the midpoint of a side, not at a corner.
That makes the first, second, and fourth block in the following script straightforward, but drawing the picture without the third block makes the circle seem just slightly too big. Students who try it, and who care about that small inaccuracy, will probably try a smaller approximation of π, and will be very frustrated that they can't get it right that way. The secret is that the starting /angle/ of the sprite when drawing the circle is also important, and shouldn't be the same as the angle for the square. It should be tilted by half the angle that the circle procedure turns between sides of the polygon that approximates the circle.
Why? Well, imagine a really coarse approximation, say a pentagon. How would you inscribe a pentagon in a square? You really don't want an entire side of the pentagon colinear with a side of the square; you want just one point, a vertex of the pentagon, to touch the square. To make the figure symmetrical, you'd turn half the turning angle of a pentagon before starting.
In the script below, the 1.5 degree turning is the result of experimentation and probably isn't exactly mathematically correct. Probably you have a hotshot geometry student who'd be glad to figure out the correct value for you.Page 4 TIF solutions are in separate projects:
U1L3p4-Kandinsky
U1L3p4-pinwheelThe problem is (deliberately) vague about what the "size" of a circle means. The solution above takes the simplest possible view, namely that the measure of size is arbitrary as long as a size-2 circle is twice the (linear dimension) size of a size-1 circle.
To get a more conventional size unit, remember that the circle is really a 120-gon. (Any large enough number would work.) Its perimeter is 120 times the length of a side. That's close to the circumference of the circle we're approximating. So if we want "size" to be the circumference, we should sayIf we want "size" to be the radius, the circumference should be 2π times that:Note, though, that if you make one of those choices, the word "size:" in the title text should really be "circumference:" or "radius:" as desired, so that the user of the block knows what to expect.