Eight turtles forming eight graphics handles and a rectangle instead of a CIRCLE

This is a quiz two followup (April 2011 quiz)

Forward 8 steps for the EVEN turtles, but FORWARD squareRootOf(128) steps or FORWARD 11.31371 steps for the ODD turtles. 8 ^ 2 + 8 ^ 2 = 64 + 64 = 128. The length of each of the two equal sides of the right triangle is 128.

cro 8 creates 8 turtles, staggered to face 0, 45, 90, 135, 180, 225, 270, 315, 360 degrees. The EVEN turtles face 0, 90, 180 ad 270 degrees.

CRO 32 turtles and have them step fd 8 or 10 steps. The 32 turtles form a perfect CIRCLE, NOT a RECTANGLE.

Quantitative Thinking - Right Triangles: Pythagorean Theorem

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The ODD turtles draw the HYPOTENUSE. The EVEN turtles draw the LEGS.

## WHAT IS IT? Even turtles walk length of a LEG, ODD do the length of hypotenuse.

```ifelse remainder who 2 = 0
[
slowWalk 8       ;; Even turtles move 8 units
]
[
slowWalk sqrt (8 ^ 2 + 8 ^ 2)
]
```

## HOW IT WORKS to do the slow walking forward moves

```TO moveEm [ n ]
ifelse remainder who 2 = 0
[
slowWalk n   wait 0.1
]
[
slowWalk sqrt (n ^ 2 + n ^ 2)   wait 0.1
]
end
```

## HOW to show the squares (PATCHES) - checkerBoard procedure

```To checkerBoard
[
ifelse remainder (pxcor + pycor) 2 = 0
[
set pcolor white
]
[
set pcolor yellow
]
]
end

```

## THINGS TO NOTICE - slowWalk procedure

```TO slowWalk [ howFar ]

repeat 20
[
fd (howFar / 20)
wait 0.1
]

end

```

## THINGS TO TRY

```TO outline8GraphicsHandles     ;; Try out the outline8GraphicsHandles

ca
checkerboard

cro 8

ask-concurrent turtles       ;; If you want the ODD turtles share a row with one even
[                            ;; turtle and share a column with another even turtle
pd                        ;; they need to WALK FORWARD the length of the hypotenuse
set pen-size 2            ;; of the sides of the right triangle (see Pythagorous)
set color black

ifelse remainder who 2 = 0
[
slowWalk 8              ;; Even turtles move 8 units
]
[
slowWalk sqrt (8 ^ 2 + 8 ^ 2)      ;; Odd turtles move square root of 128 units
]                                     ;; Odd turtle move about 11.3 units

;; 11.31371 ^ 2 =  128.0000339641
]                                  ;; 8 squared plus 3 squared = 64 + 64 = 128
END                                   ;; square root (128) = 11.31371

```

## EXTENDING THE MODEL

```TO form4corners4sides       ;; Try form4corners4sides (instead of CIRCLE of turtles)
ca                      ;; to see pattern with PU then PD then PU.
checkerboard            ;; The 8 turtles outline a RECTANGLE, not a CIRCLE...

cro 8

[
set pen-size 2
set color blue

moveEm 2

pd

moveEm 3

pu

moveEm 3
]
END
```

## NETLOGO FEATURES

This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab. It might also point out places where workarounds were needed because of missing features.

## RELATED MODELS

This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.

## CREDITS AND REFERENCES

This section could contain a reference to the model's URL on the web if it has one, as well as any other necessary credits or references.

## PROCEDURES

```TO outline8GraphicsHandles        ;; Try out the outline8GraphicsHandles

ca
checkerboard

cro 8

ask-concurrent turtles                    ;; If you want the ODD turtles share a row with one even
[                              ;; turtle and share a column with another even turtle
pd                          ;; they need to WALK FORWARD the length of the hypotenuse
set pen-size 2              ;; of the sides of the right triangle (see Pythagorous)
set color black

ifelse remainder who 2 = 0
[
slowWalk 8                         ;; Even turtles move 8 units
]
[
slowWalk sqrt (8 ^ 2 + 8 ^ 2)      ;; Odd turtles move square root of 128 units
]                                     ;; Odd turtle move about 11.3 units

;; 11.31371 ^ 2 =  128.0000339641
]                                  ;; 8 squared plus 3 squared = 64 + 64 = 128
END                                   ;; square root (128) = 11.31371

To checkerBoard
ifelse remainder (pxcor + pycor) 2 = 0
[ set pcolor white ]
[ set pcolor yellow ]
]
end

TO moveEm [ n ]
ifelse remainder who 2 = 0
[
slowWalk n wait 0.1
]
[
slowWalk sqrt (n ^ 2 + n ^ 2) wait 0.1
]
end

TO form4corners4sides                 ;; Try form4corners4sides (instead of CIRCLE of turtles)
ca                                ;; to see pattern with PU then PD then PU.
checkerboard                      ;; The 8 turtles outline a RECTANGLE, not a CIRCLE...

cro 8

[
set pen-size 2
set color blue

moveEm 2

pd

moveEm 3

pu

moveEm 3
]
END

TO slowWalk [ howFar ]

repeat 20
[
fd (howFar / 20)
wait 0.1
]

end

```