Search results
Results From The WOW.Com Content Network
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
describes a right circular conoid with the unit circle of the x-y-plane as directrix and a directrix plane, which is parallel to the y--z-plane. Its axis is the line (,,) . Special features: The intersection with a horizontal plane is an ellipse.
More generally, for any collection of points P i, weights w i, and constant C, one can define a circle as the locus of points X such that (,) =.. The director circle of an ellipse is a special case of this more general construction with two points P 1 and P 2 at the foci of the ellipse, weights w 1 = w 2 = 1, and C equal to the square of the major axis of the ellipse.
and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is =. In the special case 𝜃 = 2 π, these formulae yield the circumference of a complete circle and area of a complete disc, respectively.
A circle of finite radius has an infinitely distant directrix, while a pair of lines of finite separation have an infinitely distant focus. In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.
A cone can be generated by moving a line (the generatrix) fixed at the future apex of the cone along a closed curve (the directrix); if that directrix is a circle perpendicular to the line connecting its center to the apex, the motion is rotation around a fixed axis and the resulting shape is a circular cone.
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =
Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.