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?

- myininaya

- jamiebookeater

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- myininaya

|dw:1381254913806:dw|

- Zarkon

do I give away the answer...or just wait for someone else to figure it out :)

- myininaya

If you want someone else to discover it, then I guess we wait.

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## More answers

- 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

sure...by induction...this being the basis step (or one vertex more than the basis step)

- Zarkon

Hopefully a student will drop in and try it. :)

- 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

Well what was the reaction?

- 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

Yep, it wasn't suppose to react that way to that kinda messing.

- amistre64

kids these days, they just cant be trusted lol

- myininaya

Is the polygon a kid, now?

- 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

did i mention, my daughter is living with me now? ;)

- myininaya

So you have a polygon living with you?

- myininaya

Just remember you cannot enter into a polygon. There is no opening. You can not hop into it.

- amistre64

a 3 sided polygon that is disguising itself as a 5 sided poly of indeterminable area. We are in flatland right?

- myininaya

Yes.

- amistre64

all these polys look the same to me :)

- ganeshie8

straight lines

- ganeshie8

guess i found a method, il wait for others to try proly

- amistre64

my method is patent pending .. so no stealing it!!

- myininaya

What kinda straight lines are you talking about exactly?

- 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

|dw:1381318076833:dw|

- myininaya

|dw:1381318112397:dw|
Let m and l be parallel.

- myininaya

|dw:1381318171834:dw|
Now we have a 4-gon with the same area as that 5-gon we started out with.

- 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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