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January 25, 2026
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R1
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Simple
Advanced
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Simple
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Definition
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R2
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Definition, Flipping and Prop
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Table
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More Examples
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Complex Rotations
Rotvision
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Roticvision
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Definition
Simple
Trigonometry
Dot Product
Division
Definition
Flipping
Advanced
Roots
Definition
Simple
Expressions
Advanced
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R3
Addition
Rotation
Definition and Quaternions
Wave Number Prop
Using the Wave Number Prop
Euler and Tait-Bryan Angles
Simple Examples
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Zero Rules
More
Complex Rotations
Example 1
Example 2
Example 3
Comparing Wave Number and Quaternion Efficiency
Coordinates
Spherical
Hyperspherical
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Multiplication links to Rotation and Rotication
Dot Product
Cross Product
Division
Definition
Self Division and Unitaries
Multiplicative Inverses
Simultaneous Equations
Roots
Definition
Squares
Cubes
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
Quaternion Comparison
Quantum
Introduction
Theory
Classical Qubits
Wave Number Bloch Sphere
State Equations
Bra-Kets or Dirac’s Notation
Basis & Born’s Rule
Single and Multipart Qubits
Matrices
Superposition
Gates
Introduction
Pauli and σf
Haadamard
Circuits
Introduction
CNOT Gate
AH2 Gate
CCNOT Gate
CZ Gate
Bell States
Bellagio
Setup
Part 1
Part 2
Running the Bellagio Circuit
Calculator
Calculator
Guide
Report Bugs
Shop
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Contact
Home
About
Basics
Principles
Operations
Axioms
Axioms and Primitives
Definitions
Opposite Values
Dimensions
Axes
Operations
General
Equality
Rotation
General Axioms
Theorems
Introduction
Zero
Flipping
Distributive
Multiplicative Inverses
Quotients
Squares
More
Inequalities
Order Properties of Integers
Ratios
Property of Order
R1
Addition
Rotation
Definition, Flipping and Prop
Table
Rotvision
Multiplication
Definition
Simple
Advanced
Flipping
Division
Definition
Simple
Advanced
Flipping
Roots
Definition
Expressions
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R2
Addition
Rotation
Geometry and Trigonometry
Definition, Flipping and Prop
Simple Examples
Cartesian & Euler
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Other Rules
More Examples
Rotation and Multiplication Examples
Complex Rotations
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Dot Product
Division
Definition
Flipping
Advanced
Roots
Definition
Simple
Expressions
Advanced
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R3
Addition
Rotation
Definition and Quaternions
Wave Number Prop
Using the Wave Number Prop
Euler and Tait-Bryan Angles
Simple Examples
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Zero Rules
More
Complex Rotations
Example 1
Example 2
Example 3
Comparing Wave Number and Quaternion Efficiency
Coordinates
Spherical
Hyperspherical
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Multiplication links to Rotation and Rotication
Dot Product
Cross Product
Division
Definition
Self Division and Unitaries
Multiplicative Inverses
Simultaneous Equations
Roots
Definition
Squares
Cubes
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
Quaternion Comparison
Quantum
Introduction
Theory
Classical Qubits
Wave Number Bloch Sphere
State Equations
Bra-Kets or Dirac’s Notation
Basis & Born’s Rule
Single and Multipart Qubits
Matrices
Superposition
Gates
Introduction
Pauli and σf
Haadamard
Circuits
Introduction
CNOT Gate
AH2 Gate
CCNOT Gate
CZ Gate
Bell States
Bellagio
Setup
Part 1
Part 2
Running the Bellagio Circuit
Calculator
Calculator
Guide
Report Bugs
Shop
Downloads
Contact
Home
About
Basics
Principles
Operations
Axioms
Axioms and Primitives
