A radian is a unit of angular measure equal to the angle between two radii that enclose a section of a circle's circumference equal in length to the length of a radius. The entire angle of a circle is 2 radians and so 2 radians is equal to...

When most people think of randomness, they generally think of a condition with an apparent absence of a regular plan, pattern, or purpose. The word random is derived from the Old French word randon, meaning haphazard. The mathematical mean...

Quotient of two values. The ratio of &math.a; to &math.b; can be written &math.a;:&math.b; or as the fraction &math.a;/&math.b;. In either case, &math.a; is the antecedent and &math.b; the consequent. Ratios arise whenever comparisons are ...

Raymond Queneau was a poet and writer whose intense interest in mathematics flavored many of his works. He cofounded an artistic group called Ouvroir de litterature potentielle (Oulipo--Workshop of Potential Literature) that still influenc...

A recursive function is a function whose domain is generated by previous values of the function. A recursive function is typically defined by giving some initial value and then stating a recursion rule which defines how a given function va...

The German astronomer and mathematician Regiomontanus (1436-1476) constructed the first European observatory and established trigonometry as a separate area of study in mathematics. Regiomontanus, called after the Latinized form of his bir...

Determining the reliability of digits and calculations is important, because physical measurements have mathematical limitations. For example, suppose a ruler marked with tenths of inches is used to measure the length of an object. If the ...

René Frédéric Thom is best known as the founder of catastrophe theory, a field with numerous applications in the exact and social sciences. Catastrophe theory provides models for the description of continuous processes...

Richard Dedekind is best known for his work in number theory. He redefined irrational numbers, proposing that rational and irrational numbers form a continuum in which real numbers are located by "cuts" in the realm of rational numbers. He...

Richard Taylor is a number theorist who is perhaps best known for his collaboration with Princeton mathematician Andrew Wiles in constructing a proof of Fermat's last theorem. This famous theorem, written by lawyer and amateur mathematicia...

One of the central results in the subject of complex analysis, the Riemann mapping theorem unifies the areas of algebra, geometry, and topology. Today it is recognized as one of the most important theorems of nineteenth-century mathematics...

The English chemist, physicist, and natural philosopher Robert Boyle (1627-1691) was a leading advocate of "corpuscular philosophy." He made important contributions to chemistry, pneumatics, and the theory of matter. The seventh son and fo...

Author of the influential 1932 book The Foundations of Point Set Topology, Robert Lee Moore was a pioneer in that area of mathematics. He was a lifelong mathematics teacher and professor, as well as a fixture in the American Mathematical S...

WORK. Once, at the dawn of creation, in the Golden Age, when earth and sky were conjoined (or when there was only sky), when only children, or the first human pair, inhabited the world, there was no "work." Only God, or the g...

Roger Cotes advanced the understanding of trigonometric functionsthrough his original work on integration, functions, and the nth roots of unity. He is also remembered for his contributions to Isaac Newton's work on universal gravitation. ...

Special case of the mean-value theorem of differential calculus. It states that if a continuous curve passes through the &math.x;-axis twice within a given interval and has a unique tangent line at every point of that interval, then somewh...

In botany, the underground anchoring part of a plant. It grows downward in response to gravity, absorbs water and dissolved minerals, and stores reserve food. Primary root systems have a deep sturdy taproot (in gymnosperms and dicots; &see...

People prefer to work with round numbers because they are easy to remember and easy to use. For example, most people would rather multiply 4 x 10 rather than 3.5 x 9.5. It is important to know when a round number can be used for convenienc...

Rudjer Boscovic, also known as Ruggero Giuseppe Boscovich, was a Jesuit mathematician and astronomer. He was born in Ragusa, Croatia (now Dubrovnik, Yugoslavia) on May 18, 1711, and died in Milan, Italy in February 13, 1787. Boscovic's fat...