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Thread: Backing: Why a Rectangle is bigger than a Square

  1. #1
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    Backing: Why a Rectangle is bigger than a Square

    Twists your minds but it makes sense!

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  2. #2
    Super Member auntpiggylpn's Avatar
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    Yes, it did twist my mind and No, it doesn't make sense to me!!!
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  3. #3
    Super Member Ditter43's Avatar
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    That is one of THOSE things!!!!!AArrrggg
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  4. #4
    Super Member Latrinka's Avatar
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    Mind boggling!
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  5. #5
    Senior Member Rubesgirl's Avatar
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    I'm math challenged on my good days! This seems totally improbable. If you take the square and reposition the parts without adding on, it should be the same no matter what... right?
    Wendy in VA

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  6. #6
    Moderator QuiltnNan's Avatar
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    Quote Originally Posted by Rubesgirl View Post
    I'm math challenged on my good days! This seems totally improbable. If you take the square and reposition the parts without adding on, it should be the same no matter what... right?
    ditto. doesn't make sense to me either
    Nancy in western NY
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  7. #7
    Senior Member raynhamquilter's Avatar
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    WHAT?! I don't understand it.
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  8. #8
    Super Member mom-6's Avatar
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    Makes my brain hurt! LOL!
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  9. #9
    Super Member ptquilts's Avatar
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    the solution, courtesy of Google (of course)

    actually these fit in the category of optical illusions

    In the first diagram, the red and blue triangle have different angles. W/o using trig, you can see the slope of the red triangle is portrayed as 2/5, while the blue triangle is portrayed as 3/8. In the picture with emboldened lines, the eye can't see the difference between .4 and .375, but it is there. If the angles were the same, the blue triangle would intersect halfway between the first 2 graph points, and in the second portion of that diagram, the blue shouldn't actually cover the 8 spaces spanned by the green and light blue figures. The hole comes from the fact that you cannot calculate the total area of the first triangle as (13*5)/2=32.5, because in actuality, keeping the angles to be the same, it's (12.5*5)/2=31.25. In the second picture, to keep the angles the same, you would have to add the areas because the blue wouldn't complete a triangle, so blue=7.5*3/2=11.25, green=8,lblue=7,red=2*5/2=5, total is magically 31.25

    The second diagram is the same principal, the angles that are being matched between the 2 symetrical orange pieces and the 2 symetrical green pieces don't match. Again, .375 vs .4, the unseen gap is what equates to the differing apparent areas.

  10. #10
    Super Member DogHouseMom's Avatar
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    PTQuilts - thanks for the "translation"

    I actually see it now ... look close at the red triangle and the green triangle - especially when matched to each other in the rectangle - and you will see that where the two meet to make a completed square of both red and green ... it's not a true square.
    May your stitches always be straight, your seams always lie flat, and your grain never be biased against you.

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