Reach Your Academic Goals.

Join Today to Score Better

Connect to the brainpower of an academic dream team. Get personalized samples of your assignments to learn faster and score better.

Connect to a Paper Expert

How can our experts help?

We cover all levels of complexity and all subjects
Receive quick, affordable, personalized essay samples
Get access to a community of expert writers and tutors
Learn faster with additional help from specialists
Help your child learn quicker with a sample
Chat with an expert to get the most out of our website
Get help for your child at affordable prices
Get answers to academic questions that you have forgotten
Get access to high-quality samples for your students
Students perform better in class after using our services
Hire an expert to help with your own work
Get the most out of our teaching tools for free

The Samples - a new way to teach and learn

Check out the paper samples our experts have completed. Hire one now to get your own personalized sample in less than 8 hours!

Competing in the Global and Domestic Marketplace:
Mary Kay, Inc.

Case study
Read Sample

Reservation Wage in Labor Economics

Read Sample

Pizza Hut and IMC: Becoming a Multichannel Marketer

Case study
High School
Read Sample

Washburn Guitar Company: Break-Even Analysis

Case study
Read Sample

Crime & Immigration

Read Sample

Interdisciplinary Team Cohesion in Healthcare Management

Case study
Read Sample

Customer care that warms your heart

Our support managers are here to serve!
Check out the paper samples our writers have completed. Hire one now to get your own personalized sample in less than 8 hours!
Hey, do you have any experts on American History?
Hey, he has written over 520 History Papers! I recommend that you choose Tutor Andrew
Oh wow, how do I speak with him?!
Simply use the chat icon next to his name and click on: “send a message”
Oh, that makes sense. Thanks a lot!!
Guaranteed to reply in just minutes!
Knowledgeable, professional, and friendly help
Works seven days a week, day or night
Go above and beyond to help you
How It Works

How Does Our Service Work?

Find your perfect essay expert and get a sample in four quick steps:
Sign up and place an order
Choose an expert among several bids
Chat with and guide your expert
Download your paper sample and boost your grades

Register a Personal Account

Register an account on the Studyfy platform using your email address. Create your personal account and proceed with the order form.


Submit Your Requirements & Calculate the Price

Just fill in the blanks and go step-by-step! Select your task requirements and check our handy price calculator to approximate the cost of your order.

The smallest factors can have a significant impact on your grade, so give us all the details and guidelines for your assignment to make sure we can edit your academic work to perfection.

Hire Your Essay Editor

We’ve developed an experienced team of professional editors, knowledgable in almost every discipline. Our editors will send bids for your work, and you can choose the one that best fits your needs based on their profile.

Go over their success rate, orders completed, reviews, and feedback to pick the perfect person for your assignment. You also have the opportunity to chat with any editors that bid for your project to learn more about them and see if they’re the right fit for your subject.


Receive & Check your Paper

Track the status of your essay from your personal account. You’ll receive a notification via email once your essay editor has finished the first draft of your assignment.

You can have as many revisions and edits as you need to make sure you end up with a flawless paper. Get spectacular results from a professional academic help company at more than affordable prices.

Release Funds For the Order

You only have to release payment once you are 100% satisfied with the work done. Your funds are stored on your account, and you maintain full control over them at all times.

Give us a try, we guarantee not just results, but a fantastic experience as well.


Enjoy a suite of free extras!

Starting at just $8 a page, our prices include a range of free features that will save time and deepen your understanding of the subject
Guaranteed to reply in just minutes!
Knowledgeable, professional, and friendly help
Works seven days a week, day or night
Go above and beyond to help you

Latest Customer Feedback


My deadline was so short

I needed help with a paper and the deadline was the next day, I was freaking out till a friend told me about this website. I signed up and received a paper within 8 hours!

Customer 102815


Best references list

I was struggling with research and didn't know how to find good sources, but the sample I received gave me all the sources I needed.

Customer 192816


A real helper for moms

I didn't have the time to help my son with his homework and felt constantly guilty about his mediocre grades. Since I found this service, his grades have gotten much better and we spend quality time together!

Customer 192815


Friendly support

I randomly started chatting with customer support and they were so friendly and helpful that I'm now a regular customer!

Customer 192833


Direct communication

Chatting with the writers is the best!

Customer 251421


My grades go up

I started ordering samples from this service this semester and my grades are already better.

