If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

It may be applied to two characteristic dimensions of a three-dimensional shape.

In this relief, the two principal figures, the stern and courageous pope and the dismayed and frightened Attila, surge forward from the center into three dimensions.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions.

In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces ( see below ), or as a system of parametric equations.

Finally, Dürer discusses the Delian Problem and moves on to the ' construzione legittima ', a method of depicting a cube in two dimensions through linear perspective.

Instead, the ratio of the speed of the wind and that of the cups, the anemometer factor, depends on the dimensions of the cups and arms, and may have a value between two and a little over three.

Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect ( and, presumably, annihilate ) is three.

After the advent of quantum mechanics, work done by Landau in 1930 predicted the quantization of the Hall conductance for electrons confined in two dimensions.

In two dimensions, closed disks are compact since for any infinite number of points sampled from a disk, some subset of those points must get arbitrarily close either to a point within the disc, or to a point on the boundary.

Rotating frames and fictitious forces can often reduce the description of motion in two dimensions to a simpler description in one dimension ( corresponding to a co-rotating frame ).

The modern Cartesian coordinate system in two dimensions ( also called a rectangular coordinate system ) is defined by an ordered pair of perpendicular lines ( axes ), a single unit of length for both axes, and an orientation for each axis.

In two dimensions, the vector from the origin to the point with Cartesian coordinates ( x, y ) can be written as:

) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables.

The data warehouse bus architecture is primarily an implementation of " the bus ", a collection of conformed dimensions and conformed facts, which are dimensions that are shared ( in a specific way ) between facts in two or more data marts.

Another product rule for the cross product of two vector fields F and G in three dimensions involves the curl and reads as follows:

This means that the radio spectrum is divided into physical channels in two dimensions: frequency and time.

In two dimensions, one way to detect if point D lies in the circumcircle of A, B, C is to evaluate the determinant:

A divide and conquer algorithm for triangulations in two dimensions is due to Lee and Schachter which was improved by Guibas and Stolfi and later by Dwyer.

He proved equations for the volumes and areas of various figures in two and three dimensions, and enunciated the Archimedean property of finite numbers.

In dimension one this is the real line ; in dimension two it is the Cartesian plane ; and in higher dimensions it is a coordinate space with three or more real number coordinates.

In two or more dimensions we must use, the del or gradient operator, which generalises the first derivative, obtaining

The state's rights position was formulated by Jefferson and Madison in the Kentucky and Virginia Resolves, but in their later careers as heads of state the two proved themselves better Hamiltonians than Jeffersonians.

The result was that I found myself in the ridiculous position of having made a formal engagement by letter for the next week, only two days before my departure from London.

Fortunately, there are no cities or towns in the state, with one or two possible exceptions that are in too difficult a position to finance the proposed change.

`` We have two approaches for the technical man: the position of staff engineer, which is rated as high in salary as department manager ; ;

But during the same examination, two fingers may be inserted along the posterior wall ( the bottom of the vagina in the same position ) without any pain ; ;

Winslow Upton after graduation from Brown University and two years of graduate study, accepted a position at the Harvard Observatory.

To say this, of course, is to take up a position on one side of a controversy going on now for some two hundred years, or, at any rate, since the beginning of the distinctively modern period in theological thought.

For we have said, in effect, that of the two alternatives to his position variously represented by the other participants in the demythologizing discussion, only one is really an alternative.

Therefore, the only conceivable alternatives are those represented, on the one hand, by the two at least apparently self-consistent but mutually exclusive positions of Buri and Barth and, on the other hand, by the third but really pseudo position ( analogous to a round square ) of Bultmann.

Johnston's army was finally in position within a mile or two of Grant's force, and undetected, by the evening of April 5, 1862.

The first fossil find was dated to 4. 4 million years ago on the basis of its stratigraphic position between two volcanic strata: the basal Gaala Tuff Complex ( GATC ) and the Daam Aatu Basaltic Tuff ( DABT ).

While there are ancient relations between the Indian Vedas and the Iranian Avesta, the two main families of the Indo-Iranian philosophical traditions were characterized by fundamental differences in their implications for the human being's position in society and their view on the role of man in the universe.

For example, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other ( ortho ), one position removed from each other ( meta ), or two positions removed from each other ( para ).

Finding their position in mainland Europe precarious, they crossed to England in 330 ships in two divisions.

After the separation of the two offices the position of Astronomer Royal has been largely honorary, though he remains available to advise the Sovereign on astronomical and related scientific matters, and the office is of great prestige.

A member who accepts a service position or an organizing role is a " trusted servant " with terms rotating and limited, typically lasting three months to two years and determined by group vote and the nature of the position.

They pointed out that astrologers have only a small knowledge of astronomy and that they often do not take into account basic features such as the precession of the equinoxes which would change the position of the sun with time ; they commented on the example of Elizabeth Teissier who claimed that " the sun ends up in the same place in the sky on the same date each year " as the basis for claims that two people with the same birthday but a number of years apart should be under the same planetary influence.

Out of the 17 parliamentary votes considered by the Public Whip website to concern equal rights for homosexuals, Widdecombe took the opposing position in 15 cases, not being present at the other two votes.

An alternating magnetic field is applied at the atomizer ( graphite furnace ) to split the absorption line into three components, the π component, which remains at the same position as the original absorption line, and two σ components, which are moved to higher and lower wavelengths, respectively ( see Zeeman Effect ).

The club suffered relegation from the Welsh Football League in 2001 and has since slipped down through the next two divisions into its current position, although the future is now looking brighter.

Early board games represented a battle between two armies, and most current board games are still based on defeating opposing players in terms of counters, winning position or accrual of points ( often expressed as in-game currency ).

Nineteen-year-old rookie first baseman Fred Merkle, later to become one of the best players at his position in the league, was on first base, with teammate Moose McCormick on third with two out and the game tied.

The two armies confronted each other for several months of uncertainty, Caesar being in a much worse position than Pompey.

In Taviers on his right, he placed two battalions of the Greder Suisse Régiment, with a smaller force forward in Franquenée ; the whole position was protected by the boggy ground of the Mehaigne river, thus preventing an Allied flanking movement.