Cube (algebra) in the context of Mathematical operation

The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one thousandth of a kilogram.

Originally defined in 1795 as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre [1 cm], and at the temperature of melting ice", the defining temperature (0 °C) was later changed to the temperature of maximum density of water (approximately 4 °C). Subsequent redefinitions agree with this original definition to within 30 parts per million (0.003%), with the maximum density of water remaining very close to 1 g/cm, as shown by modern measurements.

In mathematics, a cube root of a number x is a number y that has the given number as its third power; that is ${\displaystyle y^{3}=x.}$ The number of cube roots of a number depends on the number system that is considered.

Every real number x has exactly one real cube root that is denoted ${\textstyle {\sqrt[{3}]{x}}}$ and called the real cube root of x or simply the cube root of x in contexts where complex numbers are not considered. For example, the real cube roots of 8 and −8 are respectively 2 and −2. The real cube root of an integer or of a rational number is generally not a rational number, neither a constructible number.

In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together: n = n × n × n × n.

Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 and can be written as 3 × 3.

The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n, usually pronounced as "n squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (1 × 1). Hence, a square with side length n has area n. If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).

A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The first 100 terms sequence of triangular numbers, starting with the 0th triangular number, are

(sequence A000217 in the OEIS)

7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube.

As an early prime number in the series of positive integers, the number seven has symbolic associations in religion, mythology, superstition and philosophy. The seven classical planets resulted in seven being the number of days in a week. 7 is often considered lucky in Western culture and is often seen as highly symbolic.

In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.

A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.

The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared (144), "1,000" means twelve cubed (1,728), and "0.1" means a twelfth (0.08333...).

Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses A and B, as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and finally 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: 2 (a turned 2) for ten (dek, pronounced /dɛk/) and 3 (a turned 3) for eleven (el, pronounced /ɛl/).