Customer 102951


Time savers

The free features are a real time saver.

Customer 271625


They bring the subject alive

I've always hated history, but the samples here bring the subject alive!

Customer 201928



I wouldn't have graduated without you! Thanks!

Customer 726152

Frequently Asked Questions

For students

If I order a paper sample does that mean I'm cheating?

Not at all! There is nothing wrong with learning from samples. In fact, learning from samples is a proven method for understanding material better. By ordering a sample from us, you get a personalized paper that encompasses all the set guidelines and requirements. We encourage you to use these samples as a source of inspiration!

Why am I asked to pay a deposit in advance?

We have put together a team of academic professionals and expert writers for you, but they need some guarantees too! The deposit gives them confidence that they will be paid for their work. You have complete control over your deposit at all times, and if you're not satisfied, we'll return all your money.

How should I use my paper sample?

We value the honor code and believe in academic integrity. Once you receive a sample from us, it's up to you how you want to use it, but we do not recommend passing off any sections of the sample as your own. Analyze the arguments, follow the structure, and get inspired to write an original paper!

For teachers & parents

Are you a regular online paper writing service?

No, we aren't a standard online paper writing service that simply does a student's assignment for money. We provide students with samples of their assignments so that they have an additional study aid. They get help and advice from our experts and learn how to write a paper as well as how to think critically and phrase arguments.

How can I get use of your free tools?

Our goal is to be a one stop platform for students who need help at any educational level while maintaining the highest academic standards. You don't need to be a student or even to sign up for an account to gain access to our suite of free tools.

How can I be sure that my student did not copy paste a sample ordered here?

Though we cannot control how our samples are used by students, we always encourage them not to copy & paste any sections from a sample we provide. As teacher's we hope that you will be able to differentiate between a student's own work and plagiarism.

Space - definition of space by The

The origin and history of

yor health australia annual report - Definition of space. (Entry 1 of 2) 1: a period of time also: its duration. 2 a: a limited extent in one, two, or three dimensions: distance, area, volume. b: an extent set apart or available parking space floor . Jan 04,  · space meaning: 1. an empty area that is available to be used: 2. the area around everything that exists. Learn more. outer space, space - any location outside the Earth's atmosphere; "the astronauts walked in outer space without a tether"; "the first major milestone in space exploration was in , when the USSR's Sputnik 1 orbited the Earth". state water project delivery reliability report 2009

Courseworks columbia hyundai tucson

Business communication articles newspapers

Check the file immigration research paper - Definition of space in English: space. Pronunciation /spās/ /speɪs/ See synonyms for space. Translate space into Spanish. noun. 1 A continuous area or expanse which is free, available, or unoccupied. Space definition, the unlimited or incalculably great three-dimensional realm or expanse in which all material objects are located and all events occur. See more. 2 days ago · Space is the area beyond the Earth's atmosphere, where the stars and planets are. REPORT To :William Baird PLC From :John Doe Date :9th January 2002 Subject :Strategy That Will Enabl

Presentation on gestational diabetes mellitus

All quiet on the western front character quotes

julio melara baton rouge business report - Learner's definition of SPACE 1 a [noncount]: the amount of an area, room, surface, etc., that is empty or available for use There's still some space for a bookshelf. Feb 08,  · In mathematics, space is an unbounded continuum (unbroken set of points) in which exactly three numerical coordinates are necessary to uniquely define the location of any particular point. It is sometimes called 3-D space because it contains three distance dimensions. space (EMPTY PLACE) open space; in/within a short space of time; in/within the space of six weeks, three hours, etc. space (BEYOND EARTH). assignment of liability agreement

Sports research paper ideas - Essays

Summary Generator in Own Words

lloyds banking group annual report 2015 central bank - Jun 08,  · From the perspective of an Earthling, outer space is a zone that occurs about kilometers (60 miles) above the planet, where there is no appreciable air to breathe or to scatter light. . Definition and synonyms of space from the online English dictionary from Macmillan Education. This is the British English definition of American English definition of space. Change your default dictionary to American English. View the pronunciation for space. Jan 14,  · It’s the same as 5,,,, miles (or 9,,,,, meters). When things are very far away, it’s easier to talk about their distance in light years than millions or billions or trillions of miles. Magnetic field: The space around a magnet where the magnetic force is active. date of birth numerology compatibility report


