He had style: he held his reins in a loose bunch at the third button of his checked Epsom surtout, and when the horses leaned at a curve, as if bent by the force of a gale, he leaned with them.

If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.

The set of intersections of Af, the rotated curve, with the original curve C consists of just the set of forward corner points on C corresponding to the vertex at Af, plus the vertex itself.

The curve on the card the computer spat back at him couldn't be argued with, however.

In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity.

A " drive " or " fire " or " strike " involves bowling with force with the aim of knocking either the jack or a specific bowl out of play-and with the drive's speed, there is virtually no noticeable ( or, at least, much less ) curve on the shot.

Often, low-floor trams are fitted with nonpivoting bogies and many tramway enthusiasts see this as a retrograde step, as it leads to more wear of both track and wheels and also significantly reduces the speed at which a tram can round a curve.

Bézier curves are also used in the time domain, particularly in animation and interface design, e. g., a Bézier curve can be used to specify the velocity over time of an object such as an icon moving from A to B, rather than simply moving at a fixed number of pixels per step.

The simplest method for scan converting ( rasterizing ) a Bézier curve is to evaluate it at many closely spaced points and scan convert the approximating sequence of line segments.

The curve starts at P < sub > 0 </ sub > going toward P < sub > 1 </ sub > and arrives at P < sub > 3 </ sub > coming from the direction of P < sub > 2 </ sub >.

* The curve begins at P < sub > 0 </ sub > and ends at P < sub > n </ sub >; this is the so-called endpoint interpolation property.

* A curve can be split at any point into two subcurves, or into arbitrarily many subcurves, each of which is also a Bézier curve.

An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetric cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 512 bits, all have similar difficulty at present.

* The material points forming a closed curve at any instant will always form a closed curve at any subsequent time.

With hinged, fixed or free end support conditions the deflected shape in neutral equilibrium of an initially straight column with uniform cross section throughout its length always follows a partial or composite sinusoidal curve shape, and the critical load is given by

( The coordinates here are to be chosen from a fixed finite field of characteristic not equal to 2 or 3, or the curve equation will be somewhat more complicated.

:* Iterated function systems – use fixed geometric replacement rules ; may be stochastic or deterministic ; e. g., Koch snowflake, Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge

The model assumes that there are two “ equally positioned firms ”; the firms compete on the basis of quantity rather than price and each firm makes an “ output decision assuming that the other firm ’ s behavior is fixed .” The market demand curve is assumed to be linear and marginal costs are constant.

On the other hand, the money supply curve is a horizontal line if the central bank is targeting a fixed interest rate and ignoring the value of the money supply ; in this case the money supply curve is perfectly elastic.

As price rises for a fixed money income, the consumer seeks less the expensive substitute at a lower indifference curve.

Since the starting point and ending point are fixed, S is minimized if and only if φ ' = 0, so the curve must lie on a meridian of the sphere φ = φ < sub > 0 </ sub > = constant.

* 1691-James Bernoulli shows that the catenary curve has the lowest center of gravity that any chain hung from two fixed points can have

A curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.

A spherical spiral ( rhumb line or loxodrome, left picture ) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle ( unequal to 0 ° and to 90 °) with respect to the meridians of longitude, i. e. keeping the same bearing.

He describes how shells are formed by rotating a closed curve around a fixed axis, the shape of the curve remains fixed but its size grows in a geometric progression.

Recall that the trajectory of a particle P is defined by its coordinate vector P measured in a fixed reference frame F. As the particle moves, its coordinate vector P ( t ) traces its trajectory, which is a curve in space, given by

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

A sample application of Faltings ' theorem is to a weak form of Fermat's Last Theorem: for any fixed n > 4 there are at most finitely many primitive integer solutions to a < sup > n </ sup > + b < sup > n </ sup > = c < sup > n </ sup >, since for such n the curve x < sup > n </ sup > + y < sup > n </ sup > = 1 has genus greater than 1.

Comparing the light curve, the amplitude and the radial velocity variations as compared to the light curve, Type II Cepheids constitute a different class of star with a luminosity relation offset from that of the δ Cepheids.

In astronomy, an analemma (; from Greek ἀνάλημμα " pedestal of a sundial ") is a curve representing the changing angular offset of a celestial body ( usually the Sun ) from its mean position on the celestial sphere as viewed from another celestial body ( usually the Earth ).

For these materials the yield strength is typically determined by the " offset yield method ", by which a line is drawn parallel to the linear elastic portion of the curve and intersecting the abscissa at some arbitrary value ( generally from 0. 1 % to 0. 2 %).

The equation of time is also the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth.

: A forehand or backhand shot that has an offset topspin that causes it to curve to the corners of the court, making the opponent run around and lose stamina, Ryoma first finds out about this technique from an article on a pro.

The rugged central peak of Arzachel is prominent, rising 1. 5 kilometers above the floor, and is somewhat offset to the west with a bowed curve from south to north-northeast.

It is sometimes called the offset curve but the term " offset " often refers also to translation.

The term " offset curve " is used, e. g., in numerically controlled machining ( and in other computer graphics applications ), where it describes the shape of the cut made by a round cutting piece, which is " offset " from the trajectory of the cutter by a constant distance in the direction normal to the cutter trajectory at every point.

His application of reference lines, a diameter and a tangent is essentially no different than our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates.

The steeper slope of the municipal yield curve allows participants to collect more after-tax income from the municipal bond portfolio than is spent on the interest rate swap ; the carry is greater than the hedge expense.

Drop handlebars " drop " as they curve forward and down, offering the cyclist best braking power from a more aerodynamic " crouched " position, as well as more upright positions in which the hands grip the brake lever mounts, the forward curves, or the upper flat sections for increasingly upright postures.

This is directly seen from the derivative of the Bézier curve:

* Some curves that seem simple, such as the circle, cannot be described exactly by a Bézier or piecewise Bézier curve ; though a four-piece cubic Bézier curve can approximate a circle ( see Bézier spline ), with a maximum radial error of less than one part in a thousand, when each inner control point ( or offline point ) is the distance horizontally or vertically from an outer control point on a unit circle.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

If the substituents are numbered from 1 ( highest priority ) to 4 ( lowest priority ), then the sense of rotation of a curve passing through 1, 2 and 3 distinguishes the stereoisomers.

A function from the set of real numbers to the real numbers can be represented by a graph in the Cartesian plane ; the function is continuous if, roughly speaking, the graph is a single unbroken curve with no " holes " or " jumps ".

and the length of the curve from P < sub > 1 </ sub > to P < sub > 2 </ sub > is

* Cable Sag Error Calculator – Calculates the deviation from a straight line of a catenary curve and provides derivation of the calculator and references.

Graph of cosmic microwave background spectrum measured by the FIRAS instrument on the Cosmic Background Explorer | COBE, the most-precisely measured black body spectrum in nature, the standard error of estimation | error bars are too small to be seen even in enlarged image, and it is impossible to distinguish the observed data from the theoretical curve

The curve is banked at an angle θ from the horizontal, and the surface of the road is considered to be slippery.

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 center of curvature is defined at each position s located a distance ρ ( the radius of curvature ) from the curve on a line along the normal u < sub > n </ sub > ( s ).

Cosmic censorship hypotheses should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.