Short account of "best" relations, only the least convergent arccot argument is given. The "best" (among n-term relations) is the one with the smallest arccot argument as big as possible. E.g., the best known 4-term relation is +44[57] +7[239] -12[682] +24[12943] == 1 * Pi/4 n-terms min-arg 2 5 Machin (Y?) 3 18 Gauss (Y?) 4 57 Stormer (1896) 5 192 (1993), prev: Stormer (1896) 172 6 577 (1993) 7 2,852 (1993) 8 5,357 (2006), prev: (1993) 4,246 9 34,208 (2006), prev: (1993) 12,943, prev: Gauss (Y?) 5,253 10 54,193 (2006), prev: (1993) 51,387 11 390,112 (1993) 12 1,049,433 (2006), prev: (1993) 683,982 13 3,449,051 (2006), prev: (1993) 1,984,933 14 6,826,318 (2006) 15 20,942,043 (2006) 16 53,141,564 (2006) 17 201,229,582 (2006) 18 272,525,023 (2006) 19 595,484,173 (2006) 20 1,228,810,443 (2006) 21 3,261,365,450 (2006) 22 6,829,998,457 (2006) A (Y?) means I do not know the year. All relations are given here: http://www.jjj.de/arctan/