Regular Polygons

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dpietrobon's picture
Submitted by dpietrobon on Sat, 22/02/2025 - 14:06

A polygon is a closed shape formed by straight lines. A regular polygon has sides of equal length and angles of equal size. Convex regular polygons are the common shapes we associate with 3, 4, 5, or more sides, such as the equilateral triangle, square, pentagon, hexagon, and so on.

 

To draw a regular polygon with n sides, the turtle takes equal steps forward and turns at a consistent angle after each step. Since a full rotation is 360°, the turtle must turn 360 / n degrees after every step to complete the polygon.

For example, the Logo code to draw a hexagon is:

pd repeat 6 [ fd 1 rt 360 / 6 ]

Using this idea, the procedure for drawing a polygon with n sides and radius r may be given by:

to polygon :n :r 

; Generate regular n-gon with radius r  

make "s 2 * :r * sin ( 180 / :n ) ; Side length

rt 90 fd :r rt 90 + 180 / :n ; Set initial position

pd repeat :n [ fd :s rt 360 / :n ] pu line ; Draw faces

pcoff setdc random 1000 random 1000 random 1000 settr 800 ; Set random face color

face pd repeat :n [ fd :s rt 360 / :n ] pu line ; Draw faces

rt 90 - 180 / :n fd :r rt 90 ; Reset final position

end

 

Comments

Andy's picture

Suggestions

Submitted by Andy on Thu, 27/02/2025 - 22:58.

Some suggestions for this blog:

  1. After the introduction paragraph and before the 3D world, you can insert a teaser break.  The teaser break marks the end of content to display on the homepage.
  2. The Logo codes could be formated as in my previous comment.
  3. How do you calculate the side length using :n and :r could be explained.

Thanks for sharing this excellent polygon procedure.

Andy's picture

Nice polygon with given radius

Submitted by Andy on Thu, 27/02/2025 - 22:51.

I have been teaching about polygon with given number of side for primary students. The fixed radius or a given radius would be a secondary school level challenge. I used the codes below to draw 3 polygons in the order of number of side.