R3 – Rotation Ball
Use a Tennis Ball as a Rotation Prop: A physical prop helps to understand 3d rotation. There are many digital 3d spheres on-line. They limit the user experience as they are only in 2d. It is difficult to find a physical 3d sphere to help with understanding rotation. A major requirement is to be able […]
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 […]
R2 – Rotation – Definition, Flipping and Prop
Understanding rotation in R2 is easier with the post-it-note prop.
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 – Rotation – Spherical Coordinates
This post covers the formula for spherical coordinates in R3. Examples of rotation using the formula are given. Cartesian Coordinates The Cartesian coordinates of a point are based on the intersection of perpendicular lines from the point with the x, y and z-axes. For example: the Cartesian coordinates at a point on the surface of […]
R3 – Rotation – Multiplication Table
Orthogonal Rule The layout of the R3 axes is defined as part of the Wave Number axioms. The Axioms of Rotation provide the Orthogonal rule which states that multiplication by a unitary is the equivalent of rotation around the unitary’s axis by 90o. This allows for the derivation of the R3 unitary multiplication table from rotations on the […]
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 […]