Testing ran0: volume of unit n-sphere, n = 2, 3, 4 # points pi (4/3)*pi (1/2)*pi^2 2 2.000000 0.000000 0.000000 4 3.000000 4.000000 8.000000 8 2.500000 4.000000 6.000000 16 3.250000 5.000000 4.000000 32 3.500000 4.500000 4.500000 64 3.187500 4.125000 5.250000 128 3.187500 4.250000 4.625000 256 3.093750 4.000000 4.437500 512 3.031250 3.921875 4.531250 1024 3.074219 3.898438 4.750000 2048 3.121094 4.113281 5.078125 4096 3.108398 4.103516 5.000000 8192 3.105469 4.097656 4.964844 16384 3.119873 4.139160 4.976562 32768 3.128906 4.156738 4.922852 actual 3.141593 4.188790 4.934802 Testing ran1: volume of unit n-sphere, n = 2, 3, 4 # points pi (4/3)*pi (1/2)*pi^2 2 2.000000 4.000000 0.000000 4 3.000000 2.000000 0.000000 8 2.500000 3.000000 4.000000 16 3.250000 4.500000 6.000000 32 3.375000 5.250000 6.000000 64 3.125000 4.125000 4.750000 128 3.281250 4.687500 5.375000 256 3.171875 4.312500 5.000000 512 3.226562 4.296875 4.812500 1024 3.261719 4.390625 5.031250 2048 3.152344 4.246094 4.976562 4096 3.125000 4.166016 4.921875 8192 3.139160 4.238281 5.023438 16384 3.128662 4.202637 4.930664 32768 3.141724 4.182617 4.902344 actual 3.141593 4.188790 4.934802 Testing ran2: volume of unit n-sphere, n = 2, 3, 4 # points pi (4/3)*pi (1/2)*pi^2 2 4.000000 4.000000 8.000000 4 5.000000 6.000000 12.000000 8 4.500000 5.000000 10.000000 16 4.250000 5.000000 7.000000 32 3.875000 4.250000 5.500000 64 3.562500 3.875000 5.500000 128 3.375000 3.812500 4.625000 256 3.328125 3.968750 4.750000 512 3.273438 4.109375 5.156250 1024 3.226562 4.085938 4.875000 2048 3.220703 4.156250 4.796875 4096 3.166016 4.089844 4.746094 8192 3.160645 4.115234 4.744141 16384 3.149902 4.131348 4.792969 32768 3.151489 4.167969 4.876953 actual 3.141593 4.188790 4.934802 Testing ran3: volume of unit n-sphere, n = 2, 3, 4 # points pi (4/3)*pi (1/2)*pi^2 2 4.000000 4.000000 0.000000 4 5.000000 4.000000 4.000000 8 3.500000 4.000000 6.000000 16 3.500000 4.500000 6.000000 32 3.500000 4.000000 5.500000 64 3.375000 4.500000 4.750000 128 3.375000 4.437500 5.250000 256 3.234375 4.343750 5.062500 512 3.257812 4.281250 4.906250 1024 3.230469 4.265625 4.937500 2048 3.185547 4.089844 4.773438 4096 3.182617 4.167969 4.691406 8192 3.149414 4.129883 4.726562 16384 3.151855 4.149414 4.820312 32768 3.139893 4.130859 4.854004 actual 3.141593 4.188790 4.934802