[MWForum]Creating Fraction Materials

[Wendy Petti]

Wow, this is a great Logo project!  It can certainly be done.  I would like
to make an observation about printing, to start with:

I've developed certain geometric shapes with MicroWorlds and posted them on
the Web.  Depending on whether they are viewed on a Mac or a PC at the time
of printing, they will print out in different sizes.  So we cannot give you
a one-size-fits-all answer to how many pixels = one cm when printed.  It
depends on the computer/printer setup.

But to start with, your students could run some experiments to see how many
pixels = 1 cm (or 10 cm or 20) cm on *your* particular setup.

The next thing to do is to draw circles with the turtle oriented at the
center point of the circle.
Don't use this technique:

to circle
repeat 360 [fd 5 rt 1]
end

There are two problems with that sort of circle:

1) You'll end up with short line segments instead of a perfectly curved
circle.
2) You won't be able to locate the center point (at least not easily) for
drawing the radii.

Instead, draw your circle using this approach (the examples below will draw
very small circles; I'm making no attempt to figure out the radius you'll
actually need):

to circle
repeat 360 [pu fd 100 pd fd 0 pu bk 100 rt 1]
end

However, this will give you a sort of dotted-line effect, even for this
small radius, and moreso as your radius increases in size.  This won't
actually matter if it's only meant to guide you in cutting out the fraction
circles, but there are other solutions if you need closed shapes (for
instance, if you want to fill each slice with a different color).

I've sometimes done this:

to circle
repeat 360 [fd fd 100 pd rt 90 fd 2 bk 2 lt 90 pu bk 100 rt 1]
end

Or you could try this:

to circle
repeat 3600 [pu fd 200 pd fd 0 pu bk 200 rt .1]
end

or

to circle
repeat 7200 [pu fd 200 pd fd 0 pu bk 200 rt .05]
end

or the same procedure but using division instead of a decimal:

to circle2
repeat 7200 [pu fd 200 pd fd 0 pu bk 200 rt 1 / 20]
end

Even though the math looks the same, for 1 / 20 = .05, the results are
different.

In any case, once you've drawn your circle it should be easy to divide it
into slices while the turtle is still at the center point:

to 20-slices
circle
repeat 20 [pd fd 200 bk 200 rt 360 / 20]
end

You can let the computer do the math for you that way.  You can also set up
sliders to control the size of the radius and the # of slices easily.  This
way you only need one slicing procedure to make all the sets of slices:

(using 2 sliders called radius and #slices:)

to sliced-pie
circle
repeat #slices [pd fd radius bk radius rt 360 / #slices
end


You'll need to set a large projectsize before you get started, for drawing
circles that are 20 cm in diameter.  And most likely you'll need to scroll
around the project page to see the full circle.

Good luck, and please let us know how it goes!!!!

Wendy Petti
OWL's MicroWorlds in Action
http://mia.openworldlearning.org


...
> The materials are a series of fractional circles with
> a diameter of 20cm, ranging from 1/2 to 1/20 (180
> degrees to 13 degrees).