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myininaya

  • 2 years ago

Fun Geometry Question: If given the following 5-sided polygon with area A units squared, can you find a 3-sided polygon having the same area by messing with the given polygon?

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  1. myininaya
    • 2 years ago
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    |dw:1381254913806:dw|

  2. Zarkon
    • 2 years ago
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    do I give away the answer...or just wait for someone else to figure it out :)

  3. myininaya
    • 2 years ago
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    If you want someone else to discover it, then I guess we wait.

  4. myininaya
    • 2 years ago
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    I had to play a little with it, but it looks like we can do the same process for any convex n-gon to any convex (n-k)-gon.

  5. Zarkon
    • 2 years ago
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    sure...by induction...this being the basis step (or one vertex more than the basis step)

  6. Zarkon
    • 2 years ago
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    Hopefully a student will drop in and try it. :)

  7. amistre64
    • 2 years ago
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    im kinda wondering what "messing with the given polygon" might be defined as. I tried yelling at it, but not too sure if that worked :)

  8. myininaya
    • 2 years ago
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    Well what was the reaction?

  9. amistre64
    • 2 years ago
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    it recoiled in horror and confessed to being a three sided equi-areal assessment. I then gave it a cookie and we watched NCIS together, but on mute.

  10. myininaya
    • 2 years ago
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    Yep, it wasn't suppose to react that way to that kinda messing.

  11. amistre64
    • 2 years ago
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    kids these days, they just cant be trusted lol

  12. myininaya
    • 2 years ago
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    Is the polygon a kid, now?

  13. amistre64
    • 2 years ago
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    it might as well be .... if it sits there and argues with you and spews lies at every given moment, then it has to be a kid that spends all day sitting on the couch eating the chicken potpies straight out of the freezer.

  14. amistre64
    • 2 years ago
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    did i mention, my daughter is living with me now? ;)

  15. myininaya
    • 2 years ago
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    So you have a polygon living with you?

  16. myininaya
    • 2 years ago
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    Just remember you cannot enter into a polygon. There is no opening. You can not hop into it.

  17. amistre64
    • 2 years ago
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    a 3 sided polygon that is disguising itself as a 5 sided poly of indeterminable area. We are in flatland right?

  18. myininaya
    • 2 years ago
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    Yes.

  19. amistre64
    • 2 years ago
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    all these polys look the same to me :)

  20. ganeshie8
    • 2 years ago
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    straight lines

  21. ganeshie8
    • 2 years ago
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    guess i found a method, il wait for others to try proly

  22. amistre64
    • 2 years ago
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    my method is patent pending .. so no stealing it!!

  23. myininaya
    • 2 years ago
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    What kinda straight lines are you talking about exactly?

  24. ganeshie8
    • 2 years ago
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    was saying in amistre's flatland its all straight lines he sees.. he may not even see polys :) solution looks too simple after letting it settle in my head a bit... its just to do with making few constructions to straighten up multiple sides.

  25. myininaya
    • 2 years ago
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    |dw:1381318076833:dw|

  26. myininaya
    • 2 years ago
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    |dw:1381318112397:dw| Let m and l be parallel.

  27. myininaya
    • 2 years ago
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    |dw:1381318171834:dw| Now we have a 4-gon with the same area as that 5-gon we started out with.

  28. myininaya
    • 2 years ago
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    You can do this transaction one more time to get it down to a 3-gon with the same area as the 5 or 4-gon.

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