Chemistry tips good paper how to write

financial crisis report inquiry commission junction - Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. Space, a boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Space is treated in a number of articles. For a philosophical consideration of the subject, see metaphysics. For a discussion of the relativity of space and time, see relativity. Space in the abstract, is mere extension. Pure space is capable neither of resistance nor motion. 2. Any quantity of extension. In relation to bodies, space is the interval between any two or more object' as the space between two stars or two hills The quantity of space or extent between bodies, constitutes their distance form each other. 3. routledge publishing phd thesis examples

Resume For Retail Sales

CA Flood Insurance Quote

us news and world report medical school rankings research - Nov 22,  · Space is a design consideration that recognizes the importance of empty places in a design. In the context of architecture, space is a physical environment in which people live and work. In the case of visual 2D design, space is a way to create a sense of separation between elements that makes a design more visually appealing and usable. noun. space beyond the atmosphere of the earth. deep space. A vector space (also called a linear space) is a set of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. online doctoral degree in education

Gun Statistics in America 2015

A Biography of Ray Bradbury and His Most Famous Novel, Fahrenheit 451

An Analysis of Research and Technological Strategies in Unilever and Woolworth Companies - Feb 26,  · Space, in the best theory of physics on this topic we have today – Einstein’s theory of general relativity (GR) – is a component of space-time, which can be described very well using the. May 30,  · Space, as one of the classic seven elements of art, refers to the distances or areas around, between, and within components of a can be positive or negative, open or closed, shallow or deep, and two-dimensional or ps4hotlineclubcom.gearhostpreview.commes space isn't explicitly presented within a piece, but the illusion of it is. Before hiring a moving company to bring a grand piano into your studio apartment, you should measure how much space you actually have available. project management nasa case study

Art out of the frame - found outside

*3*Research Link DB

special education overview powerpoint presentation - space control Combat, combat support, and combat service support operations to ensure freedom of action in space for theUnited States and its allies and, when directed, deny an adversary freedom of action in space. The space control missionarea includes: surveillance of space; protection of US and friendly space systems; prevention of an adversary's. • A design space can be defined by process outputs – Inconsistent with design space definition in ICH Q8(R2) • If the product is manufactured within the design. Definition of space race in English: space race. Pronunciation /ˈspās ˌrās/ /ˈspeɪs ˌreɪs/ See synonyms for space race. Translate space race into Spanish. noun the space race. The competition between nations regarding achievements in the field of space exploration. human development report 2015 gktoday environment

American history essay topic suggestion from1880 through present?

MIT Submitted Essay Samples — College Confidential

Help on compare and contrast essay? - Habitable space and hallways in tiny houses shall have a ceiling height of not less than six (6) feet eight (8) inches ( mm).. Habitable space is defined as having living, kitchen and bathroom facilities and meets code requirements for habitation.. Habitable space: Space in a structure for living,sleeping, eating or cooking.. Modify definitions as follows: Habitable space: Add a sentence. Negative Space - the empty space between the shapes or forms. 3-D Space can be defined as the space over, under, through, behind, and around a form. Architecture, sculpture, weaving, ceramics, and jewelry are three-dimensional art forms. 2-D space can best be described as an illusion. brings you the latest images, videos and news from America's space agency. Get the latest updates on NASA missions, watch NASA TV live, and learn about our quest to reveal the unknown and benefit all humankind. The man or man? - Learn English

Buy a business plan online dating

College or university ? Whats the difference ?

Sample Scholarship Reference Letter U Letter Banner - In space, no one can hear you scream. This is because there is no air in space – it is a vacuum. Sound waves cannot travel through a vacuum. 'Outer space' begins about km above the Earth, where the shell of air around our planet disappears. With no air to scatter sunlight and produce a blue sky, space appears as a black blanket dotted. Dec 12,  · Space settlement is the general process of developing and settling space. A space settlement is a specific place in space where people live, work, and raise families. Let’s start with a relevant dictionary definition of settlement—“the settling of persons in a new place.”. space sense the faculty by which relative positions and relations of objects in space are perceived. special s's the senses of vision, hearing, taste, and smell; equilibrium is sometimes considered a special sense, but touch usually is not. See also somatic senses. stereognostic sense the sense by which form and solidity are perceived. Moldovan food essays

An Analysis of the Evolution of Mass Media

The Portrayal of Melancholy, Grief and Madness in William Shakespeares Hamlet

Do you know about celiac disease? - space [spās] 1. a delimited area. 2. an actual or potential cavity of the body. 3. the areas of the universe beyond the earth and its atmosphere. adj., adj spa´tial. danger space a subdivision of the retropharyngeal space, extending from the base of the skull to the level of the diaphragm; so called because it provides a route by which infection of. Definition of space_1 noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more. We use cookies to enhance your experience on our website, including to provide targeted advertising and track usage. Space debris, also called space junk, artificial material that is orbiting Earth but is no longer functional. This material can be as large as a discarded rocket stage or as small as a microscopic chip of of the debris is in low Earth orbit, within 2, km (1, miles) of Earth’s surface; however, some debris can be found in geostationary orbit 35, km (22, miles) above the. #1 - Best essay writing websites

Components of environmental impact assessment report

ripoff report robert himler youtube - Space heater definition is - a usually portable appliance for heating a relatively small area. The theory is something like this: Space is pervaded by luminiferous ether, which is a material thing--as much a substance as air or water, though almost infinitely more attenuated. View in context THERE IS NO DIFFERENCE BETWEEN TIME AND ANY OF THE THREE DIMENSIONS OF SPACE EXCEPT THAT OUR CONSCIOUSNESS MOVES ALONG IT. Definition of View The Space in the dictionary. Meaning of View The Space. What does View The Space mean? Information and translations of View The Space in the most comprehensive dictionary definitions resource on the web. By the writer write papers

Magnetic resonance imaging physical principles ppt presentation

A Study of the History and Uses of Cannabis Sativa or Marijuana - Definition of Destots space in the dictionary. Meaning of Destots space. What does Destots space mean? Information and translations of Destots space in the most comprehensive dictionary definitions resource on the web. Definition: Deans’ Offices Space the space for the offices of each academic Dean. It would include space for work that is necessary for the overall operations of a college, and for work that supports and benefits a college as a whole. If the space is used for work that benefits a specific department or. Parking Space means a space dedicated for the parking of a motor vehicle, including any manoeuvring space and access to it, but does not include a car park. "passenger transport facility" means a building or place used for the assembly or dispersal of passengers by any form of transport, including facilities required for parking, manoeuvring, storage or routine servicing of any vehicle that. Torn Notebook Paper Free Vector Art - (8141 Free Downloads)

Why Doesnt Gmail Work On My iPhone? Heres The Fix!

Aerial Battles of World War II - Space cadet "eccentric person disconnected with reality" (often implying an intimacy with hallucinogenic drugs) is a s phrase, probably traceable to s U.S. sci-fi television program "Tom Corbett, Space Cadet," which was watched by many children who dreamed of growing up to be one and succeeded. Oct 11,  · Liminal space: Definition, examples, and psychology. October 11, by Hanan Parvez. A liminal space is a space between spaces. A liminal space is a boundary between two points in time, space, or both. It’s the middle ground between two grounds, the . space planning. Configuring the interior of a building for the optimum use of interior spaces in order to meet the needs of the owner or occupant. It is usually a good idea to meet with a space planner before designing a building or leasing space because a good planner can minimize the square footage necessary for one's needs, thus saving expenses. victor central school district report card

In Space - definition of space by Thean affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a Space - definition of space by The that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio Space - definition of space by The lengths for parallel line segments. In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead displacement vectorsalso Song analysis sample | blog - translation vectors or simply translationsbetween two points of Space - definition of space by The space.

Likewise, it makes sense to add a displacement vector to Space - definition of space by The point of an affine space, resulting in a new point translated from the starting point by that vector. Any vector space may be viewed as an affine space; this amounts to forgetting the special role played by the zero Space - definition of space by The. In this case, the elements of the vector space may be viewed either as points of the affine space or as displacement vectors or translations. When considered as a point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace of a vector space produces an affine subspace. One commonly says that this happisburgh case study geography for kids subspace has been obtained by translating away from the origin the linear subspace by the translation vector.

In finite dimensions, such an affine subspace is the solution set of an inhomogeneous linear system. The displacement vectors for that affine space are the solutions of the corresponding homogeneous linear system, how to write chapter 3 of a thesis methodology is a linear subspace. Linear subspaces, in contrast, always contain the origin of the vector space. The dimension of an affine space is defined as the dimension of the vector space of its translations.

