Each point with abscissa T on the graph represents an intersection between C and Af.

There are two types of such intersections, depending essentially on whether the curves cross at the point of intersection.

An ordinary point will be any point of intersection A such that in every neighborhood of A in the C-plane, Af meets both the interior and the exterior of C.

Any other point of intersection between C and Af will be called a tangent point.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

On C there is a Af correspondence in which the Af points cut from C by a general line, l, of the pencil correspond to the point of intersection of the image of L and the plane of the pencil.

In the simplest, the color value of the object at the point of intersection becomes the value of that pixel.

In distribution ray tracing, at each point of intersection, multiple rays may be spawned.

A metric space X is complete if and only if every decreasing sequence of non-empty closed subsets of X, with diameters tending to 0, has a non-empty intersection: if F < sub > n </ sub > is closed and non-empty, for every n, and diam ( F < sub > n </ sub >) → 0, then there is a point x ∈ X common to all sets F < sub > n </ sub >.

The intersection of the periodic orbit with the Poincaré section is a fixed point of the Poincaré map F. By a translation, the point can be assumed to be at x = 0.

These points of intersection are called equinoctial points: classically, the vernal point ( RA = 00 < sup > h </ sup > 00 < sup > m </ sup > 00 < sup > s </ sup > and longitude

There are therefore two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch.

For any point P on the minor arc BC of the circumcircle of an equilateral triangle ABC, with distances q and t from B and C respectively, and with the intersection of PA and BC being at a distance y from point P, we have that y is half the harmonic mean of q and t.

* In a convex mirror, parallel beams become divergent, with the rays appearing to diverge from a common point of intersection " behind " the mirror.

( which did not exist in Diophantus's time ), his method would be visualised as drawing a tangent to a curve at a known rational point, and then finding the other point of intersection of the tangent with the curve ; that other point is a new rational point.

In general, a node is a localised swelling ( a " knot ") or a point of intersection ( a vertex ).

The exact point of intersection of the Earth's axis and the Earth's surface, at any given moment, is called the " instantaneous pole ", but because of the " wobble " this cannot be used as a definition of a fixed North Pole ( or South Pole ) when metre-scale precision is required.

The pattern continues until a point is reached where neither firm desires “ to change what it is doing, given how it believes the other firm will react to any change .” The equilibrium is the intersection of the two firm ’ s reaction functions.

As a consequence of the third point, if a and b are coprime and br ≡ bs ( mod a ), then r ≡ s ( mod a ) ( because we may " divide by b " when working modulo a ).

Furthermore, if b < sub > 1 </ sub > and b < sub > 2 </ sub > are both coprime with a, then so is their product b < sub > 1 </ sub > b < sub > 2 </ sub > ( modulo a it is a product of invertible elements, and therefore invertible ); this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.

As a consequence of the first point, if a and b are coprime, then so are any powers a < sup > k </ sup > and b < sup > l </ sup >.

The two integers a and b are coprime if and only if the point with coordinates ( a, b ) in a Cartesian coordinate system is " visible " from the origin ( 0, 0 ), in the sense that there is no point with integer coordinates between the origin and ( a, b ).

Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers ( a, b ) to the Cartesian coordinates of every point in the set.

* The closest neighbor b to any point p is on an edge bp in the Delaunay triangulation since the nearest neighbor graph is a subgraph of the Delaunay triangulation.

When b is zero and A ≠ 0 the origin is an equilibrium ( or singular ) point of the flow, that is, if x < sub > 0 </ sub > = 0, then the orbit remains there.

The following equation on the polar coordinates ( r, θ ) describes a general ellipse with semidiameters a and b, centered at a point ( r < sub > 0 </ sub >, θ < sub > 0 </ sub >), with the a axis rotated by φ relative to the polar axis:

where s is the value of the significand ( after taking into account the implied radix point ), b is the base, and e is the exponent.

So the parameters are: a — distance from center C to either vertex b — length of a perpendicular segment from each vertex to the asymptotes c — distance from center C to either Focus point, F < sub > 1 </ sub > and F < sub > 2 </ sub >, and θ — angle formed by each asymptote with the transverse axis.

By summer 2003, most dual-band 802. 11a / b products became dual-band / tri-mode, supporting a and b / g in a single mobile adapter card or access point.

* Ebullioscopic constant ( K < sub > b </ sub >), which relates molality to boiling point elevation

In this particular equation, the constant m determines the slope or gradient of that line, and the constant term b determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.

In point of fact, this is a beige box with a bright red door, about one and a half feet square and hung from the wall about six feet from the door to Wisman's right.

A point like p gets information directly from n, but all information beyond n is indirectly relayed through n.

What I want to point out here is that all of them are ex-liberals, or modified liberals, with perhaps one exception.

Indeed, it is probable that this point is reached the moment the third level of change begins.

At that point we reach the `` closed '' historical situation: the situation in which man is no longer free to return to a status quo ante.

With regard to the change we are examining, the question is, at what point does the change become irreversible??

Such a response, of course, misses the point that in crisis order is going out of existence.

The point is that the reactionary, for whatever motive, perceives himself to have been part or a partner of something that extended beyond himself, something which, consequently, he was not able to accept or reject on the basis of subjective preference.

The maturity in this point of view lies in its recognition that no basic problem is ever solved without being clearly understood.

But that one should superimpose all these charts, run a pin through the common point, and then scale each planetary deferent larger and smaller ( to keep the epicycles from ' bumping ' ), this is contrary to any intention Ptolemy ever expresses.

His point is simply that the Tories have showered him with personal satire, despite the fact that as a private subject he has a right to speak on political matters without affronting the prerogative of the Sovereign.

This is the principal point made in this final section of Englishman No. 57, and it caps Steele's efforts in his other writing of these months to counteract the notion of the Tories as a `` Church Party '' supported by the body of the clergy.

One, a reservation on the point I have just made, is the phenomenon of pseudo-thinking, pseudo-feeling, and pseudo-willing, which Fromm discussed in The Escape From Freedom.

At this point a working definition of idea is in order, although our first definition will have to be qualified somewhat as we proceed.

Some historians have found his point of view not to their taste, others have complained that he makes the Tory tradition appear `` contemptible rather than intelligible '', while a sympathetic critic has remarked that the `` intricate interplay of social dynamics and political activity of which, at times, politicians are the ignorant marionettes is not a field for the exercise of his talents ''.

The other is that the charge for cabanas and parasols, though modest from an American point of view, still is a little high for many Athenians.

And there is one other point in the Poetics that invites moral evaluation: Aristotle's notion that the distinctive function of tragedy is to purge one's emotions by arousing pity and fear.

The point is that an ethical critic, with an assist from Freud, can seize on this theory to argue that tragedy provides us with a harmless outlet for our hostile urges.

Everyone is more or less sceptical and virtually no one has been willing to accept Lappenberg or Kemble's position on that point.

That is, there was no trace of Anglo-Saxons in Britain as early as the late third century, to which time the archaeological evidence for the erection of the Saxon Shore forts was beginning to point.

It is the triumph of rationalism and secular metaphysics which marks the point of no return.

What is wrong with advertising is not only that it is an `` outrage, an assault on people's mental privacy '' or that it is a major cause for a wasteful economy of abundance or that it contains a coercive tendency ( which is closer to the point ).