myininaya
  • myininaya
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?
Mathematics
jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
|dw:1381254913806:dw|
Zarkon
  • Zarkon
do I give away the answer...or just wait for someone else to figure it out :)
myininaya
  • myininaya
If you want someone else to discover it, then I guess we wait.

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myininaya
  • myininaya
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.
Zarkon
  • Zarkon
sure...by induction...this being the basis step (or one vertex more than the basis step)
Zarkon
  • Zarkon
Hopefully a student will drop in and try it. :)
amistre64
  • amistre64
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 :)
myininaya
  • myininaya
Well what was the reaction?
amistre64
  • amistre64
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.
myininaya
  • myininaya
Yep, it wasn't suppose to react that way to that kinda messing.
amistre64
  • amistre64
kids these days, they just cant be trusted lol
myininaya
  • myininaya
Is the polygon a kid, now?
amistre64
  • amistre64
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.
amistre64
  • amistre64
did i mention, my daughter is living with me now? ;)
myininaya
  • myininaya
So you have a polygon living with you?
myininaya
  • myininaya
Just remember you cannot enter into a polygon. There is no opening. You can not hop into it.
amistre64
  • amistre64
a 3 sided polygon that is disguising itself as a 5 sided poly of indeterminable area. We are in flatland right?
myininaya
  • myininaya
Yes.
amistre64
  • amistre64
all these polys look the same to me :)
ganeshie8
  • ganeshie8
straight lines
ganeshie8
  • ganeshie8
guess i found a method, il wait for others to try proly
amistre64
  • amistre64
my method is patent pending .. so no stealing it!!
myininaya
  • myininaya
What kinda straight lines are you talking about exactly?
ganeshie8
  • ganeshie8
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.
myininaya
  • myininaya
|dw:1381318076833:dw|
myininaya
  • myininaya
|dw:1381318112397:dw| Let m and l be parallel.
myininaya
  • myininaya
|dw:1381318171834:dw| Now we have a 4-gon with the same area as that 5-gon we started out with.
myininaya
  • myininaya
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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