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 + ⋯ times the area of the previous stage. His desired result is that the total area is times the area of the first stage. To get there, he takes a break from parabolas to introduce an algebraic lemma: Proposition 23. Given a series of areas , of which "A" is the greatest, and each is equal to four times the next in order, then Archimedes proves the proposition by first calculating On the other hand, Subtracting this equation from the previous equation yields and adding "A" to both sides gives the desired result. Today, a more standard phrasing of Archimedes' proposition