Logical symbols are part of a modern logical system for expressing rational thought and common patterns of reasoning. These symbols are used to clearly represent often times highly complex logical relationships between statements. There ar...

A tautology is a logical proposition with a special property: It is true under all circumstances. This property can be defined more precisely. Logical propositions are made up of basic propositions (usually symbolized by lower-case letters...

Maclaurin's theorem is a specific form of Taylor's theorem, or a Taylor's power series expansion, where c = 0 and is a series expansion of a function about zero. The basic form of Taylor's theorem is: n = 0 (f(n)(c)/n!)(x - c)n. When the a...

For centuries, mathematicians and artists alike have been fascinated by tessellations, also called tilings. Tessellations of a plane can be found in the regular patterns of tiles in a bathroom floor, or flagstones in a patio. They are also...

In mathematics or logic, a statement whose validity has been established or proved. It consists of a hypothesis and a conclusion, beginning with certain assumptions that are necessary and sufficient to establish a result. A system of theor...

Thomas Bayes, a Presbyterian minister, expressed a method of inductive inference in a precise and quantitative form, which lead to the development of Bayesian statistics, or Bayesian inference. His stature as a mathematician is based on on...

An almost entirely self-educated man, Thomas Simpson is most famous for the advances he made in the areas of interpolation and numerical methods of integration, although he also did work on probability theory. His enthusiasm and energy led...

In mathematics, the study of the properties of a geometric object that remains unchanged by deformations such as bending, stretching, or squeezing but not breaking. A sphere is topologically equivalent to a cube because, without breaking t...

Tosio Kato, whose career in mathematics ranged over more than 40 years, made major contributions to the field of mathematical physics. A prolific writer, he produced hundreds of published articles during his career. His most important rese...

In mathematics, a function not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Examples include the functions log &math.x;, sin ...

Transfinite numbers are infinite ordinal numbers. Informally, ordinal numbers may be represented by strings of *'s. For example, the ordinal number 0 is the string of no stars. Number 1 is *. Number 2 is ** and so on. The first transfinite...

Translation is the cellular process in which the genetic information carried by the DNA is decoded, using an RNA intermediate, into proteins. This process is also known as protein synthesis. There are two steps in the path from genes to p...

Geometric figure with three sides and three angles. Each two sides meet at a point called a vertex, and the three angles sum to 180°. A triangle with one 90° (right) angle is a right triangle. A triangle with all sides (and thus al...

In mathematics, one of six functions (sine, cosine, tangent, cotangent, secant, and cosecant) that represent ratios of sides of right triangles. They are also known as the circular functions, since their values can be defined as ratios of ...

In mathematics, one of six functions (sine, cosine, tangent, cotangent, secant, and cosecant) that represent ratios of sides of right triangles. They are also known as the circular functions, since their values can be defined as ratios of ...

Trisecting an angle is one of the three classical problems of Greek geometry, together with doubling the cube and squaring the circle. Although it is one of the oldest problems of mathematics, it is also one of the most misunderstood. The ...

In the language of mathematics and logic there are essentially two types of statements. There are basic propositions (abbreviated here by lower-case, italicized letters, e.g., p, q, etc.), like "the triangle ABC is equilateral," or "the in...

Tullio Levi-Civita's most crucial contribution to mathematics lay in his development of tensor calculus (originally called absolute differential calculus). This new calculus had a widespread effect. Although Albert Einstein's theory of rel...

The Danish astronomer Tycho Brahe (1546-1601) carried pretelescopic astronomy to its highest perfection and tried to steer a middle course between the Ptolemaic and the Copernican systems. Tycho Brahe, referred to by his first name, was bo...