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the number of vertices in a 6-cube, the fourth dodecagonal number, [8] and the seventh centered triangular number. [9] Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventh Erdős–Woods number. [10]
The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that
64 (2 6) and 729 (3 6) cubelets arranged as cubes ((2 2) 3 and (3 2) 3, respectively) and as squares ((2 3) 2 and (3 3) 2, respectively) In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together.
This translates to a hoppus foot being equal to 1.273 cubic feet (2,200 in 3; 0.0360 m 3). The hoppus board foot, when milled, yields about one board foot. The volume yielded by the quarter-girth formula is 78.54% of cubic measure (i.e. 1 ft 3 = 0.7854 h ft; 1 h ft = 1.273 ft 3). [42]
Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of “to the power of 4”. The sequence of fourth powers of integers, known as biquadrates or tesseractic numbers, is:
Equal to 1900 to 1600 BCE [2] ... Cube root of 2: 1.25992 10498 94873 16476 [Mw 6] [OEIS 8] Real root of = 46 to 120 ... Golomb–Dickman constant [64]
The sum within each gmonon is a cube, so the sum of the whole table is a sum of cubes. [7] Visual demonstration that the square of a triangular number equals a sum of cubes. In the more recent mathematical literature, Edmonds (1957) provides a proof using summation by parts. [8]
Similarly, the expression b 3 = b · b · b is called "the cube of b" or "b cubed", because the volume of a cube with side-length b is b 3. When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243.