R2 – Reversal, Remain and Zero Rules
This post describes 3 more universal rules of rotation in R2, the Reversal, Remain and Zero rules. The Reversal Rule in R2 The third universal rotation rule that applies in R2 is the Reversal rule . A rotation reverses when the result of the first rotation is multiplied by the Operator of the first computation […]
R2 – Return and Orthogonal Rules
This post describes the first 2 universal rules of rotation in R2, the Return and Orthogonal. Standard Rotation Definition Rotation is a fundamental operation in Wave Numbers and is supported by the facts expressed in its axioms. A rotation moves a point represented by Opposite Values to a location represented by other Opposite Values by a circular movement […]
R3 – Euler and Tait-Bryan Angles
Introduction This description of Euler and Tait-Bryan angles in R3 is based on the description of Euler Angles in Wikipedia. According to Euler, any rotation, R, is a combination of 3 Euler angles of rotation. There are two types of Euler Angles. The first are the classic Euler angles, also known as proper angles. The […]
R3 – Using the Rotation Ball
Standard Orientation To use the Wave Number Rotation Ball, hold it in a standard orientation before making any rotations. The standard orientation has X^ facing, Z^ to the north and Y^ to the east. The fixed x, y and z-axes The x, y and z-axes themselves do not move when rotating around them. It is […]
Operations
Introduction Wave Numbers require a re-evaluation of general mathematical operations such as addition, subtraction, rotation, multiplication and division. Operators, operations, and operands need new definitions within this system. In Wave Number mathematics, the key distinction between 1^ and 1v is that through interference they cancel each other out when they combine. Subtraction is not […]
R2 – Complex Rotations
Rotate about points other than the origin using a formula.
R2 – Rotation – Definition, Flipping and Prop
Understanding rotation in R2 is easier with the post-it-note prop.
R1 – Rotation – Multiplication Table
Orthogonal Rule The Orthogonal rule, 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 R1 multiplication table that follows. Multiplication Table The unitary multiplication table of R1 shows the result of multiplying by 1^ or 1v. Multiplying by 1^ equates […]
R1 – Rotation – Definition, Flipping and Prop
What is Rotation in R1? The Wave Number principles describe rotation as a fundamental operation. The rotation axioms support this. Rotation moves a point represented by an Opposite Value to a location represented by another Opposite Value. Rotation performs a circular movement around a single point axis represented by an Opposite Value. The single point […]
R3 – Complex Rotations – Example 1
Up to this point, we’ve focused on unitary rotations around a single axis on the unit sphere. Now, let’s delve into more complex rotations in R3, where the operand can be any combination of Opposite Values with any degree of rotation. This post introduces the Wave Number Rotation formula, based on Rodrigues’ formula for calculating […]