## 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?

1. myininaya

|dw:1381254913806:dw|

2. Zarkon

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

3. myininaya

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

4. 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.

5. Zarkon

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

6. Zarkon

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

7. 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 :)

8. myininaya

Well what was the reaction?

9. 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.

10. myininaya

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

11. amistre64

kids these days, they just cant be trusted lol

12. myininaya

Is the polygon a kid, now?

13. 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.

14. amistre64

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

15. myininaya

So you have a polygon living with you?

16. myininaya

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

17. amistre64

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

18. myininaya

Yes.

19. amistre64

all these polys look the same to me :)

20. ganeshie8

straight lines

21. ganeshie8

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

22. amistre64

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

23. myininaya

What kinda straight lines are you talking about exactly?

24. 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.

25. myininaya

|dw:1381318076833:dw|

26. myininaya

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

27. myininaya

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

28. 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.