Search results
Results From The WOW.Com Content Network
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number. There are infinitely many square triangular numbers; the first few are: 0, 1, 36, 1225, 41 616, 1 413 721, 48 024 900, 1 631 432 881, 55 420 693 056, 1 882 672 131 025 (sequence A001110 in the OEIS)
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7.
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n -gonal numbers. That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on.
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 nth coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the nth region is n times n x n.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...
Trinomial expansion. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by. where n is a nonnegative integer and the sum is taken over all combinations of nonnegative indices i, j, and k such that i + j + k = n. [1] The trinomial coefficients are given by.
A trigonometric number is a number that can be expressed as the sine or ... In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner ...