The Mathematical Field (ePub)

While writing this book, I felt intuitively that readers would want to know whether the Creator knew about the Mathematical Field. I have answered the question in one section of this book. Unfortunately, I do not know whether you will agree with me because as I mention in the book, human beings have free will.

The book shows the beauty and purity of the Mathematical Field, particularly how the numbers follow specific rules to form different systems like Binary, Octal, Decimal, Duodecimal, and Hexadecimal, where they can have different place values. It is significant that the decimal system suits human beings and our design of 10 fingers and 10 toes for counting seems to be no accident. The rules of the decimal system allows the numbers to be easily added, subtracted, multiplied and divided. Even the higher functions of calculating square roots, cube roots, Sine, Cosine, Tan, logarithms, and exponentials can be easily calculated using a simple calculating machine. The numbers form sequences and series. The arithmetic and geometric series enable easy calculation of numbers using formulae. All the periodic functions like Sine, Cosine, Tan, and ex can be expressed as a series. The Algebraic Arm has shown us how lines and curves can be expressed as simple equations, which we can visualise on the Cartesian Plane in two dimensions. Through differentiation and integration, we can sketch curves and calculate areas and volumes. In the Geometric Arm, we can visualise the points forming lines and the lines forming different slopes and different angles. Geometry also shows the different formations the lines can take-three lines to form triangles, four lines to form quadrilaterals, five lines to form pentagons, and many other shapes with more lines. Geometry also shows the purity of the conic sections forming hyperbolas, ellipses, parabolas, and circles with specific equations and characteristics that enable them to be easily sketched. The manner in which the two foci of the ellipse can come together to form the beautiful circle with one centre and one radius is amazing. Although the Cartesian Plane is more of an algebraic way of showing points in terms of x and y coordinates from an origin of (0,0), the Geometric Arm has shown that points can be described geometrically, as a distance and an angle from an origin. Geometry has also shown us how points around a circle can be drawn as Sine and Cosine waves, which generate the numerous trigonometric identities.

The Mathematical Field shows the importance of measurements, which has led to standardisation and mass production of goods and services. This has obviously made things easy for the large populations supported in the cities and towns all over the world. The Mathematical Field has also made it possible to draw and design objects before manufacture and construction; this eliminates errors and wastage.

Numbers are essentially pure producing the same results when put in equations and formulae. Human beings and the Fields of Knowledge can produce uncertain results because of the free will issue. Mathematics allows for this in Probability Theory, a branch of Arithmetic Arm. The Sporting Field is full of probability associated with the results. If five horses are running in a race, there is only a certain probability that a particular horse will win. Also, if one tossed a coin, there is only a 50% chance of getting a head and a 50% chance of not getting a head. Probability Theory shows how to calculate the chances of certain events occurring.

Finally, the Mathematical Field shows us how to sort the data accumulated in many of Fields of Knowledge to produce useful statistical data and generate formulae and applications in many other Fields of Knowledge, some of which will be considered in my next book.