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 ).

In two dimensions the position vector which has magnitude ( length ) and directed at an angle above the x-axis can be expressed in Cartesian coordinates using the unit vectors and:

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.

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

`` You know what they say about two deep dives in one day '', Artie went on, still twirling the snorkle and studying it intently.

But in our case -- and neither my wife nor I have extreme views on integration, nor are we given to emotional outbursts -- the situation has ruined one or two valued friendships and come close to wrecking several more.

The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.

He need only pick up one of the two red telephone receivers at his extreme left, right next to the big red button marked alert.

( There are two receivers in case one should be dropped and damaged.

The one apparent connection between the two is a score of buildings which somehow or other have survived and which naturally enough are called `` historical monuments ''.

When he added to his Pittsburgh commitments the directorship of the London Philharmonic Orchestra in 1958, he conducted one hundred fifty concerts within nine months, `` commuting '' between the two cities.

'' The other important difference between the two Constitutions was that the President of the Confederacy held office for six ( instead of four ) years, and was limited to one term.

Whatever pole of this contrast one emphasizes and whatever the tension between these two approaches to understanding the artistic imagination, it will be readily seen that they are not mutually exclusive, that they belong together.

I don't propose to go into their history, but I have one or two surmises.

If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.

Actually, two flags were used at the mansion -- a small one on rainy days, and a big one on bright days.

`` Little Rock is, without any flattery, one of the dullest towns in the United States and I would not have remained two hours in the place, if I had not met with some good friends who made me forget its dreariness ''.

`` They straggle at such a rate '', he told the commander-in-chief, `` that if the enemy were enterprising, they might get two from us, when we would take one of them, which makes me wish General Howe would go on, lest any incident happen to us ''.

Boniface had to uphold the sacredness of the feudal contract at all costs, for it was only as suzerain of Sicily and of the Patrimony of Peter that he had any justification for his Italian wars, but in the English-Scottish-French triangle it was almost impossible for him to recognize the claims of any one of the contestants without seeming to invalidate those of the other two.

But all the reports of this first embassy show that the two Savoyards were the heads of it, for they were the only ones who were empowered to swear for the king that he would abide by the pope's decision and who were allowed to appoint deputies in the event that one was unavoidably absent.

I don't know how and I don't know why but the two stores, the one in Margaretville and the one in Fleischmanns that had been set up as a partnership, were dissolved, separated from each other.

Catherwood, an architect in New York, had been forgotten, like Stephens, and Victor reconstructed their lives as one reconstructs, for a museum, a dinosaur from two or three petrified bones.

Blackman called the porter and had him remove everything but one bottle of brandy, and after that they would have a cocktail or two before dinner, or, on one of their walking trips, beer, or, in France and Italy, wine in moderation.

As the total number of incepting bachelors in 1629 was, according to Masson ( Life, 1:218 ) and n, two hundred fifty-nine, the twenty-four names listed in the ordo senioritatis for that year constitute slightly less than one tenth of the total number of bachelors who then incepted.

There were four from St. John's and four from Christ's, three from Pembroke, and two from each of the colleges, Jesus, Peterhouse, Queens', and Trinity, with Caius, Clare, King's, Magdalene, and Sidney supplying one each in the ordo senioritatis.

The Walnut Trees Of Altenburg includes not one war but two, and throws in a Turkish revolution along with some guerrilla fighting in the desert for good measure.