An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant.

The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis ( PF < sub > 1 </ sub > + PF < sub > 2 </ sub > = 2a ).

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil.

In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points ( the foci ) is constant.

The maximum acceleration part spaces the coils at constant distances, and synchronize the coil currents to the bucket.

This served adequately until the introduction of the steam engine, the telegraph, and rail travel, which made it possible to travel fast enough over long distances to require almost constant re-setting of timepieces as a train progressed in its daily run through several towns.

* 1998 — The Supernova Cosmology Project and High-Z Supernova Search Team discover cosmic acceleration based on distances to Type Ia supernovae, providing the first compelling evidence for a non-zero cosmological constant.

Classical Cepheids are used to determine distances to galaxies within the Local Group and beyond, and are a means by which the Hubble constant can be established.

Before calculating the distances needed at the different fields of view, the constant width of the scene has to be calculated.

A constant esotropia, as the name implies, is present all the time, with and without glasses, if worn, and at all fixation distances.

A general feature of the galaxy rotation curves that have been measured is that the rotational velocity of the stars and gas are constant as far out as they can be measured ( line B in illustration ), i. e. stars are observed to revolve around the centre of these galaxies at a constant speed over a large range of distances from the centre of the galaxy.

where is now the mass of the body under consideration, is the mass of the body being orbited, is specifically the distance between the two bodies ( which is the sum of the distances from each to the center of mass ), and is the gravitational constant.

The lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse, which is the locus of points for which the sum of the distances to each of two fixed focal points is a constant.

A Cassini oval, by contrast, is the locus of points for which the product of these distances is constant.

The first theorem is that a closed conic section ( i. e. an ellipse ) is the locus of points such that the sum of the distances to two fixed points ( the foci ) is constant.

* Prove: The sum of distances d ( F < sub > 1 </ sub >, P ) + d ( F < sub > 2 </ sub >, P ) remain constant as the point P moves along the curve.

** Consequently, the sum of distances d ( F < sub > 1 </ sub >, P ) + d ( F < sub > 2 </ sub >, P ) must be constant as P moves along the curve because the sum of distances d ( P < sub > 1 </ sub >, P ) + d ( P < sub > 2 </ sub >, P ) also remains constant.

The space probe WMAP, launched in 2001, produced data that determines the Hubble constant and the age of the Universe independent of galaxy distances, removing the largest source of error.

An ellipse can be defined as the locus of points for each of which the sum of the distances to two given foci is a constant.

A hyperbola can be defined as the locus of points for each of which the absolute value of the difference between the distances to two given foci is a constant.

The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance ( equal to 2πb if θ is measured in radians ), hence the name " arithmetic spiral ".

Some sources describe the Archimedean spiral as a spiral with a " constant separation distance " between successive turns.

There is a curve slightly different from the Archimedean spiral, the involute of a circle, whose turns have constant separation distance in the latter sense of parallel curves.

The gap between the curves of an Archimedean spiral ( right picture ) remains constant as the radius changes and hence is not a rhumb line.

Its successive turns are parallel curves with constant separation distance, a property which is often ( somewhat misleadingly ) ascribed to the Archimedean spiral.

The Archimedean spiral is often called a spiral with constant distance between its successive coils.

Like the stars, the spiral arms rotate around the center, but they do so with constant angular velocity.

Linear hashing and spiral storage are examples of dynamic hash functions that execute in constant time but relax the property of uniformity to achieve the minimal movement property.

Edison's early patents show that he also considered the idea that sound could be recorded as a spiral onto a disc, but Edison concentrated his efforts on cylinders, since the groove on the outside of a rotating cylinder provides a constant velocity to the stylus in the groove, which Edison considered more " scientifically correct ".

The spiral path of the cyclotron beam can only " sync up " with klystron-type ( constant frequency ) voltage sources if the accelerated particles are approximately obeying Newton's Laws of Motion.

Many forms observed in nature can be related to geometry, for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape.

In normal spiral DNA the bases form pairs between the two strands: A with T and C with G. Purines pair with pyrimidines mainly for dimensional reasons-only this combination fits the constant width geometry of the DNA spiral.

