Wave Number Calculator – Guide
Introduction This is the online Wave Number calculator guide. The calculator supports the R1, R2, and R3 dimensions. Chose from these using the top menu bar of the calculator. Wave Numbers use Opposite Values. Each Opposite Value consists of 3 parts. The first is the Counter. This gives the magnitude. The second part 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 […]
R3 – Cube Roots
Similar to R3 Division, cube roots in R3 are solved using simultaneous equations. Simultaneous Equations Needed The following is a method for finding R3 cube roots using simultaneous equations. For example, take the cubic equation: As described in an earlier post, the square of the expression (a? + bi? + cj?)2 is (a2? + b2i2 + c2j2). This allows […]
R3 – Square Roots
Definition The square root of an expression in R3 is made of the roots of the individual Opposite Values with the signs remaining constant. Square of an Expression Given the generic expression (a? + bi? + cj?): Note that as a result of the Zero Rules of Rotation a??b?? + b??a?? = 0, so This […]
R3 – Roots – Definition
This post covers R3 roots including their derivation. Definition Wikipedia defines the square root as ‘a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x.’ Wave Numbers uses this definition and adapts it for roots of higher degrees. The root of an Opposite Value […]
R2 – Roots – Advanced
This post covers the use or De Moivre’s formula as an advanced method of calculating roots in R2. Some examples are provided. Formula The roots of any Opposite Value can be calculated using the formula below which is based on De Moivre’s formula. This formula relies on the fact that the root of an Opposite […]
R2 – Roots – Expressions
This post looks at the roots of expressions in R2. Calculate the full root of an R2 expression as the root of the Counter times the root of the Unitary. This applies whether the Counter is known or is a variable. Example 1 Example 2 Example 3 The multiplications below show that (x^ + xi^)2 = […]
R2 – Roots – Simple
This post provides some simple examples of R2 roots. The calculations behind some of the examples are also shown. Examples Firstly, here are some examples of the roots of i^. Secondly, here are examples of the roots of iv. Finally, here are some examples of non unitary roots. Sample Calculations These calculations show how these […]
R2 – Roots – Definition
This post on R2 roots covers the definition of roots and how roots are derived from the R2 multiplication table. Examples of square, cube and higher roots are given. Definition Wikipedia defines the square root as ‘a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or ) […]
R1 – Roots – Expressions
This post examines some examples of the full roots of expressions in R1. Calculate the full root as the root of the Counter times the root of the Unitary. Examples Conclusion Our online calculator can help with the calculation of the roots of R1 expressions. Next: Exponentiation Previous: Roots Definition