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The Product Types Ontology: Class Definition for "Two-dimensional space"

This page is part of http://www.productontology.org/, a huge, precise dictionary of product types and brand names for marking up Web sites with schema.org or the GoodRelations e-commerce standard.

Breaking news: schema.org has just implemented our proposal to define an additionalType property with the use of this service in mind!

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http://www.productontology.org/

On this page: Usage(schema.org/Microdata, RDFa, Facebook) Contact Information Caching Policy License Acknowledgments References

pto:Two-dimensional_space (rdf:type owl:Class)

URI http://www.productontology.org/id/Two-dimensional_space
rdfs:subClassOf gr:ProductOrService, http://schema.org/Product
rdfs:label Two-dimensional space (as a class or brand name of products of services)
Translation(s):  Hapësira dy-dimensionale@sq; 

rdfs:comment

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured. The space is flat because any two lines transversed by a third line perpendicular to both of them are parallel, meaning they never intersect and stay at uniform distance from each-other. Two-dimensional spaces can also be curved, for example the sphere and hyperbolic plane, sufficiently small portions of which appear like the flat plane, but on which straight lines which are locally parallel do not stay equidistant from each-other but eventually converge or diverge, respectively. Two-dimensional spaces with a locally Euclidean concept of distance but which can have non-uniform curvature are called Riemannian surfaces.Some surfaces are embedded in three-dimensional Euclidean space or some other ambient space, and inherit their structure from it; for example, ruled surfaces such as the cylinder and cone contain a straight line through each point, and minimal surfaces locally minimize their area, as is done physically by soap films. Lorentzian surfaces look locally like a two-dimensional slice of relativistic spacetime with one spatial and one time dimension; constant-curvature examples are the flat Lorentzian plane (a two-dimensional subspace of Minkowski space) and the curved de Sitter and anti-de Sitter planes. Other types of mathematical planes and surfaces modify or do away with the structures defining the Euclidean plane. For example, the affine plane has a notion of parallel lines but no notion of distance; however, signed areas can be meaningfully compared, as they can in a more general symplectic surface. The projective plane does away with both distance and parallelism. A two-dimensional metric space has some concept of distance but it need not match the Euclidean version. A topological surface can be stretched, twisted, or bent without changing its essential properties. An algebraic surface is a two-dimensional set of solutions of a system of polynomial equations. Some mathematical spaces have additional arithmetical structure associated with their points. A vector plane is an affine plane whose points, called vectors, include a special designated origin or zero vector. Vectors can be added together or scaled by a number, and optionally have a Euclidean, Lorentzian, or Galilean concept of distance. The complex plane, hyperbolic number plane, and dual number plane each have points which are considered numbers themselves, and can be added and multiplied. A Riemann surface or Lorentz surface appear locally like the complex plane or hyperbolic number plane, respectively. Mathematical spaces are often defined or represented using numbers rather than geometric axioms. One of the most fundamental two-dimensional spaces is the real coordinate space, denoted \R^2, consisting of pairs of real-number coordinates. Sometimes the space represents arbitrary quantities rather than geometric positions, as in the parameter space of a mathematical model or the configuration space of a physical system. More generally, other types of numbers can be used as coordinates. The complex plane is two-dimensional when considered to be formed from real-number coordinates, but one-dimensional in terms of complex-number coordinates. A two-dimensional complex space – such as the two-dimensional complex coordinate space, the complex projective plane, or a complex surface – has two complex dimensions, which can alternately be represented using four real dimensions. A two-dimensional lattice is an infinite grid of points which can be represented using integer coordinates. Some two-dimensional spaces, such as finite planes, have only a finite set of elements. (Source: Wikipedia, the free encyclopedia, see http://en.wikipedia.org/wiki/Two-dimensional_space)

Note: The extraction of the abstract from the Wikipedia page may sometimes yield imperfect results. We are improving the algorithm regularly.

is rdfs:domain of gr:category gr:color gr:condition gr:depth gr:hasEAN_UCC-13 gr:hasGTIN-14 gr:hasMPN gr:hasManufacturer gr:hasStockKeepingUnit gr:height gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo gr:weight gr:width
is rdfs:range of gr:includes gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo

Note: This is a generic list. Some of the properties may not be applicable to this particular type of object.