Definitions
Opposite Values
Dimensions
Axes
Operations
General
Equality
Rotation
General Axioms
Theorems
Introduction
Zero
Flipping
Distributive
Multiplicative Inverses
Quotients
Squares
More
Inequalities
Order Properties of Integers
Ratios
Property of Order
R1
Addition
Rotation
Definition, Flipping and Prop
Table
Rotvision
Multiplication
Definition
Simple
Advanced
Flipping
Division
Definition
Simple
Advanced
Flipping
Roots
Definition
Expressions
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R2
Addition
Rotation
Geometry and Trigonometry
Definition, Flipping and Prop
Simple Examples
Cartesian & Euler
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Other Rules
More Examples
Rotation and Multiplication Examples
Complex Rotations
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Dot Product
Division
Definition
Flipping
Advanced
Roots
Definition
Simple
Expressions
Advanced
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R3
Addition
Rotation
Definition and Quaternions
Wave Number Prop
Using the Wave Number Prop
Euler and Tait-Bryan Angles
Simple Examples
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Zero Rules
More
Complex Rotations
Example 1
Example 2
Example 3
Comparing Wave Number and Quaternion Efficiency
Coordinates
Spherical
Hyperspherical
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Multiplication links to Rotation and Rotication
Dot Product
Cross Product
Division
Definition
Self Division and Unitaries
Multiplicative Inverses
Simultaneous Equations
Roots
Definition
Squares
Cubes
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
Quaternion Comparison
Quantum
Introduction
Theory
Classical Qubits
Wave Number Bloch Sphere
State Equations
Bra-Kets or Dirac’s Notation
Basis & Born’s Rule
Single and Multipart Qubits
Matrices
Superposition
Gates
Introduction
Pauli and σf
Haadamard
Circuits
Introduction
CNOT Gate
AH2 Gate
CCNOT Gate
CZ Gate
Bell States
Bellagio
Setup
Part 1
Part 2
Running the Bellagio Circuit
Calculator
Calculator
Guide
Report Bugs
Shop
Downloads
Contact
Menu
Home
About
Basics
Principles
Operations
Axioms
Axioms and Primitives
Definitions
Opposite Values
Dimensions
Axes
Operations
General
Equality
Rotation
General Axioms
Theorems
Introduction
Zero
Flipping
Distributive
Multiplicative Inverses
Quotients
Squares
More
Inequalities
Order Properties of Integers
Ratios
Property of Order
R1
Addition
Rotation
Definition, Flipping and Prop
Table
Rotvision
Multiplication
Definition
Simple
Advanced
Flipping
Division
Definition
Simple
Advanced
Flipping
Roots
Definition
Expressions
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R2
Addition
Rotation
Geometry and Trigonometry
Definition, Flipping and Prop
Simple Examples
Cartesian & Euler
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Other Rules
More Examples
Rotation and Multiplication Examples
Complex Rotations
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Dot Product
Division
Definition
Flipping
Advanced
Roots
Definition
Simple
Expressions
Advanced
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
R3
Addition
Rotation
Definition and Quaternions
Wave Number Prop
Using the Wave Number Prop
Euler and Tait-Bryan Angles
Simple Examples
Table
Universal Rules of Rotation
Return and Orthogonal Rules
Reversal, Remain and Zero Rules
More
Complex Rotations
Example 1
Example 2
Example 3
Comparing Wave Number and Quaternion Efficiency
Coordinates
Spherical
Hyperspherical
Rotvision
Rotication
Roticvision
Multiplication
Definition
Simple
Trigonometry
Multiplication links to Rotation and Rotication
Dot Product
Cross Product
Division
Definition
Self Division and Unitaries
Multiplicative Inverses
Simultaneous Equations
Roots
Definition
Squares
Cubes
Exponentiation
Definition
Fractions, Flip Sign and Rules
Logs
Quaternion Comparison
Quantum
Introduction
Theory
Classical Qubits
Wave Number Bloch Sphere
State Equations
Bra-Kets or Dirac’s Notation
Basis & Born’s Rule
Single and Multipart Qubits
Matrices
Superposition
Gates
Introduction
Pauli and σf
Haadamard
Circuits
Introduction
CNOT Gate
AH2 Gate
CCNOT Gate
CZ Gate
Bell States
Bellagio
Setup
Part 1
Part 2
Running the Bellagio Circuit
Calculator
Calculator
Guide
Report Bugs
Shop
Downloads
Contact
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