Multimagic square 36, 100, ... Value for Trimagic squares 1, 50, 675, 4624, ... Similarly the tetramagic sequence 4-Power 0, 1, 16, 81, 256, 625, 1296, ... Sum of 4-Power 0, 1, 17, 98, 354, 979, 2275, ... Sums for Tetramagic squares 0, 1, 177, ... The first known bimagic square has order 8 and magic constant 260 and a bimagic constant of 11180. It has been conjectured by Bensen and Jacoby that no nontrivial bimagic squares of order less than 8 exist. This was shown for magic squares containing the elements 1 to "n" by Boyer and Trump. However, J. R.
1/4 + 1/16 + 1/64 + 1/256 + ⋯ for triangles, as in the figure on the right: if the large triangle has area 1, then the largest black triangle has area , and so on. The figure as a whole has a self-similarity between the large triangle and its upper sub-triangle. A related construction making the figure similar to all three of its corner pieces produces the Sierpiński triangle. Archimedes encounters the series in his work "Quadrature of the Parabola". He is finding the area inside a parabola by the method of exhaustion, and he gets a series of triangles; each stage of the construction adds an area