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The relationship of being homologous; a homologous relationship.
specifically, such relationship in the context of the geometry of perspective.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Qualifier: projective geometry
Topics: geometry, mathematics, sciences
Examples
- 1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61, Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology].
- 1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11, Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Qualifier: projective geometry
Topics: geometry, mathematics, sciences
Examples
- If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: algebraic-topology, mathematics, sciences, topology
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
Given a chain complex {Gn} and its associated set of homomorphisms {Hn}, the rule which explains how each Hn maps Gn into the kernel of Gn+1.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: algebra, mathematics, sciences
Examples
- Because of their connection with both homology and cohomology, chain complexes are an important topic of study in homological algebra.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
The relationship, between elements, of being in the same group of the periodic table.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: chemistry, natural-sciences, physical-sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
The relationship, between organic compounds, of being in the same homologous series.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: chemistry, natural-sciences, organic-chemistry, physical-sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: biology, human-sciences, natural-sciences, psychology, sciences
Examples
- 2000, Julie A. Hawkins, Chapter 2: A survey of primary homology assessment, Robert Scotland, R. Toby Pennington (editors), Homology and Systematics, Taylor & Francis, The Systematics Association, page 22, The objective of this study is to classify approaches to primary homology assessment, and to quantify the extent to which different approaches are found in the literature by examining variation in the ways characters are defined and coded in a data matrix.
Meaning relationships
Synonyms: none provided
Antonyms: heterology
The relationship of being homologous; a homologous relationship.
The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin; (evolutionary theory) specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between mammalian flippers and hands.
specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between mammalian flippers and hands.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Qualifier: evolutionary theory
Topics: biology, human-sciences, natural-sciences, psychology, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: heterology
The relationship of being homologous; a homologous relationship.
The presence of the same series of bases in different but related genes.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: biology, genetics, medicine, natural-sciences, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship of being homologous; a homologous relationship.
The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: anthropology, human-sciences, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
the quality of being similar or corresponding in position or value or structure or function
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Broader terms: similarity
From Latin homologia, from Ancient Greek ὁμολογία (homología, “agreement, assent”); compare French homologie. By surface analysis, homo- + -logy. In topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.
Across languages
Translations
53 source translations are retained for this English entry.
-
Catalan:
homologia
— homologous relationship
-
Finnish:
samankaltaisuus
— homologous relationship
-
Finnish:
homologia
— homologous relationship
-
French:
homologie
— homologous relationship
-
German:
Homologie
— homologous relationship
-
Irish:
homalógacht
— homologous relationship
-
Italian:
omologia
— homologous relationship
-
Portuguese:
homologia
— homologous relationship
-
Romanian:
omologie
— homologous relationship
-
Finnish:
samankaltaisuus
— geometry: automorphism representing a perspective projection
-
Finnish:
homologia
— geometry: automorphism representing a perspective projection
-
German:
Homologie
— geometry: automorphism representing a perspective projection
-
Irish:
homalógacht
— geometry: automorphism representing a perspective projection
-
Portuguese:
homologia
— geometry: automorphism representing a perspective projection
-
Romanian:
omologie
— geometry: automorphism representing a perspective projection
-
Chinese Mandarin:
同调
(tóngdiào)
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
Chinese Mandarin:
同调论
(tóngdiàolùn)
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
Finnish:
homologia
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
German:
Homologie
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
Irish:
homalógacht
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
Portuguese:
homologia
— algebraic topology: way of associating a sequence of groups to a sequence of topological spaces
-
Chinese Mandarin:
同调
(tóngdiào)
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
Chinese Mandarin:
同调群
(tóngdiàoqún)
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
Finnish:
homologia
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
German:
Homologie
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
Irish:
homalógacht
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
Portuguese:
homologia
— algebra: rule by which each member of a chain complex maps into the kernel of the next
-
Finnish:
homologia
— biology, psychology: relationship of having a common evolutionary or developmental origin
-
German:
Homologie
— biology, psychology: relationship of having a common evolutionary or developmental origin
-
Irish:
homalógacht
— biology, psychology: relationship of having a common evolutionary or developmental origin
-
Romanian:
omologie
— biology, psychology: relationship of having a common evolutionary or developmental origin
-
Finnish:
homologia
— chemistry: relationship of being in the same group of the periodic table
-
French:
homologie
— chemistry: relationship of being in the same group of the periodic table
-
German:
Homologie
— chemistry: relationship of being in the same group of the periodic table
-
Irish:
homalógacht
— chemistry: relationship of being in the same group of the periodic table
-
Italian:
omologia
— chemistry: relationship of being in the same group of the periodic table
-
Portuguese:
homologia
— chemistry: relationship of being in the same group of the periodic table
-
Spanish:
homología
— chemistry: relationship of being in the same group of the periodic table
-
Finnish:
homologia
— organic chemistry: relationship of being in the same homologous series
-
French:
homologie
— organic chemistry: relationship of being in the same homologous series
-
German:
Homologie
— organic chemistry: relationship of being in the same homologous series
-
Irish:
homalógacht
— organic chemistry: relationship of being in the same homologous series
-
Italian:
omologia
— organic chemistry: relationship of being in the same homologous series
-
Portuguese:
homologia
— organic chemistry: relationship of being in the same homologous series
-
Spanish:
homología
— organic chemistry: relationship of being in the same homologous series
-
Finnish:
homologia
— genetics: presence of the same series of bases in related genes
-
French:
homologie
— genetics: presence of the same series of bases in related genes
-
German:
Homologie
— genetics: presence of the same series of bases in related genes
-
Irish:
homalógacht
— genetics: presence of the same series of bases in related genes
-
Italian:
omologia
— genetics: presence of the same series of bases in related genes
-
Portuguese:
homologia
— genetics: presence of the same series of bases in related genes
-
Spanish:
homología
— genetics: presence of the same series of bases in related genes
-
German:
Homologie
— anthropology: relationship of possessing shared characteristics attributed to a common ancestor
