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  2. Magic square - Wikipedia

    en.wikipedia.org/wiki/Magic_square

    The primary square is obtained by rotating the root square counter-clockwise by 90 degrees, and replacing the numbers. The resulting square is an associative magic square, in which every pair of numbers symmetrically opposite to the center sum up to the same value, 26. For e.g., 16+10, 3+23, 6+20, etc.

  3. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. This shows that the square of the n th triangular number is equal to the sum of the first n cube numbers. Also, the square of the n th triangular number is the same as the sum of the cubes of the integers 1 to n.

  4. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.

  5. Pentagonal number - Wikipedia

    en.wikipedia.org/wiki/Pentagonal_number

    The number x is pentagonal if and only if n is a natural number. In that case x is the nth pentagonal number. For generalized pentagonal numbers, it is sufficient to just check if 24x + 1 is a perfect square. For non-generalized pentagonal numbers, in addition to the perfect square test, it is also required to check if

  6. Squared triangular number - Wikipedia

    en.wikipedia.org/wiki/Squared_triangular_number

    A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.

  7. Square triangular number - Wikipedia

    en.wikipedia.org/wiki/Square_triangular_number

    Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .

  8. Super Bowl Squares: How Much Are Your Numbers Worth? - AOL

    www.aol.com/news/2013-02-01-super-bowl-squares...

    After all 100 spaces are filled, the digits 0 to 9 are randomly assigned to rows and columns. ... The numbers are based on a $50 a square game, with a $625 payout for the 1st and 3rd quarters, a ...

  9. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    The left side of this identity describes a square number, while the right side describes a triangular number, so the result is a square triangular number. Falcón and Díaz-Barrero (2006) proved another identity relating Pell numbers to squares and showing that the sum of the Pell numbers up to P 4n +1 is always a square: