Here's the question you clicked on:
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?
|dw:1381254913806:dw|
do I give away the answer...or just wait for someone else to figure it out :)
If you want someone else to discover it, then I guess we wait.
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.
sure...by induction...this being the basis step (or one vertex more than the basis step)
Hopefully a student will drop in and try it. :)
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 :)
Well what was the reaction?
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.
Yep, it wasn't suppose to react that way to that kinda messing.
kids these days, they just cant be trusted lol
Is the polygon a kid, now?
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.
did i mention, my daughter is living with me now? ;)
So you have a polygon living with you?
Just remember you cannot enter into a polygon. There is no opening. You can not hop into it.
a 3 sided polygon that is disguising itself as a 5 sided poly of indeterminable area. We are in flatland right?
all these polys look the same to me :)
guess i found a method, il wait for others to try proly
my method is patent pending .. so no stealing it!!
What kinda straight lines are you talking about exactly?
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.
|dw:1381318076833:dw|
|dw:1381318112397:dw| Let m and l be parallel.
|dw:1381318171834:dw| Now we have a 4-gon with the same area as that 5-gon we started out with.
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.