Author |
Topic: Find area of 22224444 octagon (Read 2466 times) |
|
Aryabhatta
Uberpuzzler
Gender: 
Posts: 1321
|
Find the area of a polygon with sides 4,4,4,4,2,2,2,2 inscribed in a circle.
(See attached image).
|
|
 IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
 |
Re: Find area of 22224444 octagon
« Reply #1 on: Apr 1st, 2009, 11:16am » |
 Quote  Modify
|
If I could solve 8 atan(1/r) + 8 atan(2/r) = 2 pi as quickly as quickmath, I'd happily give you the answer. But as it is, it would feel a bit like cheating.
[edit]
I wondered why a much simpler solution gave a different answer, but I got my edges wrong way around again.. Should have used arcsin, rather than arctan.
But the easy way is to rearrange the segments to form a square with the corners missing, which quickly gives (2 sqrt(2) + 4)2 - 4 = 20 + 16 sqrt(2)
[/edit]
|
| « Last Edit: Apr 1st, 2009, 11:34am by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Aryabhatta
Uberpuzzler
Gender:
Posts: 1321
|
|
Re: Find area of 22224444 octagon
« Reply #2 on: Apr 2nd, 2009, 8:48am » |
Quote Modify
|
Right towr! There is an easy way and a hard way. Apparently you found both easy 
|
| « Last Edit: Apr 2nd, 2009, 8:48am by Aryabhatta » |
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Find area of 22224444 octagon
« Reply #3 on: Apr 2nd, 2009, 8:57am » |
Quote Modify
|
The advantage of the hard way is that it works in general for circle-circumscribed polygons. But I wouldn't know how to do it without help from a maths program or some further studying.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print