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Thread: Help Constructing an n-gon

  1. #1

    Help Constructing an n-gon

    I am trying to construct an inscribed n-gon to represent a pizza with n slices. This is for my 7th grade fraction lessons.

    I know it could be done, but could someone please direct me to an article on creating an overlay.


  2. #2
    Sketchpad Developer
    Join Date
    Oct 2010
    Hi Msenjo,

    I'm not sure what you want when you mention "an article on creating an overlay," but I can give you a simple method for constructing an n-gon based on the center point and a vertex.

    1. Start with segment AB. Point A will be the center, and B will be one vertex.
    2. Create parameter n for the number of sides.
    3. Calculate the central angle for each slice: 360°/n. With the calculation selected, choose Transform | Mark Angle.
    4. Select point A and choose Transform | Mark Center.
    5. Select point B and the segment, and choose Transform | Rotate.
    6. Construct the segment from B to its rotated image. [See page "Ready" of the attached sketch.]
    Click image for larger version

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    Now you have one side: you can iterate to create the remaining n-1 sides:
    7. Calculate n-1. Label this calculated value depth.
    8. Select in order vertex B and the calculation depth.
    9. Hold the Shift key, and choose Transform | Iterate to Depth.
    10. A dialog box appears to let you choose the object to which you will iterate point B.
    11. Click in the sketch on the rotated image of B. (If the dialog box covers the rotated image, move the dialog box out of the way.)
    12. Click Iterate in the dialog box. The polygon appears. [See page "n-gon" of the attached sketch.]
    Click image for larger version

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    To inscribe this polygon in a circle, point A must the the center of the circle, and point B must be a point on the circle.

    There are other variants. For instance, to start with a single slice, everything remains the same except for step 6. For the new step 6, construct the segment from point A to point B' (the rotated image of B). Then select in order points A, B, and B', and choose Construct | Arc on Circle. This creates the first piece; now continue with step 7. [See pages "Slice" and "Pizza" of the attached sketch.]

    I hope this is useful!

    Attached Files
    Last edited by Stek; 10-01-2012 at 04:02 AM.

  3. #3
    Thank you so much! Regarding the overlay question, I was just hoping there was a way to layer a picture of a pizza behind the sketch. If not, I will print one and project over it on the whiteboard!!!

    Thanks again,

  4. #4
    Sketchpad Developer
    Join Date
    Oct 2010
    Matt, you can do this pretty easily. Just grab a picture of a pizza from the web (take one yourself the next time you order one), and paste the picture into Sketchpad. There's a whole set of ready-to-use pictures in the Picture Gallery (Help | Picture Gallery), but unfortunately none of them are of pizzas, which is why you'll need to locate your own picture.

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