" The small-angle formula can be used to convert such an angular measurement into a distance / size ratio.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas ( such as the Pythagorean formula for the distance ) do not hold.

A point in Euclidean space may be identified by a tuple of real numbers, and distances are defined using the Euclidean distance formula.

Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun.

Tartaglia is also known for having given an expression ( Tartaglia's formula ) for the volume of a tetrahedron ( including any irregular tetrahedra ) as the Cayley – Menger determinant of the distance values measured pairwise between its four corners:

The Hubble constant becomes relevant when converting an observed redshift z into a distance d using the formula d ≈ ( c / H ) × z.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

The solar energy available at any distance, d, from the Sun can be calculated by the formula E = 1367 / d² watts per square meter, where d is measured in astronomical units.

For a circular aperture, the diffraction-limited image spot is known as an Airy disk ; the distance x in the single-slit diffraction formula is replaced by radial distance r and the sine is replaced by 2J < sub > 1 </ sub >, where J < sub > 1 </ sub > is a first order Bessel function.

where R denotes the distance to the source point P and R ' denotes the distance to the reflected point P. A consequence of this expression for the Green's function is the Poisson integral formula.

In analytic geometry, the distance between two points of the xy-plane can be found using the distance formula.

This distance formula can also be expanded into the arc-length formula.

In this book you can find a formula to estimate the distance from a point outside the Mandelbrot set to the boundary of the Mandelbrot set ( and a similar formula for the Julia sets ), and one can wonder why the creator did not use this function instead of the potential function, because it grows in a more natural way ( see the formula in the articles Mandelbrot set and Julia set ).

In mathematics, the Euclidean distance or Euclidean metric is the " ordinary " distance between two points that one would measure with a ruler, and is given by the Pythagorean formula.

By using this formula as distance, Euclidean space ( or even any inner product space ) becomes a metric space.

Considering only ( ℓmn ) planes intersecting one or more lattice points ( the lattice planes ), the perpendicular distance d between adjacent lattice planes is related to the ( shortest ) reciprocal lattice vector orthogonal to the planes by the formula:

He took a lead on the enemy, using a distance of five of the radii in his circular sight and then added another.

The Reverend James Doran had scarcely completed Pat Conyers' last rites on Boot Hill in the township of Petrie, when shots were heard in the distance.

But the farmers outsmarted Washington by shortening the distance between the rows and pouring on the fertilizer.

Off in the distance a searchlight flashed on, its beam slashing the sky.

Even at this short distance they were only vague shapes, setting up the machine gun on a small knoll so that it could fire above the heads of the rest of the patrol.

The extent of such interference -- which may be so slight as to be undetectable at any point where either of the stations renders a usable signal, or may be so great as to virtually destroy the service areas of both stations -- depends on many factors, among the principal ones being the distance between the stations, their respective radiated power, and, of particular significance here, the time of day.

But during nighttime hours the skywave radiations are reflected from the ionosphere, thereby creating the possibility of one station's rendering service, via skywave, at a much greater distance than it can through its groundwave signal, and at the same time vastly complicating the interference problem because of the still greater distance over which these skywave signals may cause interference to the signals of stations on the same and closely adjacent frequencies.

This is done by measuring the distance from the surface on which the tire is resting to the center of the rear axle shaft.

Rich in Christian and Moslem art, Istanbul is today a fascinating museum of East and West that recently became a seaside resort as well with the development of new beaches on the Bosphorus and the Sea of Marmara only a short distance from the center of town.

Going through the Imperial Gate in the wall, I entered the grounds of Topkapi Palace, home of the Sultans and nerve center of the vast Ottoman Empire, and walked along a road toward another gate in the distance, past the Church of St. Irene, completed by Constantine in 330 A.D. on my left, and then, just outside the second gate, I saw a spring with a tap in the wall on my right -- the Executioner's Spring, where he washed his hands and his sword after beheading his victims.

Changes of intensity on the cell were achieved by use of a wire screen and by varying the distance of the light source from the cell.

The last column shows the rate of exchange that would have been observed at a relative intensity of 4 ( 14.7 cm. distance ) calculated on the assumptions that the incident light intensity is inversely proportional to the square of the distance of the lamp from the cell and that the rate is directly proportional to the incident light intensity.

Pioneer 1, recorded a decrease in flux with distance from the Earth on the basis of 11 counts in 9 hours.

However nothing on four legs was supposed to be faster than a lion over a short distance, unless it was a cheetah.

It was enough for people to know that at one time he had looked down the street at the fleshy suppleness of a woman he had consumed -- watching her become thinner and thinner in the distance, as thin as the seams on her stockings, and still thinner.

Even at that distance, with no sound but the sound of the tractor, I could tell the fierce mark of brutality on the boy.

He never gets home until late, and he has to distance himself from the natural pity that he feels for the victims ; otherwise, he would not be able to go on.

The part of the function that depends on the distance from the nucleus has nodes ( radial nodes ) and decays as e < sup >(- distance )</ sup > from the nucleus.

Depending on the distance Van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between 380 and 1, 520 Earth radii.

The center of an atomic projectile striking this plane has geometrically a definite probability of passing within a certain distance of one of these points.

If the axes are named x, y, and z, then the x coordinate is the distance from the plane defined by the y and z axes.

The distance is to be taken with the + or − sign, depending on which of the two half-spaces separated by that plane contains p. The y and z coordinates can be obtained in the same way from the ( x, z ) and ( x, y ) planes, respectively.

The Euclidean distance between two points of the plane with Cartesian coordinates and is

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.

The combination of focal length, subject distance, and format size defines magnification at the film / sensor plane.

The ellipse can also be defined as the set of points such that the distance from any point in that set to a given point in the plane ( a focus ) is a constant positive fraction less than 1 ( the eccentricity ) of the perpendicular distance of the point in the set to a given line ( called the directrix ).

One way to think of the Euclidean plane is as a set of points satisfying certain relationships, expressible in terms of distance and angle.

One is translation, which means a shifting of the plane so that every point is shifted in the same direction and by the same distance.

Due to its small size and its distance from the plane of the Milky Way, Equuleus contains no notable deep sky objects.

: how many colors are needed to color the plane so that no two points at unit distance apart have the same color?

An alternate description of this distortion is to consider the length c along the unique trigonal axis ( after the distortion has begun ) and a as the distance in the plane perpendicular to c. In the cubic phase this reduces to

Only about 1 % of all distance travelled was by plane in 2002.

# Plano-polar, in which points in a plane are defined by a distance from a specified point along a ray having a specified direction with respect to a base line or axis ;

It is easy enough to " translate " between polar and rectangular coordinates in the plane: let, as above, direction and distance be and respectively, then we have

* Local topocentric coordinates are azimuth ( direction angle within the plane of the horizon ) and elevation angle ( or zenith angle ) and distance.

In terms of Cartesian coordinates p, the distance from the minor axis, and z, the distance above the equatorial plane, the equation of the ellipse is

* 1927 October 6The seventh CGPM adjusts the definition of the metre to be the distance, at, between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least diameter, symmetrically placed in the same horizontal plane at a distance of from each other.