R3 – Multiplication Links to Rotation and Rotication – Part 2
R3 Multiplication Link between Formulae: The R3 multiplication and rotication formulae also demonstrate how multiplication links to rotication. The post on multiplication use of trigonometry gives the formula for multiplication as: Part 1 of this post shows how the rotication formula can be rewritten in terms of Opposite Value types as: The multiplication calculations below […]
R3 – Multiplication Links to Rotation and Rotication – Part 1
Introduction: This post starts with a description of long multiplication in R3. It then describes the R3 multiplication links to rotation and rotication and how the different operations move a point. Long Multiplication Calculate (5^ + 7iv + 2j^)*(4v + 6iv + 4jv) = (20^ + 30iv + 66jv) by long multiplication and using the R3 multiplication table. For example: 4v […]
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 […]
R1 – Multiplication – Flipping
The specific rotation of an Opposite Value a to its equivalent with the Opposite Sign changed is called flipping.
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 – 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 […]
R3 – Multiplication – Cross Product
Cross product multiplication in R3 uses the same approach as in classical mathematics. The cross product of the points and is written as and is given by the formula: Unlike for dot-product, the Opposite Signs are used in multiplication. For example: Conclusion Try this example of R3 cross product multiplication with our online calculator. […]
R3 – Multiplication – Dot Product
Dot product multiplication in R3 uses the same approach as in classical mathematics. The dot product of the points and is written as and is given by the formula where a flip () precedes the Counters when the Opposite Value is or : For example: Euclidean Geometry Wikipedia describes dot product as follows: […]
R3 – Multiplication – Advanced
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