Mathematical Trivia

• Evens round pieces are even and odds are odd.
• The round pieces in the third column are the squares of those in the fourth.
• The triangles in the 2nd column are the sums of the rounds in the next two columns on the same row.
• The squares in the second column are formed by adding the respective triangles: i.e. 15 = 9 + 6 and 45 = 25 + 20.
• The pyramids are formed by a sum of squares which are the values of their component pieces. i.e. 91 = 6**2 + 5**2 + 4**2 + 3**2 + 2**2 + 1**2 and 190 = 8**2 + 7**2 + 6**2 + 5**2 + 4**2.
• The squares in the first column are obtained from the squares in the second column and the rounds in the fourth column from the following formula:
  round = n, square in second column = s then ((2n + 1) / n + 1)) s = square in second column.