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If each book had a mass of 100 grams, all of them would have a total mass of 10 93 kilograms. In comparison, Earth's mass is 5.97 × 10 24 kilograms, [5] the mass of the Milky Way galaxy is estimated at 1.8 × 10 42 kilograms, [6] and the total mass of all the stars in the observable universe is estimated at 2 × 10 52 kg. [7]
A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube.
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (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 maps a number to its cube. It is an odd function, as
A centered cube number is a centered figurate number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with i 2 points on the square faces of the i th layer.
189 is a centered cube number [1] and a heptagonal number. [2] The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in two ways: 4 3 + 5 3 and 6 3 + (−3) 3. [3] The smallest number that can be written as the sum of two positive cubes in two ways is 1729. [4]
In mathematics, the centered polyhedral numbers are a class of figurate numbers, each formed by a central dot, surrounded by polyhedral layers with a constant number of edges. The length of the edges increases by one in each additional layer.
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.