Trademark Disclaimer:  Since this service returns class descriptions for potentiall any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. We assume no liability for the absence of trademark rights and other damages. See the section "License" below for details.

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Usage

The following shows how to model that you offer to sell [a/an/some] Two-dimensional space for $ 19.99.

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Microdata / Use with http://schema.org/Product

One of the most powerful usages of the class definitions from this site is to describe the type of your page and product for the schema.org product markup in Microdata syntax much more precisely.

Simply add the full URI of a class from this site, e.g. http://www.productontology.org/id/Two-dimensional_space as an additional type as follows:

<div itemscope itemtype="http://schema.org/Product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Two-dimensional_space" />
    <!-- other schema.org properties go in here -->
</div>		

Note: In HTML5, it is valid to use the <link> element in the body of a HTML document.

Here is a complete example:

<!DOCTYPE html>
<html>
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Two-dimensional_space</title>
</head>
<body>
<div itemscope itemtype="http://schema.org/Product" itemid="#product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Two-dimensional_space" />
    <span itemprop="name">.. a short name for the object ...</span>
    Product description: 
    <span itemprop="description">... a longer description ...</span>
    <div itemprop="offers" itemscope itemtype="http://schema.org/Offer" itemid="#offer">
        <span itemprop="price">$19.99</span> 
        <link itemprop="availability" href="http://schema.org/InStock" />In stock
    </div>
</div>
</body>
</html>

Turtle Syntax

@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix pto: <http://www.productontology.org/id/> .
@prefix gr: <http://purl.org/goodrelations/v1#> .
@prefix foo: <http://example.com/> .

# The object
foo:myObject a <http://www.productontology.org/id/Two-dimensional_space> ;
	a gr:SomeItems ;
	gr:name "... a short name for the object ..."@en ;
	gr:description "... a longer description ..."@en .

# The agent (person or company) who is offering it
foo:ACMECorp a gr:BusinessEntity ;
	gr:legalName "ACME Corp" ;
	gr:offers foo:Offer .
		
# The offer to sell it
foo:Offer a gr:Offering ;
	gr:includes foo:myObject;
	foaf:page <http://URI_of_the_page_containing_the_offer.com>;
	gr:hasBusinessFunction gr:Sell ;
	gr:validFrom "2011-01-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:hasPriceSpecification
         [ a gr:UnitPriceSpecification ;
           gr:hasCurrency "USD"^^xsd:string ;
           gr:hasCurrencyValue "19.99"^^xsd:float ;
           gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ] .

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDFa

<!DOCTYPE html>
<html version="HTML+RDFa 1.1" xmlns="http://www.w3.org/1999/xhtml">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Two-dimensional_space</title>
</head>
<body>
<div xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:foaf="http://xmlns.com/foaf/0.1/"
     xmlns:gr="http://purl.org/goodrelations/v1#"
     xmlns:pto="http://www.productontology.org/id/"
     xmlns:foo="http://example.com/"
     xmlns:xsd="http://www.w3.org/2001/XMLSchema#">

