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Math prodigy, recluse, and Shen Yufei's husband. He develops a possible solution to the three-body problem. Pan Han (潘寒) Biologist, friend/acquaintance of Shen Yufei and Wei Cheng, and member of the Frontiers of Science. Sha Ruishan (沙瑞山) Astronomer, one of Ye Wenjie's students. Mike Evans (麦克·伊文斯)
Proof of the sum-and-difference-to-product cosine identity for prosthaphaeresis calculations using an isosceles triangle. The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems.
In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group G and a positive integer n , one asks for the smallest value of k such that every sequence of elements of G of size k contains n terms that sum to 0 .
As of today, this problem remains unsolved. Progress has been slow. Many of the same methods work for this problem and for Gauss's circle problem, another lattice-point counting problem. Section F1 of Unsolved Problems in Number Theory [2] surveys what is known and not known about these problems.
If you're having problems reading and retrieving your AOL Mail, the following troubleshooting steps: Use AOL Basic Mail. AOL Basic Mail gives you a way to see your emails in a simpler layout. This can often help when you're having problems retrieving mail on a slower connection speed. Reset your web settings
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners.
The ability to chain formulas together is what gives a spreadsheet its power. Many problems can be broken down into a series of individual mathematical steps, and these can be assigned to individual formulas in cells. Some of these formulas can apply to ranges as well, like the SUM function that adds up all the numbers within a range.
For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ratio 2, one can use the general solution for the sum of a geometric series with base 1 and ratio , obtaining , but this summation method fails for 1 + 1 + 1 + 1 + ⋯, producing a division by zero.