A Regular Polygon Recipe

Section 20.3 A Regular Polygon Recipe

You undoubtedly have recognized that there are some similarities to drawing shapes like the square or hexagon. It turns out there is a general pattern to drawing any regular (all sides are the same length and all angles are the same size) geometric shape.

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Let’s look at a few more examples. Here’s a triangle:

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And here’s a pentagon:

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Notice that the only code that is “inside” the for loop (indented after it) are the parts we want to repeat. We only want to end_fill once, so it is not indented. It is not part of the code that is repeated.

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The only two things that are different between the two programs are the number of repetitions in the loop and the angle the turtle turns.

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Any time we want to make a regular polygon, we need the turns to all sum up to

360 .

In the triangle example

3 * 120 = 360

and in the pentagon example

5 * 72 = 360 .

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Change the ?? in line 7 below to the amount to turn each time to draw a 12-sided polygon (called a dodecagon). If you get it right the turtle will draw a 12-sided closed polygon.

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Checkpoint 20.3.1.

How much does mia need to turn in the program above to create a closed dodecagon (12-sided figure)? Only one of these works.

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15
This one will not close
30
Exactly! 12 * 30 = 360
12
No, 12 * 12 is 144, which is not a multiple of 360
90
This one will generate a square, three times. 12 * 90 = 1080 = 360 * 3

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Now that we have identified a pattern, it is a bit silly to write separate functions like square and dodecagon for all the shapes. They are all basically the same and we don’t like repeating ourselves.

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In this case, the way to avoid repeating ourselves is to make an abstraction - a procedure that can draw any polygon. It will take parameters to control how many sides there are and how long to make each side.

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Checkpoint 20.3.2.

Arrange the blocks in the correct order and indentation to make the polygon procedure. This procedure will use begin_fill and end_fill to make the shapes be colored.

Those commands do not need to be repeated - we only want to use each one once - so make sure they are not

You will not need to use all of them.

def polygon(turtleName, sides, size)
---
 turtleName.begin_fill()
---
 for s in range(sides):
---
 for s in range(size)  #paired
---
  turtleName.forward(size)
---
  turtleName.forward(sides)  #paired
---
  turtleName.left(360 / sides)
---
  turtleName.turn(sides / 360)  #paired
---
 turtleName.end_fill()

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Once you have figured out the procedure, add it to the program below:

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