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Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them; [3] in fact, it is the smallest positive integer with at least nine ...
A triangular number or triangle number counts objects arranged in an ... There are infinitely many triangular numbers that are also square numbers; e.g., 1, 36, 1225.
Square triangular number 36 depicted as a triangular number and as a square number. 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:
The triangular number sequence is the representation of the numbers in the form of equilateral triangle arranged in a series or sequence. These numbers are in a sequence of 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on.
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
Since 36 is also triangular, 666 is a doubly triangular number. [5] Also, 36 = 15 + 21 where 15 and 21 are triangular as well, whose squares (15 2 = 225 and 21 2 = 441) add to 666 and have a difference of 216 = 6 × 6 × 6.
All 36 (= (1 + 2 + 3) ... The sum of the i th row is i times a triangular number, from which it follows that the sum of all the rows is the square of a triangular number.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.