R3 – Logs
Definition This post covers the definition of R3 logs, logarithm formulae and provides some examples. Wikipedia defines logs as follows: ‘In mathematics, logarithm (log) is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.’ Logs are useful in expressing […]
R3 – Exponentiation – Definition
Introduction This post covers the definition of R3 Exponentiation in Wave Numbers. In Wikipedia, exponentiation is defined as follows: ‘Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as “b raised to the power of n”. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: bn = […]
R3 – Roots – Definition
This post covers R3 roots including their derivation. Definition Wikipedia defines the square root as ‘a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x.’ Wave Numbers uses this definition and adapts it for roots of higher degrees. The root of an Opposite Value […]
R3 – Division – Definition
What is R3 Division? In the context of R3, division is defined as the inverse operation of multiplication. The result of dividing an operand by an operator is an expression such that when the operator is multiplied by this result, it yields the original operand. R3 division is a scalar operation that incorporates rotation through […]
R3 – Multiplication – Definition
What is R3 Multiplication? Multiplication in R3 is a scalar operation that incorporates rotation through Opposite Types and Signs. It follows a “times-add” process, with the Opposite Sign of the result determined by the multiplication table. It differs from R1 and R2 multiplication because it now brings in the concept of rotation in real space compared […]
R2 – Logs
This post covers the definition of R2 logs, logarithm formulae and provides some examples. Definition Wikipedia defines logs as follows: ‘In mathematics, logarithm (log) is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.’ Logs are useful in expressing […]
R2 – Exponentiation – Definition
Introduction This post covers the definition of R2 Exponentiation in Wave Numbers. It also includes reciprocals and examples. In Wikipedia, exponentiation is defined as follows: ‘Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as “b raised to the power of n”. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that […]
R2 – Roots – Definition
This post on R2 roots covers the definition of roots and how roots are derived from the R2 multiplication table. Examples of square, cube and higher roots are given. Definition Wikipedia defines the square root as ‘a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or ) […]
R2 – Division – Definition
What is R2 Division? R2 division is the inverse of R2 multiplication. The result of division of an operand by an operator is described by a math expression. Multiplying the operator with the result gives the operand. For example: It is a scalar type operation that takes into account the Opposite Signs. As the inverse of […]
R2 – Multiplication – Definition
What is R2 Multiplication? Multiplication in R2 is similar to multiplication of complex numbers in classical maths. It is a scalar type operation that takes into account rotation through the Opposite Signs. It can be considered a ‘times-add’ operation with the Opposite Sign of the result dependent on the R2 multiplication table. This means […]