The document describes several programs created in MicroWorlds to generate different geometric shapes. The programs use variables, loops, and conditional statements to manipulate a turtle to draw the shapes. One program draws a star by repeating a section that increases the turtle's forward distance and changes its color. Another creates a disco bowling ball by calling a separate "turn" program and repeating a loop to draw concentric circles in different colors. A third makes a pinwheel with petals of a specified size by dividing 360 degrees by the number of petals.

1. Geometry Through
MicroWorlds
By Jesse McDougall

2. Contents
 Shooting Star 2………………………………………………………………………………………………….3
 Disco Bowling Ball .…………………………………………………………………………………………..4
 Sharp-Cog ………………………………………………………………………………………………………….5
 Disco Slinky ……………………………………………………………………………………………………….6
 Flag Wave …….……………………………………………………………………………………………………7
 Windmill Blowtoy ………………………………………………………………………………………………8

3. Shooting Star 2
The program works by first clearing the graphics. Then,
the turtle named ‘music’ plays music that I created as
the second turtle draws. The second turtle sets the
background to black, sets it’s heading to 355° and then
moves with the pen up to specified coordinates on a
Cartesian plane. A variable called ‘count’ is set to 410.
Then the turtle does ‘count’ times of the next section of
the program. The next section sets the colour to :i plus
1. Since it says dotimes, :i starts as zero and increments
by one every time. The next section of the program
repeats five times. It goes forward :i pixels and right
turns 144°. Then it waits 0.01 turtle seconds, right turns
one tenth and goes forward two tenths and repeats, the
object increasing in size, curving and changing the colour.
If you remove the internal lines the star or decagon has
two sets of five equal angles: five acute (36°) and five
obtuse (252°). Even though the shape increases in size,
the angles never change. If you don’t remove the lines
there are five 108° angles, five 36° angles and ten 72°
angles. The end result of this shape is not a polygon as
three of the sides are curved. I figured out how to do
this while learning about variables and changing colour
with my Dad.

4. Disco Bowling Ball
This program works with lots of other programs so I’ll explain them all.
The first program is ‘turn’. In the command box, you decide what the
radius is and how much of the circumference you want to turn and in
which direction. Then, ‘turn’ sets a variable of the circumference as 2
times the radius times pi. It then repeats the absolute value of how
much of the circumference you entered in the commands box. (The
absolute value of negative three would be three). It goes forward the
circumference divided by three hundred and sixty. Then there is an
ifelse statement that says if degrees is less than zero, left turn one
degree or else right turn one degree.
The second program is a bowling ball. It says to ‘turn’ that the radius
of the circle is 300 divided by pi and that the percentage of the
circumference is 360 (a full circle). Then it sets the turtle’s heading to
the right and tells it to lift the pen up, go forward fifty and put the pen
down. It then repeats the following 360 times: right turn one, forward
a tenth, creating the first finger hole. After this it puts the pen up and
moves the turtle forward twenty and then puts the pen down again.
Next, it repeats the following 360 times to create the second finger
hole: right turn one degree, forward one tenth. The program sets the
turtle’s heading to 315 degrees, puts the pen up, goes forward 18.2,
puts the pd and repeats the following 360 times to create the last finger
hole: right turn one degree, forward a tenth. Then it puts the pen up,
sets the turtle’s heading right and goes forward 20. It waits five turtle
seconds and then fills the ball.
‘Discobowl’ works by doing bowling ball and repeats the following
twelve and a half times. The programs optional 1,2,3,4,5,6 and 7 all
set the colour to a different colour, sets the turtle’s heading and puts
the pen up, and it goes forward ten. Then it fills the space with the set
colour, creating a disco effect. Geometrically, a perfect circle has no
angles and only one side so a turn of 360 degrees would have infinite
angles. I figured out how to do this by making optional effects and a
bowling ball for a challenge and then combining the two.

