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Thread: Exterior Angles--how to

  1. #1
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    Exterior Angles--how to

    TeacherJ had a great idea to post step-by-step directions about how to create sketches.

    There is a sketch on Sketchpad Lesson Link about Exterior Angles that is pretty cool. It lets you shrink a pentagon to a point. As it shrinks you watch the exterior angles become the angles that sum to 360degrees. One of my teachers wanted to learn how it was constructed. I took the file apart and tried to make quadrilateral that would do the same thing. (Attached here). Unfortunately, it seems that 1-2 of the angles always "become" right angle(s) as the quadrilateral shrinks. I'm hoping that someone here can figure out my mistake.
    Attached Files
    Amber M. Smith
    Secondary Math Curriculum Technology Coach
    Cypress-Fairbanks ISD
    http://tinyurl.com/AmberSmithcfisd

  2. #2
    It seems like this is a problem not just on page J. The angles just have to be close enough to 90 degrees before shrinking for the problem to show up. On previous pages, if you adjust the quadrilateral, you can duplicate this error. On page J, you can prevent the right angle from showing up by adjusting the figure before shrinking. I still don't have an answer as to *why* it does this, though.

  3. #3
    Amber, this how-to sketch is fantastic. Thanks for sharing. I learned new techniques.

    I was able to duplicate the magically-appearing right angle on the "Pentagon Dilation" page by changing the target point dilation to something smaller (like 0.05px/biggest of 5) and making some of the exterior angles close-ish to 90.

    As far as I can tell, you're doing most everything right. I'm not an expert, so take what I say with some skepticism. I think the magically appearing right angle is caused by tolerance settings for detecting right angles in the program itself. When the target point dialation is close to 0 *and* when an angle is close to 90, it gives you something similar to a rounding error.

    My guess is that you'll need to either stay away from almost-right angles or change your equation for the target point dilation.

  4. #4
    Sketchpad Developer
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    teacherdraper is correct. There is a rounding error introduced when the 3 points of an angle are within a small fraction of a pixel from each other and the angle is close to 90 degrees. This is something we are we are looking into, and hope to resolve it in a future maintenance release.

  5. #5
    Wow, that was very good detective work, teacherdraper! Thanks, Jon for giving us the technical reason for the behavior.

  6. #6
    @all: Thanks.

    @jbrooks: I'm not that bothered by the rounding error, actually, now that I know that it's there. It would be great if you could eliminate it, of course, but calculators have us used to looking for rounding errors.

  7. #7
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    Thanks All! So good to know what was causing the issue and that it was because of a rounding error.
    Amber M. Smith
    Secondary Math Curriculum Technology Coach
    Cypress-Fairbanks ISD
    http://tinyurl.com/AmberSmithcfisd

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