<!-- The agent (person or company) who is offering it -->
   <div about="#ACMECorp" typeof="gr:BusinessEntity">
      <div property="gr:legalName">ACME Corp</div>
      <div rel="gr:offers">
<!-- The offer to sell it -->	
         <div about="#offer" typeof="gr:Offering">
            <div rel="gr:hasBusinessFunction" resource="http://purl.org/goodrelations/v1#Sell"></div>
            <div rel="gr:includes">
<!-- The object -->	
               <div about="#myObject" typeof="http://www.productontology.org/id/Two-dimensional_space">
                  <div rel="rdf:type" resource="http://purl.org/goodrelations/v1#SomeItems"></div>
                  <div property="gr:description" xml:lang="en">... a longer description ...</div>
                  <div property="gr:name" xml:lang="en">.. a short name for the object ...</div>
               </div>
            </div>
            <div rel="foaf:page" resource="http://URI_of_the_page_containing_the_offer"></div>
            <div rel="gr:hasPriceSpecification">
               <div typeof="gr:UnitPriceSpecification">
                  <div property="gr:hasCurrency" content="USD" datatype="xsd:string">$ </div>
                  <div property="gr:hasCurrencyValue" datatype="xsd:float">19.99</div>
                  <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00" 
					   datatype="xsd:dateTime"></div>
               </div>
            </div>
            <div property="gr:validFrom" content="2011-01-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
            <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
         </div>
      </div>
   </div>
</div>
</body>
</html>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDF/XML

<?xml version="1.0" encoding="UTF-8" ?>
<rdf:RDF xmlns:gr="http://purl.org/goodrelations/v1#" 
  xmlns:pto="http://www.productontology.org/id/" 
  xmlns:xsd="http://www.w3.org/2001/XMLSchema#" 
  xmlns:foaf="http://xmlns.com/foaf/0.1/" 
  xmlns:foo="http://example.com/" 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<!-- The object -->
  <rdf:Description rdf:about="http://example.com/myObject">
    <rdf:type rdf:resource="http://www.productontology.org/id/Two-dimensional_space"/>    
    <rdf:type rdf:resource="http://purl.org/goodrelations/v1#SomeItems"/>
    <gr:name xml:lang="en">... a short name for the object ...</gr:name>
    <gr:description xml:lang="en">... a longer description ...</gr:description>
  </rdf:Description>
<!-- The agent (person or company) who is offering it -->
  <gr:BusinessEntity rdf:about="http://example.com/ACMECorp">
    <gr:legalName>ACME Corp</gr:legalName>
    <gr:offers rdf:resource="http://example.com/Offer" />
  </gr:BusinessEntity>
<!-- The offer to sell it -->   
  <gr:Offering rdf:about="http://example.com/Offer">
    <gr:includes rdf:resource="http://example.com/myObject" />
    <foaf:page rdf:resource="http://URI_of_the_page_containing_the_offer"/>
    <gr:hasBusinessFunction rdf:resource="http://purl.org/goodrelations/v1#Sell"/>
    <gr:validFrom rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-01-24T00:00:00+01:00</gr:validFrom>
    <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-12-24T00:00:00+01:00</gr:validThrough>
    <gr:hasPriceSpecification>
      <gr:UnitPriceSpecification>
        <gr:hasCurrency rdf:datatype="http://www.w3.org/2001/XMLSchema#string">USD</gr:hasCurrency>
        <gr:hasCurrencyValue rdf:datatype="http://www.w3.org/2001/XMLSchema#float">19.99</gr:hasCurrencyValue>
        <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
          2011-12-24T00:00:00+01:00</gr:validThrough>
      </gr:UnitPriceSpecification>
    </gr:hasPriceSpecification>
  </gr:Offering>

</rdf:RDF>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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SPARQL Query

prefix foaf: <http://xmlns.com/foaf/0.1/> 
prefix xsd: <http://www.w3.org/2001/XMLSchema#> 
prefix pto: <http://www.productontology.org/id/> 
prefix gr: <http://purl.org/goodrelations/v1#> 
prefix foo: <http://example.com/> 

# Find the cheapest offer for a Two-dimensional_space

SELECT * WHERE{
?company gr:offers ?offer .
?offer a gr:Offering .
?offer gr:hasBusinessFunction gr:Sell .
OPTIONAL {?offer rdfs:label ?label } .
OPTIONAL {?offer gr:name ?label } .
OPTIONAL {?offer rdfs:comment ?label } .
OPTIONAL {?offer gr:description ?label } .
?offer gr:hasPriceSpecification ?p .
?p a gr:UnitPriceSpecification .
?p gr:hasCurrency ?currency .
?p gr:hasCurrencyValue ?price .
?offer gr:includes ?product .
?product a <http://www.productontology.org/id/Two-dimensional_space> .
}
ORDER BY (?price)
LIMIT 10

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Facebook Open Graph Protocol

You can also use the class definitions from this site for better describing the type of your page or product for the Facebook Open Graph Protocol.

