BOUNDS ON PI - DOUBLE PRECISION BINOMIAL THEOREM VERSION.
                                                              N     SIDES    SIDE LENGTH   PI - LOWER BOUND   PI - UPPER BOUND
                                                               3       8.        .765367     3.061467458921     4.959315235374
                                                                4      16.        .390181     3.121445152258     3.878006734963
                                                                5      32.        .196034     3.136548490546     3.477392565633
                                                                6      64.        .098135     3.140331156955     3.302370812490
                                                                7     128.        .049082     3.141277250933     3.220307554543
                                                                8     256.        .024543     3.141513801144     3.180543968220
                                                                9     512.        .012272     3.141572940367     3.160968277095
                                                               10    1024.        .006136     3.141587725277     3.151255641334
                                                               11    2048.        .003068     3.141591421511     3.146417964326
                                                               12    4096.        .001534     3.141592345570     3.144003766021
                                                               13    8192.        .000767     3.141592576585     3.142797824426
                                                               14   16384.        .000383     3.141592634339     3.142195142707
                                                               15   32768.        .000192     3.141592648777     3.141893874079
                                                               16   65536.        .000096     3.141592652387     3.141743257818
                                                               17  131072.        .000048     3.141592653289     3.141667954200
                                                               18  262144.        .000024     3.141592653515     3.141630303519
                                                               19  524288.        .000012     3.141592653571     3.141611478460
                                                               20 1048576.        .000006     3.141592653585     3.141602066002