Other Talk "Otterville" plus Religion/Politics

Math Problem Help

Old 08-22-05, 08:17 AM
DVD Talk Hero
Thread Starter
Join Date: Nov 1999
Posts: 36,980
Math Problem Help

Anyone know the name of this math problem or any links with info on it. I solved it, just wanted to see if there was anything else on it.

You take a 1 x 1 square. Draw 4 quarter circles with a radius of 1 with the center of each at the four vertices of the square. Compute the area of the intersection.

Last edited by Venusian; 08-22-05 at 08:47 AM.
Venusian is offline  
Old 08-22-05, 08:20 AM
DVD Talk Legend
Charlie Goose's Avatar
Join Date: Jul 2000
Location: Sesame Street (the apt. next to Bob's)
Posts: 20,199
Charlie Goose is offline  
Old 08-22-05, 08:44 AM
DVD Talk Legend
Join Date: Apr 1999
Location: Aostin, TX, USA
Posts: 19,876
Y2K Falcon is offline  
Old 08-22-05, 10:03 AM
DVD Talk Hero
Join Date: Jul 2001
Location: MI
Posts: 25,043
That can't be right, because it evaluates to ~2.05, and you started with a 1 x 1 square, and excluded part of it.
OldDude is offline  
Old 08-22-05, 10:21 AM
Join Date: Sep 1999
Location: Memphis, TN
Posts: 11,544
Ugh. Damn signs. I screwed up a sign in one of my steps. Amongst another couple of mistakes . Sorry. Fixed now.

Detailed solution:
The intersection area can be described as a smaller square surrounded by four areas with a circle segment on each side. The arc of each of those circle segments is 30 degrees. You can figure this out by sheer geometry.
-Since the arc is 30, you can use the Law of Cosines to get the length of that side of the small square in the center as sqrt( 2 - sqrt(3)). The area of the center square is therefore 2 - sqrt(3).
-The area of that whole sector is 30/360 * pi = pi/12. The area of the isoceles triangle from one corner to the opposite side of that square is (.5 * sin 30) = 1/4. The area, therefore, of the segment on the edge of the center square is pi/12 - 1/4.
-Then you add the area of the center square and the area of the 4 segments surrounding it and you get 2 - sqrt(3) + 4 * (pi/12 - 1/4) = 2 - sqrt(3) + pi/3 -1 = 1 + pi/3 - sqrt(3).

Last edited by Otto; 08-22-05 at 10:38 AM.
Otto is offline  
Old 08-22-05, 10:44 AM
DVD Talk Hero
Join Date: Jul 2001
Location: MI
Posts: 25,043
Agreed. I had a solution that evaluated numerically to that 30 minutesago, but I made half a dozen mistakes "simplifying" it to that form. Finally got the form to agree with the number. Numerically, is is 0.3151 of the area of the square.
OldDude is offline  

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is On
Trackbacks are Off
Pingbacks are Off
Refbacks are Off

Thread Tools
Search this Thread

Archive Advertising Cookie Policy Privacy Statement Terms of Service

Copyright 2018 MH Sub I, LLC dba Internet Brands. All rights reserved. Use of this site indicates your consent to the Terms of Use.