Shapes Preschool Activities and CraftsCome and have fun with. Visit a theme to find activities that include easy instructions and a list of materials needed. You will find crafts, printable activities, and related. Circle Wikipedia. Circle. A circle black which is measured by its circumference C, diameter D in cyan, and radius R in red its centre O is in magenta. A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve which divides 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, or to the whole figure including its interior in strict technical usage, the circle is only the boundary and the whole figure is called a disc. A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations. A circle is a plane figure bounded by one line, and such that all right lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre. Euclid. Elements Book I. Circle Triangle Square' title='Circle Triangle Square' />Terminology. Annulus the ring shaped object, the region bounded by two concentric circles. Arc any connected part of the circle. A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre equivalently it is the curve. A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the. Japan-3-Extended-Circle-Triangle-Square-1080x675.jpg' alt='Circle Triangle Square' title='Circle Triangle Square' />Centre the point equidistant from the points on the circle. Chord a line segment whose endpoints lie on the circle. Circumference the length of one circuit along the circle, or the distance around the circle. Diameter a line segment whose endpoints lie on the circle and which passes through the centre or the length of such a line segment, which is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord, and it is twice the radius. Disc the region of the plane bounded by a circle. Lens the intersection of two discs. Passant a coplanar straight line that does not touch the circle. Radius a line segment joining the centre of the circle to any point on the circle itself or the length of such a segment, which is half a diameter. Sector a region bounded by two radii and an arc lying between the radii. Segment a region, not containing the centre, bounded by a chord and an arc lying between the chords endpoints. Secant an extended chord, a coplanar straight line cutting the circle at two points. Semicircle an arc that extends from one of a diameters endpoints to the other. In non technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, that is technically called a half disc. Kenninji is a temple of the Zen sect, one of the main branches of Japanese Buddhism. A triangle is a 3sided polygon sometimes but not very commonly called the trigon. Every triangle has three sides and three angles, some of which may be the same. Circle Triangle Square' title='Circle Triangle Square' />A half disc is a special case of a segment, namely the largest one. Tangent a coplanar straight line that touches the circle at a single point. Chord, secant, tangent, radius, and diameter. History. The compass in this 1. Gods act of Creation. Notice also the circular shape of the halo. The word circle derives from the Greek kirkoskuklos, itself a metathesis of the Homeric Greek krikos, meaning hoop or ring. The origins of the words circus and circuit are closely related. Circular piece of silk with Mongol images. The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. 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. Some highlights in the history of the circle are 1. BCE The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 2. Analytic results. Length of circumference. The ratio of a circles circumference to its diameter is pi, an irrationalconstant approximately equal to 3. Thus the length of the circumference C is related to the radius r and diameter d by C2rd. C2pi rpi d. ,Area enclosed. Area enclosed by a circle area of the shaded square. As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circles circumference and whose height equals the circles radius,7 which comes to multiplied by the radius squared Arear. Area pi r2. ,Equivalently, denoting diameter by d,Aread. Area frac pi d24approx 0. The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality. Equations. Cartesian coordinates. Manual For Brother Intellifax 4100E. Circle of radius r  1, centre a, b  1. In an xy. Cartesian coordinate system, the circle with centre coordinates a, b and radius r is the set of all points x, y such thatxa2yb2r. This equation, known as the Equation of the Circle, follows from the Pythagorean theorem applied to any point on the circle as shown in the adjacent diagram, the radius is the hypotenuse of a right angled triangle whose other sides are of length x a and y b. If the circle is centred at the origin 0, 0, then the equation simplifies tox. The equation can be written in parametric form using the trigonometric functions sine and cosine asxarcost,displaystyle xar,cos t,ybrsintdisplaystyle ybr,sin t,where t is a parametric variable in the range 0 to 2, interpreted geometrically as the angle that the ray from a, b to x, y makes with the positive x axis. An alternative parametrisation of the circle is xar. In this parametrisation, the ratio of t to r can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the x axis see Tangent half angle substitution. However, this parametrisation works only if t is made to range not only through all reals but also to a point at infinity otherwise, the bottom most point of the circle would be omitted. In homogeneous coordinates each conic section with the equation of a circle has the formx. It can be proven that a conic section is a circle exactly when it contains when extended to the complex projective plane the points I1 i 0 and J1 i 0. These points are called the circular points at infinity. Polar coordinates. In polar coordinates the equation of a circle is r. For a circle centred at the origin, i. When r. 0 a, or when the origin lies on the circle, the equation becomesr2acos. In the general case, the equation can be solved for r, givingrr. Note that without the sign, the equation would in some cases describe only half a circle. Complex plane. In the complex plane, a circle with a centre at c and radius r has the equation zcrdisplaystyle z cr,. In parametric form this can be written zreitcdisplaystyle zreitc.