R3 – Multiplication Use of Trigonometry
This post covers the use of trigonometry in R3 multiplication. It also describes a trigonometric formula for multiplication. Finding the angles φx, φy and φz R3 multiplication uses trigonometry when it uses the cosines of the angles φx, φy and φz in the multiplication formula later in this post. The following is a description of […]
R3 – Multiplication – Simple
This post looks at some simple R3 multiplication of Opposite Values together and using counters. The examples show the distributivity of R3 multiplication. However, they also show that R3 multiplication is not associative or commutative. R3 Unitary Multiplication Table * 1^ 1v i^ iv j^ jv 1^ 1^ 1v j^ jv iv i^ 1v 1^ […]
R3 – Multiplication – Definition
What is R3 Multiplication? Multiplication in R3 is a scalar operation that incorporates rotation through Opposite Types and Signs. It follows a “times-add” process, with the Opposite Sign of the result determined by the multiplication table. It differs from R1 and R2 multiplication because it now brings in the concept of rotation in real space compared […]
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 – 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 ) […]
R2 – Multiplication – Dot Product
Dot product multiplication in R2 uses the same approach as in classical maths by using the formula: Dot product of a.b = (ax*bx) + (ay*by) where ax, bx, ay and by are the Counters of the Opposite Values a and b. For example: The dot product is based on the Counters of the Opposite Values […]
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 […]