bonanova Posted May 9, 2013 Report Share Posted May 9, 2013 How much of the area of a 3 4 5 right triangle can be covered by three non overlapping circles completely contained by the triangle? 1 1 Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 9, 2013 Report Share Posted May 9, 2013 How much of the area of a 3 4 5 right triangle can be covered by three non overlapping circles completely contained by the triangle? 60% Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted May 9, 2013 Report Share Posted May 9, 2013 73.09% if biggest r =1 Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted May 9, 2013 Report Share Posted May 9, 2013 74.13% if biggest r =1 medium r = 0.5195 big r = 0.382 Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 10, 2013 Report Share Posted May 10, 2013 77% .53 =r1 1.01=r2 .41=r3 looks like i am approaching 80% Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted May 13, 2013 Author Report Share Posted May 13, 2013 I programmed the Malfatti circles for this problem. They give 66.27% coverage, thought initially to be optimal, clearly not. Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted May 13, 2013 Report Share Posted May 13, 2013 I programmed the Malfatti circles for this problem. They give 66.27% coverage, thought initially to be optimal, clearly not. but 1.01 for r1 is stepping on the line..the limit is 1 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted May 14, 2013 Author Report Share Posted May 14, 2013 I programmed the Malfatti circles for this problem. They give 66.27% coverage, thought initially to be optimal, clearly not. but 1.01 for r1 is stepping on the line..the limit is 1 The incircle has radius of 1. Good catch ... The competition is still open. I'll mark it solved at 74.13 until/unless a better number comes in. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted May 14, 2013 Report Share Posted May 14, 2013 darn Quote Link to comment Share on other sites More sharing options...
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bonanova
How much of the area of a 3 4 5 right triangle can be covered
by three non overlapping circles completely contained by the triangle?
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