Monday, November 14, 2016

The Supermoon Period

  A supermoon occurs when a full moon and lunar perigee occur at approximately the same time. There was one just before sunrise this morning, 14 Nov 2016.  To find out when the next one will occur we can compute the average time between supermoons using two lunar periods.

So supermoons are spaced about 13½ calendar months apart and the next one should occur at the beginning of January 2018 followed by one about the middle of February 2019. The Lunarian gives the following circumstances for these events.

Lunar perigee 1 Jan 2018 21:48
Full Moon      2 Jan 2018 02:24

Lunar perigee 19 Feb 2019 09:02
Full moon      19 Feb 2019 15:53

The computed interval for the Supermoon Period seems to work quite well. One can expect some variation for this time interval due to the nonuniform motion of the Earth in its orbit.

Wednesday, November 9, 2016

Magic Squares

  A magic square is an n x n grid of numbers whose rows, columns and diagonals all have the same sum. One can create a magic square by filling a 4 x 4 matrix with 7 numbers in the positions below. I included the numbers of the election date, 11/8/2016, in the bottom left corner. The remaining 3 numbers were chosen at random. If one knows the value of the sums, Σ, one can immediately solve for some of the unknowns.

We can use the unused equations to separate the the known variables from the unknown variables as follows and solve the system of equations for the unknowns k, l, o & p. One of the equations is redundant so we choose 4 for which the determinant of matrix, M, is nonzero. Here the determinant D = |M| = 2.

Filling the calculated values into our magic we get the following matrix which checks out correctly.

Each value of Σ generates a new magic square. One can try to choose the minimum value for Σ for which all the numbers are non-negative.