R2 – Rotation and Multiplication – Examples
This post gives examples of R2 unitary rotations and the equivalent multiplications. A Double Rotation in R2 and its Equivalent Multiplication Take for example two rotations of 45^o around the z-axis from the point located at (1^, 0): A rotation of π^/4 ↺ 1^ moves a point at 1^ to (√2/2^, √2/2i^). See this in […]
R2 – Rotation – Multiplication Table
Orthogonal Rule used to Derive Multiplication Table The Axioms of Rotation provide the Orthogonal rule that states that multiplication by a unitary is the equivalent of rotation around the unitary’s single point axis by 90o. This allows the derivation of the R2 unitary multiplication table that follows. Multiplication by i^ Using the post-it note prop, it […]
R2 – Rotation – Cartesian & Euler
This post describes the role of Cartesian Coordinates and Euler’s formula in R2 Wave Number Rotation. Cartesian Coordinates and Euler’s Formula in R2 The Cartesian coordinates of a point are based on the intersection of perpendicular lines from the point with the x and y axes. For example: The Cartesian coordinates at π^/4 or 45^o […]
R2 – Rotation – Simple
This post gives some simple R2 examples of clockwise and counterclockwise rotations around the origin. Counterclockwise Examples Other R2 Rotations A similar set of clockwise R2 rotations can be done using v values of π. For example: πv/2 ↺ 1^ = iv: Other R2 rotation values of π^ or πv allow the movement of a […]
R2 – Addition
R2 Addition in Wave Numbers math is straightforward. Opposite Values with Opposite Signs cancel each other out through interference. It is commutative and associative. See examples below: Examples Conclusion Try these examples of R2 addition with our online calculator. Next: Rotation Previous: R1 Logs
R1 – Logs
This post covers the definition of R1 logs with details of the logarithmic formulae and 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 […]
R1- Exponentiation – Definition
This post covers the definition of exponentiation in R1. It also includes reciprocals and examples. Introduction 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 […]
R1 – Roots – Expressions
This post examines some examples of the full roots of expressions in R1. Calculate the full root as the root of the Counter times the root of the Unitary. Examples Conclusion Our online calculator can help with the calculation of the roots of R1 expressions. Next: Exponentiation Previous: Roots Definition
R1 – Roots – Definition
This post on R1 roots covers the definition of roots and how roots are derived from the multiplication table. It includes examples of square, cube and higher roots. Definition Wikipedia defines a root as: ‘an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: ‘ Wave […]
R1 – Roots – Addition
The root of x for any operation is defined in the Basics Operation section as the Opposite Value that undergoes an operation with itself to get x. The additional root, +n√, of an Opposite Value x is the Opposite Value that when added to itself n times gives the number x. The additional root […]