Simply define the namespace prefix pto: in the <html> element of your page

<html version="HTML+RDFa 1.1" 
	xmlns="http://www.w3.org/1999/xhtml" 
	xmlns:pto="http://www.productontology.org/id/" 
	>

and use the compact URI (CURIE) pto:Two-dimensional_space in combination with og:type as follows:

	<meta property="og:type" content="pto:Two-dimensional_space"/>

A complete example is here.

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Contact Information

Univ.-Prof. Dr. Martin Hepp

E-Business and Web Science Research Group
Chair of General Management and E-Business
Universität der Bundeswehr München
Werner-Heisenberg-Weg 39
D-85579 Neubiberg, Germany

Phone: +49 89 6004-4217
eMail: mhepp(at)computer.org (preferred mode of communication)
Web: http://www.heppnetz.de/
Web: http://www.unibw.de/ebusiness/

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Caching Policy

In order to minimize the load on the Wikipedia API, all requests are cached internally for 72 hours. This means that changes to the English Wikipedia will be available in this service within 72 hours or less if the same entry has been requested before. Classes not requested within the last six hours are always guaranteed to be in sync with the latest version in Wikipedia.

The RDF/XML dump file is updated every 12 hours only.

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License

The class definition text is taken from Wikipedia, the free encyclopedia under a Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license. Accordingly, the ontology class definitions are available under the very same license.

Trademark Disclaimer:  Since this service returns class descriptions for potentially any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. If you want us to block a certain name, please send your request including proof of your rights on the name to our contact address listed below.. Any of the trademarks, service marks, collective marks, design rights or similar rights that are mentioned, used, or cited in this service are the property of their respective owners. Their use here does not imply that you may use them for any purpose other than for the same or a similar informational use as contemplated by the original authors of the underlying Wikipedia articles under the CC-BY-SA and GFDL licensing schemes. Productontology.org is neither endorsed by nor affiliated with any of the holders of any such rights and as such cannot grant any rights to use any otherwise protected materials. Your use of any such or similar incorporeal property is at your own risk.

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Acknowledgements

Thanks to Stefano Bertolo, Julien Chaumond, Bob Ferris, Kingsley Idehen, Axel Polleres, Andreas Radinger, Alex Stolz, and Giovanni Tummarello for very valuable feedback, and to Katharina Siorpaes and Daniel Bachlechner, who contributed to the initial analysis of the stability of Wikipedia URIs back in 2007.

The work on The Product Types Ontology has been supported by the German Federal Ministry of Research (BMBF) by a grant under the KMU Innovativ program as part of the Intelligent Match project (FKZ 01IS10022B).

BMBF logo

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References

Wikipedia: Two-dimensional space, available at http://en.wikipedia.org/wiki/Two-dimensional_space.

Hepp, Martin: GoodRelations: An Ontology for Describing Products and Services Offers on the Web, Proceedings of the 16th International Conference on Knowledge Engineering and Knowledge Management (EKAW2008), Acitrezza, Italy, September 29 - October 3, 2008, Springer LNCS, Vol 5268, pp. 332-347.

Hepp, Martin; Siorpaes, Katharina; Bachlechner, Daniel: Harvesting Wiki Consensus: Using Wikipedia Entries as Vocabulary for Knowledge Management, IEEE Internet Computing, Vol. 11, No. 5, pp. 54-65, Sept-Oct 2007.

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