Suppose that, in the course of an investigation, you stumble upon a string of whole numbers. You are convinced that there must be a pattern, but you cannot find it. All you have to do is to type the string into a database called OEIS — or simply “Slone’s” — and, if the string is recognized, an entire infinite sequence is revealed. If the string belongs to several sequences, several choices are offered. OEIS is a great boon to both professional mathematicians and applied scientists in fields like physics, chemistry, astronomy and biology.
The Home page of OEIS: https://oeis.org
Continue reading ‘The Online Encyclopedia of Integer Sequences’
we can usually find 
, whereas we may not be able to find 
.
. The number of atoms in the universe is estimated to be about 
. When we consider permutations of large sets, even more breadth-taking numbers emerge.
changed by one part in a million.
. Although the angular momentum did not change, the rotation axis moved in the body frame. The nut continued to flip back and forth, although there were no forces or torques acting on it.
, 
, 
using the integral
the amplitude and wrote 
. It can be difficult to understand what motivated his definitions. We will define the elliptic functions 
for which the function is zero. A simple iterative method was devised by Isaac Newton and refined by Joseph Raphson. It is known either as Newton’s method or as the Newton-Raphson method. It usually produces highly accurate approximations to the roots of the equation 
.
“
For many decades, a search has been under way to find a theory of everything, that accounts for all the fundamental physical forces, including gravity. The dictum “physics is geometry” is a guiding principle of modern theoretical physics. Einstein’s General Theory of Relativity, which emerged just one hundred years ago, is a crowning example of this synergy. He showed how matter distorts the geometry of space and this geometry determines the motion of matter. The central idea is encapsulated in an epigram of John A Wheeler:
From cheetahs chasing gazelles, through coastguards saving shipwrecked sailors, to missiles launched at enemy aircraft, strategies of pursuit and evasion play a role in many areas of life (and death). From pre-historic times we have been solving such pursuit problems. The survival of our early ancestors depended on their ability to acquire food. This involved chasing and killing animals, and success depended on an understanding of relative speeds and optimal pursuit paths.
, the ratio of the circumference of a circle to its diameter. We review several historical methods and describe a recently-discovered and completely original and ingenious method.
Family of trajectories with fixed initial speed and varying launch angles. Two particular trajectories are shown in black. 
characterizes the intrinsic geometry of a surface.
The rational numbers are countable: they can be put into one-to-one correspondence with the natural numbers. In previous articles we showed how the rationals can be presented as a list that includes each rational precisely once. One approach leads to the 
