The equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = r < sup > 2 </ sup > is the equation for any circle with a radius of r.

For example, P might be the circle with radius 1 and center ( 0, 0 ): P =

Developed by Frits Zernike in the 1930s, Zernike's polynomials are orthogonal over a circle of unit radius.

A centre spot denotes the center of the field and a circle of radius 5 m is centered at it.

The curvature of the fretboard is measured by the fretboard radius, which is the radius of a hypothetical circle of which the fretboard's surface constitutes a segment.

# The radius of the circle does not change in time.

The negative shows that the acceleration is pointed towards the center of the circle ( opposite the radius ), hence it is called " centripetal " ( i. e. " center-seeking ").

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Polar unit vectors at two times t and t + dt for a particle with trajectory r ( t ); on the left the unit vectors u < sub > ρ </ sub > and u < sub > θ </ sub > at the two times are moved so their tails all meet, and are shown to trace an arc of a unit radius circle.

As a particular example, if the particle moves in a circle of constant radius R, then dρ / dt

The radius of curvature of the path is ρ as found from the rate of rotation of the tangent to the curve with respect to arc length, and is the radius of the osculating circle at position s. The unit circle on the left shows the rotation of the unit vectors with s.

A geometric approach to finding the center of curvature and the radius of curvature uses a limiting process leading to the osculating circle.

From a qualitative standpoint, the path can be approximated by an arc of a circle for a limited time, and for the limited time a particular radius of curvature applies, the centrifugal and Euler forces can be analyzed on the basis of circular motion with that radius.

Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red.

The equation of a circle is ( x − a )< sup > 2 </ sup > + ( y − b )< sup > 2 </ sup > = r < sup > 2 </ sup > where a and b are the coordinates of the center ( a, b ) and r is the radius.

For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 4.

In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.

This is a circle with a 10-meter ( 33 feet ) radius, with the pin at its center.

To draw the orbit with a pair of compasses the centre of the circle should be offset from the focus by an amount equal to the eccentricity multiplied by the radius.

The radius of the directrix circle is greater than the distance between the center of this circle and the focus ; thus, the focus is inside the directrix circle, as is the entire ellipse.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

By moving the unit vectors so their tails coincide, as seen in the circle at the left of the image above, it is seen that u < sub > ρ </ sub > and u < sub > θ </ sub > form a right-angled pair with tips on the unit circle that trace back and forth on the perimeter of this circle with the same angle θ ( t ) as r ( t ).

The positive constant r is the radius of this circle.

The area of a regular polygon is also given in terms of the radius r of its inscribed circle and its perimeter p by

The area of a regular n-gon in terms of the radius r of its circumscribed circle and its perimeter p is given by

Like a circle, which is in two dimensions, a sphere is the set of points which are all the same distance r from a given point in space.

* a 1-sphere is a circle of radius r

A small circle below a letter is used to mark both the schwa ( e ̥) and syllabic consonants ( r ̥ or l ̥, for instance ).

If an object moves with angular velocity ω around a circle of radius r centered at the origin of the x-y plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

For example, consider a circle of radius r. The main pieces of information a program needs in order to draw this circle are

The power P passing through a circle of radius r in the transverse plane at position z is

A cycloid generated by a circle of radius r = 2

The cycloid through the origin, generated by a circle of radius r, consists of the points ( x, y ), with

Rod shifted his eager eyes from the milling group out in the circle long enough to reply, `` I ain't much of a hand for Dare-Base and Farmer-in-the-Dell, but I'd sure like to get in on the handhold and wrestles ''.

The magic circle is, in fact, a symbol of and preparation for the metaphysical orgasm ''.

Hall, for example, was quite explicit on this point when he said states outside European civilization must formally enter into the circle of law-governed countries.

He left at his death sketches, drawn to scale, for the rest of the circle.

The hotly debated plan for the capital's Franklin D. Roosevelt Memorial, a circle of huge tablets engraved with his speeches ( and promptly dubbed by one of its critics, `` Instant Stonehenge '' ), is another of Udall's headaches, since as supervisor of the National Parks Commission he will share in the responsibility for building it.

Additionally, consider for instance the unit circle S, and the action on S by a group G consisting of all rational rotations.

With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

The circle symbol for aromaticity was introduced by Sir Robert Robinson and his student James Armit in 1925 and popularized starting in 1959 by the Morrison & Boyd textbook on organic chemistry.

In this way the circle symbol for a 6c – 6e bond can be compared to the Y symbol for a 3c – 2e bond.

We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point ; on the other hand, in each of two planes lines O ' and O " are separately formed ( in neighboring planes ellipses are formed ), and in a plane between O ' and O " a circle of least confusion.

** Atkinson independently discovered the Midpoint circle algorithm for fast drawing of circles by using the sum of consecutive odd numbers.

" WIR " is both an abbreviation of Wirtschaftsring and the word for " we " in German, reminding participants that the economic circle is also a community.

The team then flies to its show venue for the upcoming weekend on Thursday, conducting " circle and arrival " orientation maneuvers upon arrival.

The proper copyright notice for sound recordings of musical or other audio works is a sound recording copyright symbol (< font size =" 5 "></ font >, the letter p inside a circle ), which indicates a sound recording copyright, with the letter p indicating a " phonorecord ".

Other common shapes for churches include a circle, to represent eternity, or an octagon or similar star shape, to represent the church's bringing light to the world.

A bit more formally: we represent a point on the unit circle by its angle, in radians, going from-π to π for simplicity.

It is based on the semaphore symbols for " N " ( two flags held 45 degrees down on both sides, forming the triangle at the bottom ) and " D " ( two flags, one above the head and one at the feet, forming the vertical line ) ( for Nuclear Disarmament ) within a circle.

* inside the unit circle for discrete time, when the Z-transform is used.

Examples include cardboard cutouts, which can be used to make tassels, fringe, and many other items ; a pom-pom circle, used to make pom-poms ; a tape measure and a gauge measure, both used for measuring crocheted work and counting stitches ; a row counter ; and occasionally plastic rings, which are used for special projects.

First, for any two distinct points P and Q in the plane, let L ( P, Q ) denote the unique line through P and Q, and let C ( P, Q ) denote the unique circle with center P, passing through Q.