π in the sky!

In this post I shall discuss the nature of π as a mathematical constant and reveal its relationship with the fabric of space. As an irrational number π represents the ratio of a circle’s circumference to its diameter. An irrational number is a real number that cannot be expressed as a ratio (a/b), where (a) and (b) are integers and (b≠0).

Returning briefly to the cubical universe, which we considered in a previous post, if the observer there begins to probe his world at the level of the individual cubes defining his space and decides to form different geometries at that level, he could do so only by using those cubes. He would have no other means. Using cubes to define circles, he would soon discover that the geometric properties of his circles vary according to the orientation of the cubes. For example, the number of elements defining the diameter of the same circle could vary depending upon the orientation of the cubes in the circumference. Therefore, in a universe defined by cubical elements π, as the ratio of the units of length of a circle’s circumference to that of its diameter, cannot be constant. Continue reading “π in the sky!”

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Complex Numbers Unravelled

In mathematics and in physics, the reality behind complex numbers remains mysterious. Although they are essential to solving fundamental problems in science and engineering, their true relationship with the physical world is unknow. For example, why do they have two components- referred to as real and imaginary parts? Why is the imaginary part closely linked to the square root of minus one? And most importantly, what is their relationship with physical reality. In this post, I answer those questions and unravel the mystery of complex numbers. Continue reading “Complex Numbers Unravelled”