Using a logarithmic spiral shape results in a constant angle between the cam and the rock at each contact point ; this constant angle is designed to always provide the necessary friction to hold a cam in equilibrium.

Through our conscience, along with meaningful and consistent progress, the spiral will result in growth, change, and constant improvement.

That is, a vehicle following the spiral at constant speed will have a constant rate of angular acceleration.

A diagonal line of constant damping in the s-plane maps around a spiral from ( 1, 0 ) in the z plane as it curves in toward the origin.

That is, the sampled response appears as a lower frequency and better damped as well since the root in the z-plane maps equally well to the first loop of a different, better damped spiral curve of constant damping.

In the fourth of his Norton lectures of 1958 – 59, titled " Repetition in Music " ( Chávez 1961, 55 – 84 ), he described a mode of composition already observable in many of his compositions since the 1920s, in which " The idea of repetition and variation can be replaced by the notion of constant rebirth, of true derivation: a stream that never comes back to its source ; a stream in eternal development, like a spiral …" ( Chávez 1961, 84 ).

that is, he is suspect, guilty, punishable, as is anyone in Mann's stories who produces illusion, and this is true even though the constant elements of the artist-nature, technique, magic, guilt and suffering, are divided in this story between Jacoby and Lautner.

His desires are so strong that he needs constant reassurance of his mother's love for him and what she expects of him, in order to overcome them.

Factors involved in the displacement formula are the bore diameter of the engine's cylinders, the length of the piston stroke, the number of cylinders in the engine, and a constant.

They are the result of a constant and careful contest with the elements.

If a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.

The first two forces are directly interrelated and depend upon film thickness, whereas Af is independent of these two and is a constant for a given knife/coating combination.

Consultation with a reputable wine dealer and constant experimentation -- `` steering ever from the known to the unknown '' -- are the requisites.

What is surprising and pleasant is that Mantle and Maris, under constant pressure from writers and photographers, are trying to be cooperative.

Even Professor Arnold Toynbee, agreeing with his son, does so in these terms: `` Compared to continuing to incur a constant risk of the destruction of the human race, all other evils are lesser evils.

Since amphibians are cold-blooded, they must find ways to keep their blood at a constant temperature to maintain homeostasis.

statistical significance results are independent of constant bias and

Axons are distinguished from dendrites by several features, including shape ( dendrites often taper while axons usually maintain a constant radius ), length ( dendrites are restricted to a small region around the cell body while axons can be much longer ), and function ( dendrites usually receive signals while axons usually transmit them ).

In 1976 the International Astronomical Union ( IAU ) revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant ( k ) takes the value when the units of measurement are the astronomical units of length, mass and time.

In particular, time intervals measured on the surface of the Earth ( terrestrial time, TT ) are not constant when compared to the motions of the planets: the terrestrial second ( TT ) appears to be longer in Northern Hemisphere winter and shorter in Northern Hemisphere summer when compared to the " planetary second " ( conventionally measured in barycentric dynamical time, TDB ).

Absolute temperature measurement is uniquely determined by a multiplicative constant which specifies the size of the " degree ", so the ratios of two absolute temperatures, T < sub > 2 </ sub >/ T < sub > 1 </ sub >, are the same in all scales.

Our initial conditions are 100, 000 pa of pressure, 1000 cc volume, and 300 K of temperature, so our experimental constant is:

# If adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively ( like altitude on a contour map ), then as the eye moves towards the axes ( towards the south-west ), it sees the density of isotherms stay constant, but it sees the density of adiabats grow.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

This means that in most real-world setups where machines are added a few at a time, only one or two tries are needed before the address effectively become constant.

The monotony between battles, the constant threat of artillery fire and bombardments, the struggle to find food, the lack of training of young recruits ( meaning lower chances of survival ), and the overarching role of random chance in the lives and deaths of the soldiers are described in detail.

However the efficiencies of any two " reasonable " implementations of a given algorithm are related by a constant multiplicative factor called a hidden constant.

When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant.