Geometrically, one studies the Euclidean plane ( 2 dimensions ) and Euclidean space ( 3 dimensions ).

* A simple anthropic argument for why there are 3 spatial and 1 temporal dimensions.

Right angle weave lends itself better as a technique to 3D beading, but peyote stitch offers the advantage of more tightly knit beads, which is sometimes necessary to properly portray an object in 3 dimensions.

The geometric interpretation of curl as rotation corresponds to identifying bivectors ( 2-vectors ) in 3 dimensions with the special orthogonal Lie algebra so ( 3 ) of infinitesimal rotations ( in coordinates, skew-symmetric 3 × 3 matrices ), while representing rotations by vectors corresponds to identifying 1-vectors ( equivalently, 2-vectors ) and so ( 3 ), these all being 3-dimensional spaces.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

The 4: 3 screen has dimensions of and area, while the widescreen is,.

In Chaosmosis, Guattari proposes an analysis of subjectivity in terms of four dimensions: ( 1 ) material, energetic, and semiotic fluxes ; ( 2 ) concrete and abstract machinic phylums ; ( 3 ) virtual universes of value ; and ( 4 ) finite existential territories.

* ( for ideal mixtures ) is the concentration in dimensions of of substance ) length < sup >− 3 </ sup >, example

* is the concentration in dimensions of of substance ) length < sup >− 3 </ sup >, example

The dimensions of the factors correspond to the 1 photon + 3 vector bosons + 8 gluons of the standard model.

Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x ' - axis are collinear, the y-axis is parallel to the y ' - axis, and the z-axis parallel to the z ' - axis.

The dimensions of density are mass divided by volume with units: kg / m < sup > 3 </ sup > or g / cm < sup > 3 </ sup >.

However, this theory needs to be generalized in ( 2 + 1 ) or ( 3 + 1 ) dimensions although, in principle, the field equations are amenable to such generalization as shown with the inclusion of a one-graviton process and yielding the correct Newtonian limit in d dimensions if a dilaton is included.

This is further complicated by the fact that gravitons can propagate in ( 3 + 1 ) dimensions and consequently that would imply gravitons and dilatons exist in the real world.

This is inadequate to describe gravity in 3 + 1 dimensions which has local degrees of freedom according to general relativity.

At close range, fine control of the tip in all three dimensions when near the sample is typically piezoelectric, maintaining tip-sample separation W typically in the 4-7 Å ( 0. 4-0. 7 nm ) range, which is the equilibrium position between attractive ( 3 < W < 10Å ) and repulsive ( W < 3Å ) interactions.

In 3 dimensions, the volume inside a sphere ( that is, the volume of a ball ) is derived to be

While most small corporations do not have a 2 / 3 vote requirement, in the exact opposite, most large corporations especially those incorporated in Delaware, do have a 2 / 3 vote requirement.

The probability of a player hitting all 20 numbers on a 20 spot ticket is approximately 1 in 3. 5 quintillion ( 1 in 3, 535, 316, 142, 212, 180, 000 to be exact ).

In 1964, at the 12th CGPM conference, the original definition was reverted to, and thus the litre was once again defined in exact relation to the metre, as another name for the cubic decimetre, that is, exactly 1 dm < sup > 3 </ sup >.

Opinions vary as to the prophet's exact date, but nearly all scholars agree that Malachi prophesied during the Persian period, and after the reconstruction and dedication of the second temple in 516 BC ( compare Malachi 1: 10 ; Malachi 3: 1, Malachi 3: 10 ).

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

There are two different types of SU ( 3 ) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry which rotates different flavors of quarks to each other, or flavor SU ( 3 ).

Since clause 3 provides that Members of the House of Representatives are apportioned state-by-state and that each state is guaranteed at least one Representative, exact population equality between all districts is not guaranteed and, in fact, is currently impossible, because while the size of the House of Representatives is fixed at 435, several states had less than 1 / 435 of the national population at the time of the last reapportionment in 2000.

