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A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are the same distance from a given point called the centre. The common distance of the points of a circle from its center is called its radius. Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. In everyday use the term "circle" may be used interchangeably to refer to either the boundary of the figure (known as the perimeter) or to the whole figure including its interior, but in strict technical usage "circle" refers to the perimeter while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.

[edit] Further terminology The diameter of a circle is the length of a line segment whose endpoints lie on the circle and which passes through the centre of the circle. This is the largest distance between any two points on the circle. The diameter of a circle is twice its radius. The term "radius" can also refer to a line segment from the centre a circle to its perimeter, and similarly the term "diameter" can refer to a line segment between two points on the perimeter which passes through the centre. In this sense, the midpoint of a diameter is the centre and so it is composed of two radii.

Chord, secant, tangent, and diameter.Arc, sector, and segment

A chord of a circle is a line segment whose two endpoints lie on the circle. The diameter, passing through the circle's centre, is the largest chord in a circle. A tangent to a circle is a straight line that touches the circle at a single point. A secant is an extended chord: a straight line cutting the circle at two points. An arc of a circle is any connected part of the circle's circumference. A sector is a region bounded by two radii and an arc lying between the radii, and a segment is a region bounded by a chord and an arc lying between the chord's endpoints. [edit] History

The compass in this 13th century manuscript is a symbol of God's act of Creation. Notice also the circular shape of the halo The circle has been known since before the beginning of recorded history.[citation needed] It is the basis for the wheel[citation needed], which, with related inventions such as gears[citation needed], makes much of modern civilization possible.[citation needed] In mathematics, the study of the circle has helped inspire the development of geometry and calculus.[citation needed] Early science, particularly geometry and Astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.[citation needed] Some highlights in the history of the circle are:

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1700 BC – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π.[1] 300 BC – Book 3 of Euclid's Elements deals with the properties of circles. 1880 – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.[2]

Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159 in the usual decimal notation (see the table for its representation in some other bases). π is one of the most important mathematical and physical constants: many formulae from mathematics, science, and engineering involve π.[1] π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which means that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) 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 π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture. The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737.[2] The constant is occasionally also referred to as the circular constant, Archimedes' constant (not to be confused with an Archimedes number), or Ludolph's number (from a German mathematician whose efforts to calculate more of its digits became famous).

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Lower-case π is used to symbolize the constant. The name of the Greek letter π is pi, and this spelling is commonly used in typographical contexts when the Greek letter is not available, or its usage could be problematic. It is not normally capitalised (Π) even at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced like "pie" in English, which is the conventional English pronunciation of the Greek letter. In Greek, the name of this letter is pronounced /pi/. The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle.[3] π is Unicode character U+03C0 ("Greek small letter pi").[4]