Search results
Results from the WOW.Com Content Network
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 base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
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.
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 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
120 is . the factorial of 5, i.e., ! =.; the fifteenth triangular number, [2] as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is the smallest number to appear six times in Pascal's triangle (as all triangular and tetragonal numbers appear in it).
The number of domino tilings of a 4×4 checkerboard is 36. [10] Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. [11] The sum of the integers from 1 to 36 is 666 (see number of the beast). 36 is also a ...
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} .
In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions that are also triangular numbers. That is, if T n = n ( n + 1 ) / 2 {\displaystyle T_{n}=n(n+1)/2} denotes the n {\displaystyle n} th triangular number, then the doubly triangular numbers are the numbers of the form ...