As the Dodo and Rodrigues Solitaire are in all likelihood part of the Indo-Australian radiation that produced the 3 small subfamilies mentioned above with the fruit doves and-pigeons ( including the Nicobar Pigeon ), they are here included as a subfamily Raphinae, pending better material evidence of their exact relationships.

More specifically, the exact position of Madrid is 3 ° 40 ´ of longitude west of Greenwich, England, and 40 ° 23 ´ north of the equator.

During the first four games, the Knicks took Games 1 and 3, and the Heat took Games 2 and 4, the exact opposite of the year before.

It is partially true: if a short exact sequence of groups is left split or a direct sum ( conditions 1 or 3 ), then all of the conditions hold.

However, if a short exact sequence of groups is right split ( condition 2 ), then it need not be left split or a direct sum ( neither condition 1 nor 3 follows ): the problem is that the image of the right splitting need not be normal.

Robin Hood is reputed to have been buried near Hartshead, although the exact place is not known, as the gravestone has been moved at least 3 times.

The precise cause of his death is uncertain, as is the exact date ( 3 or 4 November ).

According to this webcomic, calculating the exact coordinates of a world line is " embarrassingly simple ", and the deletion of the world line specified is executed by making a call and entering the coordinates of the world line, and pressing 3.

A crew also receives several days ' worth of Philmont trail food, packaged in bags which feed two people each ; the exact quantity depends on the crew's itinerary and the day on which it is scheduled to reach the next commissary ( see below ), but is usually 3 days worth of food.

On December 3, revolutionary Su Liangbi led troops in a massacre of a large number of Manchus ( the exact number is not known ).

A hand held flare burns for 3 minutes and can be used to localize or pinpoint more precisely the exact location or position of the party in trouble.

Let us label with s ( s = 1, 2, 3, ...) the exact states ( microstates ) that the system can occupy, and denote the total energy of the system when it is in microstate s as E < sub > s </ sub >.

In late 2003, the city of Dallas approved construction project plans to restore Dealey Plaza to its exact appearance on November 22, 1963., voters had approved US $ 500, 000 of the $ 3, 000, 000 needed.

If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).

The notation ∇ × F has its origins in the similarities to the 3 dimensional cross product, and it is useful as a mnemonic in Cartesian coordinates if we take ∇ as a vector differential operator del.

If a vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).

The three-dimensional Euclidean space R < sup > 3 </ sup > is a vector space, and lines and planes passing through the origin ( mathematics ) | origin are vector subspaces in R < sup > 3 </ sup >.

Vectors 3 through 15 were used to report various errors: bus error, address error, illegal instruction, zero division, CHK & CHK2 vector, privilege violation, and some reserved vectors that became line 1010 emulator, line 1111 emulator, and hardware breakpoint.

Oliver Heaviside FRS ( ( 18 May 1850 – 3 February 1925 ) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations ( later found to be equivalent to Laplace transforms ), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.

This plane can also be constructed by starting from R < sup > 3 </ sup > viewed as a vector space, see below.

Furthermore, for mathematicians, according to this formula the gluon color field can be represented by a SU ( 3 )- Lie algebra-valued " curvature "- 2-form where is a " vector potential "- 1-form corresponding to G and is the ( antisymmetric ) " wedge product " of this algebra, producing the " structure constants " f < sup > abc </ sup >.

If values are stored by reference, e. g. objects, null references can be used and so the cluster can be represented by a vector containing 3 slots for value pointers plus 4 slots for child references in the tree.

* P. Halmos, A Hilbert Space Problem Book, Springer, New York 1982 ( problem 3 contains version for vector spaces with coordinate systems ).

For example, the sum of the vectors ( 1, 2, 3 ) and (− 2, 0, 4 ) is the vector

A vector in the Cartesian plane, showing the position of a point A with coordinates ( 2, 3 ).

where a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub > are called the vector components ( or vector projections ) of a on the basis vectors or, equivalently, on the corresponding Cartesian axes x, y, and z ( see figure ), while a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub > are the respective scalar components ( or scalar projections ).

Scalar multiplication of a vector by a factor of 3 stretches the vector out.

Vector calculus ( or vector analysis ) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space The term " vector calculus " is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.