Maths notation is often overly complex. Let’s see how this can be better:
Heard of Skewes’ Number? It is the number above which must fail (assuming that the Riemann hypothesis is true), where is the prime counting function and is the logarithmic integral. Isaac Asimov featured the Skewes number in his science fact article “Skewered!”
Zipf’s law /ˈzɪf/, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. The law is named after the American linguist George Kingsley Zipf (1902–1950), who popularized it and sought to explain it (Zipf 1935, 1949), though he did not claim to have originated it.
Remember the working on Taylor Series from your A-level Math MF15? This video walks you through what would be the Taylor’s Series of a polynomial.
Surprised? Can you figure out why this is the case?
The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess of 10120, based on about 103 initial moves for White and Black and a typical game lasting about 40 pairs of moves.
Did you also know there are over 9 million different possible positions after three moves each. There are over 288 billion different possible positions after four moves each. The number of distinct 40-move games is far greater than the number of electrons in the observable universe.
We see objects all the time and our brains decode the 3D shapes, but how do computers model these shapes and why break it all down to triangles?
So you still think prime numbers are random?
Take a look at this really cool project, it kinda reminds me of the sieve of Eratosthenes: El Patrón de los Números Primos: Prime Number Patterns – Jason Davies
You can examine more on divisor plot as well.
Prime numbers has mystified mathematicians for centuries, there seems to be a pattern but mathematicians aren’t able to find a method to predict the next sequence or understand what exact cause prime numbers to be the sequence it currently is.
Carlo Séquin on his search for the elusive “fourth type of Klein bottle”.
In mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.