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.

The light is not focused to a point but forms an Airy disk having a central spot in the focal plane with radius to first null of

The quantum mass of an electron, the Compton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius.

The most massive collection of molecular clouds in the galaxy forms an asymmetrical ring around the galactic center at a radius of 120 parsecs ; the largest component of this ring is the Sagittarius B2 complex.

The disk forms a symmetric feature that is centered on the star, and the outer radius averages.

The covalent radius, r < sub > cov </ sub >, is a measure of the size of an atom that forms part of one covalent bond.

For example, the apparent hydrodynamic radius of a typical protein domain might be 14 Å and 36 Å for the folded and unfolded forms, respectively.

* the radius along its length via the interosseous membrane that forms a syndesmoses joint

When a tube of a narrow bore, often called a capillary tube, is dipped into a liquid and the liquid wets the tube ( with zero contact angle ), the liquid surface inside the tube forms a concave meniscus, which is a virtually spherical surface having the same radius, r, as the inside of the tube.

Any non-rotating and non-charged mass that is smaller than its Schwarzschild radius forms a black hole.

The method can be visualized by considering a thin horizontal rectangle at y between on top and on the bottom, and revolving it about the y-axis ; it forms a ring ( or disc in the case that ), with outer radius f ( x ) and inner radius g ( x ).

The traditional or secant ogive is a surface of revolution of the same curve that forms a Gothic arch ; that is, a circular arc, of greater radius than the diameter of the cylindrical section (" shank "), is drawn from the edge of the shank until it intercepts the axis.

The distal end of the radius forms a palpable point called the styloid process.

The radius of curvature at γ ( s ) is, in magnitude, the radius of the circle which forms the best approximation of the curve to second order at the point: that is, it is the radius of the circle making second order contact with the curve, the osculating circle.

As a result of the Law of Laplace, if an aneurysm forms in a blood vessel wall, the radius of the vessel has increased.

A radius grinder ( or radius tool grinder ) is a special grinder used for grinding the most complex tool forms, and is the historical predecessor to the CNC tool and cutter grinder.

This forms a debris disk around an orbital radius of 16 Astronomical Units from the star.

If this arc is drawn so that it meets the shank at zero angle ( that is, the distance of the centre of the arc from the axis, plus the radius of the shank, equals the radius of the arc ), then it is called a tangential or spitzer ogive.

The sharpness of this ogive is expressed by the ratio of its radius to the diameter of the cylinder ; a value of one half being a hemispherical dome, and larger values being progressively more pointed.

The profile of this shape is also formed by a segment of a circle, but the base of the shape is not on the radius of the circle defined by the ogive radius.

Also, the chosen ogive radius must be greater than twice the length of the nose cone.

Tire size can be determined in several ways but the one that is the easiest and as accurate as any is by measuring the effective radius of a wheel and tire assembly.

This is true because of savings in utility lines and the fact that your buildings have a useful radius equal in all directions.

If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.

If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

The radius is calculated from the mass by assuming spheres of density Af except for the smallest particles, which must have a higher mass density to remain in the solar system in the presence of solar-radiation pressure.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

This measure is the ratio of the length of a circular arc by its radius.

An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with an angular frequency of radians per day ; or that length such that, when used to describe the positions of the objects in the Solar System, the heliocentric gravitational constant ( the product GM < sub >☉</ sub >) is equal to ()< sup > 2 </ sup > AU < sup > 3 </ sup >/ d < sup > 2 </ sup >.

According to Archimedes in the Sandreckoner ( 2. 1 ), Aristarchus of Samos estimated the distance to the Sun to be 10, 000 times the Earth's radius ( the true value is about 23, 000 ).

The color of amethyst has been demonstrated to result from substitution by irradiation of trivalent iron ( Fe < sup > 3 +</ sup >) for silicon in the structure, in the presence of trace elements of large ionic radius, and, to a certain extent, the amethyst color can naturally result from displacement of transition elements even if the iron concentration is low.

It's noteworthy that this record's peak emittance black-body wavelength of 6, 400 kilometers is roughly the radius of Earth.

On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.

If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.

This distance replaces the angle u in the preceding considerations ; and the aperture, i. e. the radius of the entrance pupil, is its maximum value.