R2 – Multiplication -Trigonometry
This post covers features of a point in R2 and two methods for the multiplication of points. The first method is to multiply the R2 coordinates directly. The second method is to use multiplication formulae based on R2 trigonometry. Features of a Point The distance R of any point (a, b) from the origin is […]
R2 – Multiplication – Simple
This post looks at some simple multiplication of Opposite Values together and using counters. The examples show the commutativity, associativity and distributivity of R2 math multiplication. R2 Unitary Multiplication Table * 1^ 1v i^ iv 1^ 1^ 1v i^ iv 1v 1v 1^ iv i^ i^ i^ iv 1v 1^ iv iv i^ 1^ 1v […]
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 […]
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