pi is a mathematical constant whose value is the ratio of any circle circumference to its diameter in Euclidean space this is the same value as the ratio of a circle area to the square of its radius.
The symbol p was first proposed by the Welsh mathematician William Jones in 1706. It is approximately equal to 3.14159 in the usual decimal notation. p is one of the most important mathematical and physical constants many formulae from mathematics, which means that its value cannot be expressed exactly as a fraction m, where m and n are integers.
Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers can be equal to its value proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics.
Throughout the history of mathematics, there has been much effort to determine p more accurately and to understand its nature fascination with the number has even carried over into non mathematical culture.
The Greek letter p, often spelled out pi in text, was adopted for the number from the Greek word for perimeter, first by William Jones in 1707, and popularized by Leonhard Euler in 1737.
A definition is a formal passage describing the meaning of a term. The term to be defined is the definiendum. A term may have many subtly different senses or meanings. For each such sense, a definiens is a cluster of words that defines that specific sense of the term.
A chief difficulty in managing definition is the need to use other terms that are already understood or whose definitions are easily obtainable. The use of the term in a simple example may suffice. By contrast, a dictionary definition has additional details, typically including an etymology showing snapshots of the earlier meanings and the parent language.
Like other words, the term definition has subtly different meanings in different contexts. A definition may be descriptive of the general use meaning, or stipulative of the speaker immediate intentional meaning.
In formal languages like mathematics, a stipulative definition guides a specific discussion. A descriptive definition can be shown to be right or wrong by comparison to general usage, but a stipulative definition can only be disproved by showing a logical contradiction.
A precising definition extends the descriptive dictionary definition of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition.
Stevenson has identified persuasive definition as a form of stipulative definition which purports to describe the true or commonly accepted meaning of a term, while in reality stipulating an altered use.
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