Donald E Knuth, designer of the \TeX mathematical typesetting system.
Mathematicians owe a great debt of gratitude to Donald Knuth. A renowned American computer scientist and mathematician, Knuth is an emeritus professor at Stanford University. He is author of many books, including the multi-volume work, The Art of Computer Programming.
Knuth is the author of the powerful and versatile mathematical typesetting system called TeX. The original version, designed and written by Knuth, was released in 1978.
TeX is a powerful system for typesetting mathematical formulae. It is ideal both for simple mathematical notes with few formulas and for more complex documents and books involving subtle and sophisticated mathematical typography. TeX is used by almost all research mathematicians. It is also popular in computer science, engineering, physics, statistics, and and many other sciences.
of points in the plane 
(Fig. 1a). How large a circle is required to enclose them. More specifically, what is the minimum radius of such a bounding circle? The answer is given by Jung’s Theorem.
for s=1.1 (red), s=1.01 (blue) and s=1.001 (black).
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.
