November 2, 2024
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Definition – Operations

Introduction

This post defines the Wave Number math operations: Addition, rotation, rotication, multiplication and flipping.

Addition

a + b denotes the result of adding two Opposite Values a and b. This result is referred to as the sum of a and b.

Rotation (↺?)

The second operation is rotation. a? b denotes the result of rotating an Opposite Value b by the angle a. This result is referred to as the rotation of b by a. The angle a can be expressed in degrees or radians. When a has a ^ Opposite Sign, ab represents a counterclockwise rotation, and when a has a v Opposite Sign, the operation performs a clockwise rotation. 

The symbol ?  represents the point or axis of rotation indicated by Opposite Values. If the symbol is blank, assume the rotation is around an imaginary z-axis, a point at the origin (0, 0) in R1 and R2.

If blank in R3, assume the rotation is around the z-axis (0, 0, j^). When included, it represents a rotation around the point indicated in R1 and R2 and the axis indicated in R3.

Rotication (R↺? )

The third operation is rotication. a R↺?  b denotes the rotication of an Opposite Value b by the angle a. This result is referred to as the rotication of b by a . Rotication consists of two steps. The first step is a rotation of b by a. The second step multiplies the result of this rotation by the magnitude of the axis of rotation.

Multiplication

The fourth operation is multiplication. a*b  or ab denotes the result of multiplying two Opposite Values a and b. This result is referred to as the product of a and b. Multiplication is assumed when an Opposite Value precedes or follows a round bracket, or when two round brackets are adjacent.

Flipping


The final operation is flipping, which specifically rotates an Opposite Value a to its equivalent with the Opposite Sign changed. This corresponds to flipping from one side of the axis to the other. The superscript symbol () denotes the flipping operation. Consequently, flipping  a results in the additive inverse of  a, such that aa= 0.

The number 0 is special and does not have an Opposite Type or Sign. Flipping 0 makes no sense. However, calculations may yield 0, in which case 0 = 0.

Flipping necessitates the use of an alternative orthogonal axis to the one on which the point is located. This can be a real axis, such as the x-axis in R2 for a point on the y-axis, or the imaginary z-axis in R1 or R2.

 

Next: General Definitions

Previous: Operations

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