Hatless, in an overcoat of rough blue wool, I was given a proud farewell by my mother and father, and I set out into the strangely still streets of Brooklyn.

After the frames and transom are set up on the jig and temporarily braced, a piece of three-inch-wide mahogany ( only widths will be given since the 13/16-inch thickness is used throughout ) is butted between frames one and two below the line of the keelson.

We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

Household circuit breakers typically provide a maximum of 15 A or 20 A of current to a given set of outlets.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

* In the myth of Psyche and Eros, Psyche is given ambrosia by Hermes upon her completion of the quests set by Aphrodite and her acceptance on Olympus.

When a specific allophone ( from a set of allophones that correspond to a phoneme ) must be selected in a given context ( i. e. using a different allophone for a phoneme will cause confusion or make the speaker sound non-native ), the allophones are said to be complementary ( i. e. the allophones complement each other, and one is not used in a situation where the usage of another is standard ).

* An example of a non-unitary associative algebra is given by the set of all functions f: R → R whose limit as x nears infinity is zero.

On a more abstract level, model theoretic arguments hold that a given set of symbols in a theory can be mapped onto any number of sets of real-world objects — each set being a " model " of the theory — providing the interrelationships between the objects are the same.

A key point which is often overlooked is that published lower bounds for problems are often given for a model of computation that is more restricted than the set of operations that you could use in practice and therefore there are algorithms that are faster than what would naively be thought possible.

Since algorithms are platform-independent ( i. e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system ), there are significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.

This established the existence of the phenomenon of aberration beyond all doubt, and also allowed Bradley to formulate a set of rules that would allow the calculation of the effect on any given star at a specified date.

Rather, we may form the set of all objects that have a given property and lie in some given set ( Zermelo's Axiom of Separation ).

The tiles were given a metallic sheen to simulate the varying scales of the monster, with the color grading from green on the right side, where the head begins, to deep blue and violet in the center, to red and pink on the left side of the building.

Next, each player ( including the dealer ) is given four tiles with which to make two hands of two tiles each.

The key element of pai gow strategy is to present the optimal front hand and rear hand given four tiles dealt to the player.

Like the game Pentominoes, the goal is to use all of your tiles, and a bonus is given if the monomino is played on the very last move.

In many recent tile-matching games, the matching criterion is to place a given number of tiles of the same type so that they adjoin each other.

* Word Craft a game of rearranging word tiles given a dictionary definition or bit of trivia

One, given by Jan Brożek and proved much later by Thomas Hales, is that the hexagon tiles the plane with minimal surface area.

He also observed that this conjecture would imply the existence of an algorithm to decide whether a given finite set of tiles can tile the plane.

For example, the set of 13 tiles given above is an aperiodic set published by Karel Culik II in 1996.

A more detailed description of the history, manufacture and properties of porcelain tiles is given in the article “ Porcelain Tile: The Revolution Is Only Beginning .”

The RDP contains 4KB of on-chip TMEM ( texture memory ) in which the RDP can reference up to eight textures ( so called, " tiles ") at any given time.

Originally the floor was covered with Minton encaustic tiles ( given to the Sutherlands by the factory ) but Nancy Astor had them removed in 1906 and the present flagstones laid.

Other challenges for Rubik's Magic include reproducing given shapes ( which are often three-dimensional ), sometimes with certain tiles required to be in certain positions and / or orientations.

A review of an iPad / iPhone / iPod Touch application named Cyberchase Math Match ( in which the player " tap the tiles to match up CYBERCHASE math problems with their solutions ") was given a rating of 3 / 5 stars and advised for ages 8 and up.

" It was also given a rating of 5 / 5 for educational value " The game tests your memory like a traditional memory game, but half of the tiles have a math problem or an answer to match up.

Consideration was also given to the risks of elements of the procedure which would involve the ISS arm being used to carry Stephen K. Robinson below the shuttle, possibly the use of a sharp tool which has potential to damage the EVA suit or shuttle tiles.

A given set of tiles might admit periodic tilings — that is, tilings which remain invariant after being shifted by a translation ( for example, a lattice of square tiles is periodic ).

Mapping is the term given to the creation of the characters ' environment and surroundings by using 32x32 pixel " tiles ".

Six of the building tiles are " Alhambra tiles ;" these are taken out of the bag and one is given to each player.

Trader tiles are given to each player at the start of the game, and are placed adjacent to any tile.

A circle is a simple shape of Euclidean geometry that is the set of points in the plane that are equidistant from a given point, the

A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm.

A point in the Euclidean plane is a constructible point if, given a fixed coordinate system ( or a fixed line segment of unit length ), the point can be constructed with unruled straightedge and compass.

The result of applying a Euclidean transformation to a point is given by the formula

An example of an affine transformation which is not a Euclidean motion is given by scaling.

The space R of real numbers and the space C of complex numbers ( with the metric given by the absolute value ) are complete, and so is Euclidean space R < sup > n </ sup >, with the usual distance metric.

So, given an integral domain R, it is often very useful to know that R has a Euclidean function: in particular, this implies that R is a PID.

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

* The three-dimensional Euclidean space R < sup > 3 </ sup > with the Lie bracket given by the cross product of vectors becomes a three-dimensional Lie algebra.

More generally, if a given manifold is thought of as an embedded submanifold of Euclidean space one can picture the tangent space in this literal fashion.

In the Euclidean space R < sup > n </ sup >, the distance between two points is usually given by the Euclidean distance ( 2-norm distance ).

For example, in the " game " of Euclidean geometry ( which is seen as consisting of some strings called " axioms ", and some " rules of inference " to generate new strings from given ones ), one can prove that the Pythagorean theorem holds ( that is, you can generate the string corresponding to the Pythagorean theorem ).

In mathematics, the Euclidean distance or Euclidean metric is the " ordinary " distance between two points that one would measure with a ruler, and is given by the Pythagorean formula.

In Cartesian coordinates, if p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >,..., p < sub > n </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >,..., q < sub > n </ sub >) are two points in Euclidean n-space, then the distance from p to q, or from q to p is given by:

In the Euclidean plane, if p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) then the distance is given by

Examples include the decision problem forms of finding the greatest common divisor of two numbers, and determining what answer the extended Euclidean algorithm would return when given two numbers.

* Maxwell's equations allow us to use a given set of initial conditions to deduce, for every point in Euclidean space, a magnitude and direction for the force experienced by a charged test particle at that point ; the resulting vector field is the electromagnetic field.

In geometry, a hyperplane of an n-dimensional space V is a " flat " subset of dimension n − 1, or equivalently, of codimension 1 in V ; it may therefore be referred to as an ( n − 1 )- flat of V. The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly ; in all cases however, any hyperplane can be given in coordinates as the solution of a single ( due to the " codimension 1 " constraint ) algebraic equation of degree 1 ( due to the " flat " constraint ).

Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.

A complex structure gives rise to a conformal structure by choosing the standard Euclidean metric given on the complex plane and transporting it to X by means of the charts.

Contrast this with Euclidean geometry, in which a line has one parallel through a given point, and hyperbolic geometry, in which a line has two parallels and an infinite number of ultraparallels through a given point.