5. Sharp Cog
The program commences with ‘turn’. Then it
does ‘petal’. When you type petal in the
commands box you type a number with it for the
size of the petal to be stored in a variable. The
program tells the turtle to repeat the following
two times: forward the petal’s size, ‘turn’ the
petal’s size multiplied by two with a ninety
degree ‘turn’. Then, it goes forward the petal’s
size times two, ‘turn’s the petal’s size times two
and negative ninety finishing with a one hundred
and eighty degree turn.
‘Pinwheel’ is the third program. ‘Pinwheel’
begins by hiding the turtle and clearing the
graphics. After this it repeats the following how
ever many petals you ask for: make a size
twenty petal, right turn 360 divided by how
many petals so there will always be the perfect
amount of petals on each shape.
A sharp cog is a ‘pinwheel’ with ninety petals,
looking like a sharp cog, hence the name. This is
not a polygon as it has curvy sides. Although this
shape has curvy lines, it still has angles. Despite
a 1080 pinwheel’s look, it still isn’t a circle as
three hundred and sixty divided by one thousand
and eighty is not as accurate as pi. I learnt how
to do this by watching a YouTube clip with
something very similar and altering the program
slightly.
A Sharp Cog
A 1080 Petal
Pinwheel

6. Disco Slinky
The program begins by clearing the
graphics. Then it say do the following
360 while making :i zero and every time
it goes through the loop it adds one to :i.
It sets the colour to :i hence the
different colours. After this it sets the
turtles heading to :i and ‘turn’s 100 and -
360.
A circle is not a polygon as it has curved
sides. The shape when finished looks like
one large circle but there are spaces in
between the circles so it isn’t round. I
figured this out really easily after doing
many similar programs and just applying
my knowledge.
An Incomplete Disco
Slinky

7. Flag Wave
This program begins by clearing the graphics, hiding
the turtle and putting the pen down. It the sets
three variables: “a becomes one, “size becomes
one and count becomes 99950. Then the program
repeats the following :count times: Set the turtle’s
position on the Cartesian plane to the origin, move
the turtle forward :size and set the turtle’s heading
to :a. It then sets the colour to :a and repeats the
following four times: forward :size, right turn
ninety degrees. Finally, it makes “a :a + 1 and
“size :size + 0.05, making the shape increase in size
and change colour. The shape to the right has two
sides; one curved and one straight. One of these
flags is a line with a square on top but it still isn’t a
polygon as the flag isn’t enclosed (a line sticks out).
I figured out how to do this by making disco square
which is exactly the same except it doesn’t stick
out like a flag. I just added forward :size (circled)
and made something new.

8. Windmill Blowtoy
The first program is ‘test_vars’. It first sets two variables: “a and
“b. In this case it sets both to one hundred and forty. Then, it
makes “c the square root of the sum of :a squared and :b squared
(pythagoras theorem). It then makes the turtle move backwards
:a, right turn ninety and forward :b. Next, left turn the arc
tangent of :a divided by :b. Finally, the turtle moves forward :c
(the hypotenuse). The second program is ‘windmill blowtoy’.
This program begins by clearing the graphics, hiding the turtle,
putting the pen down and repeating ‘test_vars’ eight times. It
makes this shape because at the end of the program I don’t tell
the turtle to turn back to it’s original heading. Next, the
program sets two variables: “angle and “colour. Then it set the
colour to eight, put the pen up and repeats the following 151
times: Set the turtles position to the origin. Then, it makes
“colour :colour + ten, hence the changing colour. It sets the
turtles heading to angle, moves the turtle forward twenty. It sets
the colour to the variable :colour and fills the space that the
turtle is in. Then it makes “angle :angle + 45 so it goes forward
into the next triangle the next time around. I figured out how to
do this by learning about variables with my dad and because my
excellent teacher Mrs. Watson set me the challenge of making
‘one of those blow toys you buy at a fair’. This shape is my only
polygon in this power point and it is a “hexadecagon”.