Squares and Circles: How Many Intersections?Date: 02/27/2002 at 18:52:25 From: Ashley S. Subject: Squares and Circles Our algebra class was given a problem on a test asking us the greatest possible number of times a square's edge can intersect with a circle when it is placed on top. They can be any size. The answer the teacher had was 4, but our entire grade is convinced it can be done in 8 different places, if done at the perfect sizes. We were wondering if you can solve this disagreement. Thank you, Ashley S. and 4th hour algebra Date: 02/27/2002 at 20:10:17 From: Doctor Ian Subject: Re: Squares and Circles Hi Ashley, Try this: 1. Draw a circle. . . . . . . . . . . . . 2. Draw a square whose center is also at the center of the circle, and which is just big enough so that the circle touches it at the center of each of its sides. (This is the smallest square that will fit completely around the circle.) +-------.-------+ | . . | |. .| | | . . | | |. .| | . . | +-------.-------+ 3. Draw another square whose center is the center of the circle, and which is just big enough to touch the circle at its corners. (This is the largest square that will fit completely inside the circle.) +-------.-------+ | . . | |.+-----------+.| | | | | . | | . | | | | |.+-----------+.| | . . | +-------.-------+ 4. Now draw _any_ square whose center is at the center of the circle, smaller than the first square, and larger than the second: +-------------+ |.............| |. +-------+ .| |. | | .| |. | | .| |. +-------+ .| |.............| +-------------+ In how many places does this square intersect the circle? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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