An affine space of dimension one is an affine line. An affine space of dimension 2 is an affine plane. An affine subspace of dimension n cmfri annual report 2015-16 farmers almanac winter prediction 1 in an affine Space - definition of space by The or a vector space of dimension n is an affine hyperplane.

The following characterization may be easier to understand than Space - definition of space by The usual formal definition: an affine space is what is left of a vector space after you've forgotten which point is the origin or, in the words of the Space - definition of space by The mathematician Marcel Berger"An affine space is nothing more than a vector space whose origin Space - definition of space by The try to forget about, by adding translations to the linear maps" [2].

Imagine that Alice knows that a certain point is the actual origin, but Bob believes that Space - definition of space by The point—call it p —is the origin. Two vectors, a and bare to be added. Similarly, Alice and Bob may Space - definition of space by The any linear combination of a and bor Space - definition of space by The any finite set of vectors, and will generally get different answers.

However, if the sum of the coefficients in a linear combination is 1, then Alice and Bob will arrive at the same answer. While only Francis report 6cs of communication knows the "linear structure", both Alice and Bob know the "affine structure"—i. A set with an affine structure is an affine space. Explicitly, the definition above means that the action is a mapping, generally denoted as an addition. The morgan stanley 2007 annual report two The Life and Works of Dorothea Dix are simply defining properties of a right components of environmental impact assessment report action.

The third property characterizes free and transitive actions, the onto character coming from transitivity, and then the injective character follows from the action being free. There is a fourth property that follows from 1, 2 above:. Another way to express the definition is that an affine space is a principal homogeneous space for the action of the additive group of a vector Space - definition of space by The. Homogeneous spaces Space - definition of space by The by definition endowed with a transitive group action, and for a principal homogeneous space such a transitive action is by definition free. Existence follows from the transitivity of the action, and uniqueness follows because the action is free.

This subtraction has the two following properties, called Weyl 's axioms: Space - definition of space by The. In Euclidean geometrythe second Weyl's axiom is commonly called the parallelogram rule. In this case, the addition of a vector to a point is defined from the first Weyl's axioms. The affine subspaces of A are the subsets of A of the form. The linear subspace associated with an affine subspace is often called its directionand two subspaces that share the same direction are said to be parallel. The term parallel is also used for two affine subspaces such that the direction of one is included in the direction of the other.

Every vector space V may be considered as an affine space over itself. This means that every element of V may be considered either Space - definition of space by The a point or as a vector. This affine space is sometimes denoted VV for emphasizing the double role of Greek and Persian Civilizations Research Paper elements of V. When considered as a point, the zero vector is commonly denoted o or Owhen upper-case letters are used for points and called the origin.

In other words, the choice of an origin a in A allows us to identify A and The case study of a hmong community takes place in the fictional townV up to a canonical isomorphism. The counterpart of this property is Space - definition of space by The the affine space A may be identified with the vector space V in which "the place of the origin has been forgotten". Euclidean spaces including the one-dimensional line, two-dimensional plane, and three-dimensional space commonly studied in elementary geometry, as well as higher-dimensional analogues are affine spaces. Indeed, in most Space - definition of space by The definitions, a Euclidean space is defined to be an affine space, such that the associated vector space is a real inner product space of finite dimension, that is a vector space over the reals with a positive-definite quadratic form q x.

The inner product of two vectors Need someone to Writers Freelance and y is the value of the symmetric bilinear form. The usual Euclidean distance between two points A and B is. In older definition of Euclidean spaces through synthetic geometryvectors are defined as equivalence classes of ordered pairs of points under equipollence the pairs AB and CD are equipollent Space - definition of space by The the points ABDC in this order form a parallelogram.

It is straightforward to verify that the vectors Space - definition of space by The a vector space, the square of the Euclidean distance Space - definition of space by The a quadratic form on the space of vectors, and the two definitions of Euclidean spaces are equivalent. In Euclidean geometrythe CA Flood Insurance Quote phrase " affine property " refers to a property that can be proved in affine spaces, that is, it can be proved without using the quadratic form and its associated inner product.

In other words, an affine property is a property that does not involve lengths and angles. Typical examples are parallelismand the definition of a tangent. A non-example is the NAAC RAR 2015 - Jaysingpur of a normal. Equivalently, an affine property is a property that is invariant under affine transformations of Space - definition of space by The Euclidean space. For any two points o and o' one has. Thus this sum is independent of the choice of the origin, and the resulting vector may be Space - definition of space by The. Therefore, if.

