Euler’s Identity Formula.
Gauss said that if the truth of this formula is not immediately apparent to you, you will never be a top notch mathematician.
Even for those of us who do not immediately see the truth of this formula, we can nevertheless recognize the breathtaking beauty of an equation that relates so many fundamentals: zero, one, addition, multiplication, exponents, pi, i, and e. Truly staggering!
Proven to be very useful in engineering applications, yet whatever this number represents, it cannot be measured physically. Imaginary numbers are numbers that do not live on the number line! You will find them, however, on a number plane. Thus, these entities are simply numbers of higher dimension.
Alpha – the Fine Structure Constant
One of the fundamental physical constants in the universe: approximately 1/137. This is the number that determines the strength of the electromagnetic force; it is related to the “gaps” between the electron’s orbital energies. If it were different, nothing in the universe would work the same: electrons would not orbit, there would be no differentiation between matter and radiation.
Therefore, this number controls the nature of the universe.
Alpha is strange in that it is a dimensionless constant, meaning it is just a number and not a measurement of length, energy, time, mass or any other dimension of physics, yet neither is it one of the mathematical constants.
Feynman said that all good physicists sit up at night worrying about alpha: “is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.”
The Pythagorean Theorem
New proofs are found for this equation every year.
“To this day, the theorem of Pythagoras remains the most important single theorem in the whole of mathematics.” – J. Bronowski The Ascent of Man
Misunderstood as a theorem about triangles, PT can actually apply to any shape, measure any distance. Any formula with a squared term is under its influence.
Here are some surprising uses of the Pythagorean Theorem
Newton’s Law of Universal Gravitation
This discovery was the culminating moment of the scientific revolution, Man’s closest glimpse into the Mind of God. It is said that the apple fell to Newton from the Tree of Knowledge in the Garden of Eden itself.
Maxwell’s Equations of electromagnetism
10,000 years from now, these equations will be looked upon as the most significant event in the history of the 19th century. Did you learn about this in your history class?
Special Theory of Relativity
E = mc2
Matter and Energy are one and the same. Matter is Energy looped back upon itself, a snake biting its own tail.
General Theory of Relativity
This is the curvature of space-time. Unintuitive in the extreme, this equation represents a conquest of pure thought over pure experience. “The theory appeared to me then, and it still does, the greatest feat of human thinking” – Max Born
The Schwarzschild Radius
Given the mass of an object, This is the radius at which the object becomes dense enough to become a black hole
This is the basic equation of quantum theory. Mathematicians say it is as inexhaustible as mathematics itself.
The Black-Scholes Equation
This formula crashed Long Term Capital Management in the 1990’s. Despite this fact, Wall Street has been ever since in search of a formula that can eliminate risk. Each time they think they have found it, they haven’t.
This is the equation that tanked Enron in 2001.
The Gaussian Copula Formula