September 21, 2026
Wave Numbers replace negative numbers with Hat and Vee Opposite Values. Opposite Values with the same Counter cancel each other, creating a new framework for arithmetic and rotation.
The Wave Number Calculator is now available for R1, R2 and R3. Try out Addition, Multiplication, Division, Roots, Dot and Cross products and some other exotic operations such as Rotation and Rotication.
The Wave Number system is a new mathematical framework that operates without negative or imaginary numbers. Built around the concept of Opposite Values, it provides a complete set of mathematical operations and offers computational advantages over quaternions for rotations.
Explore how Wave Numbers can represent qubits, rotations and quantum states using an intuitive geometric framework.
Explore rotation, coordinates and quantum states with our educational Cartesian, Quaternion, Wave Number and Bloch Sphere balls
R3 Multiplication Link between Formulae: The R3 multiplication and rotication formulae also demonstrate how multiplication links to rotication. The post on multiplication use
The Wave Numbers system comprises of the ^ Opposite Values (called ‘Hat’ Opposites) and the v Opposite Values (called ‘Vee’ Opposites). All the Opposite Values in the Wave Numbers system start from 0.
Introduction: This post starts with a description of long multiplication in R3. It then describes the R3 multiplication links to rotation and rotication
Comparison of Wave Number and Quaternion Multiplication Tables: An earlier post makes a detailed comparison of the Wave Number Multiplication table and the
Rotation: In this post, we delve into the Return and Orthogonal rules of rotation within the three-dimensional space R3. These principles are foundational
Use a Tennis Ball as a Rotation Prop: A physical prop helps to understand 3d rotation. There are many digital 3d spheres on-line.
Categories: Addition, Axioms, Bloch, Bra-kets, Calculus, Cartesian, Circuits, Coordinates, Cross-Product, Cube, Roots, Cubes, Curves, Dirac, Division, Dot-Product, Equality, Equations, Euler, Exponentation, Expression, Flipping, Gates, Geometry, Hyperspheres, Inequality, Integers, Inverses, Linear, Logs, Multiplication, Operations, Primitives, Principles, Props, Quadratic, Quantum, Quaternions, Qubits, R1, R2, R3, Roots, Rotation, Rotication, Simultaneous Equations, Spheres, Squares, States, Superposition, Tables, Theorems, Trigonometry, Unitaries, Zero.