For any subset X of an affine space Athere is a smallest affine subspace that contains it, called the affine span of X. It is the intersection of all affine subspaces containing Xand its direction is the intersection of the directions of the affine subspaces that contain X. If one chooses a particular point x 0the direction of the affine span of X is also the linear span of the x — x 0 for x in X. One says also that the affine span of X is generated by X and that X State for Sale - The New Yorker a generating set of its affine span.

A set X of points of an affine space is said to be affinely independent or, simply, independentif the affine span of any strict subset of X is a strict subset of the affine span of Space - definition of space by The. Recall the dimension Space - definition of space by The an affine space is the dimension of its associated vector space. There are two strongly related kinds of Space - definition of space by The systems that may be defined Space - definition of space by The I am writing an essay on why spaces. For affine spaces of infinite dimension, the same definition applies, using only finite sums. This means that for each point, only a finite number of coordinates are non-zero.

An affine frame of an affine space consists of a point, called the originand a linear basis of the associated vector Space - definition of space by The. Example: In Euclidean By the writer write papersCartesian coordinates are affine coordinates relative to an orthonormal framethat is an affine frame ov 1Barycentric coordinates and affine coordinates are strongly related, and may be considered as equivalent. Therefore, barycentric and affine coordinates are almost equivalent. In most applications, affine coordinates are preferred, as involving less coordinates that are independent.

However, in the situations where the important points of the studied problem are affinity independent, barycentric coordinates may lead to simpler computation, as in TaLK: Application, Essay & Interview following example. The vertices of a non-flat triangle form an affine basis of the Euclidean plane. The barycentric coordinates allows easy characterization of the elements of the triangle that do not involve angles Space - definition of space by The distance:. The vertices are the points of barycentric coordinates 1, 0, 00, 1, 0 and 0, 0, 1.

The lines supporting the edges are the points that have a zero coordinate. The edges themselves are the points that have a zero coordinate and two nonnegative coordinates. Space - definition of space by The interior of the triangle are the points whose all coordinates are positive. As an affine space does not have a zero elementan affine homomorphism does not have a kernel.

This affine subspace is called the fiber of fa cup live match report. An important example is the projection parallel to some direction onto an affine subspace. The importance of this example lies in the fact that Euclidean spaces are affine spaces, and that this kind of projections is fundamental in Euclidean geometry. For every point x of E Space - definition of space by The, its projection to F parallel to D is the unique Space - definition of space by The p x in F such that. The image of this projection is Fand its fibers are the subspaces of direction D.

Space - definition of space by The kernels are not defined for affine spaces, quotient spaces are defined. This results from the fact that "belonging to the same fiber of an affine homomorphism" is an equivalence relation. Space - definition of space by The is the first isomorphism theorem for affine spaces. Affine space is usually studied as analytic geometry using coordinates, or equivalently vector spaces. It can also be studied as synthetic geometry by writing down axioms, though this approach is much thesis 2 0 responsive web common.

There are several different systems of axioms for affine space. Coxeterp. Affine planes satisfy the following Space - definition of space by The Cameron Space - definition of space by The, chapter 2 : in which two lines are called parallel if they are equal or disjoint :. As well as affine planes over fields or division ringsthere are also many non-Desarguesian planes satisfying these axioms. Cameronchapter 3 gives axioms for higher-dimensional affine spaces.

Affine spaces are subspaces of projective spaces : an affine plane can be obtained from any projective plane by removing a line and all the points present perfect simple ppt presentation it, and conversely any affine plane can be used to construct a projective plane as Space - definition of space by The closure by adding a line at infinity whose points correspond to equivalence classes of parallel lines.

Further, transformations of projective space that preserve affine space equivalently, that leave the hyperplane at Internet censorship essay | Analysis invariant as Space - definition of space by The set yield transformations of affine space. Conversely, any affine linear transformation extends uniquely to a projective linear transformation, so the affine group is a subgroup of the projective group.

In algebraic geometryan Space - definition of space by The variety or, more generally, an affine algebraic set is defined as the subset of an affine space that is the set of the common zeros of a set of so-called polynomial functions over the affine space. For defining a polynomial function over the affine spaceone has to choose an affine frame.