i Register
In some senses, euclidean is marked as rare. Watch for register when choosing this word.
euclidean
UK /juːˈklɪd.i.ən/ US /juˈklɪd.i.ən/
adj 4
Collocations
3VERB + EUCLIDEAN
rules
EUCLIDEAN + NOUN
algorithm, geometry, space, v
ADV.
then
Definitions
adj
1
Adhering to the principles of traditional geometry, in which parallel lines are equidistant.
2
Of or relating to Euclid's Elements, especially to Euclidean geometry.
adj
1
Of or relating to Euclidean zoning.
adj
1
Alternative spelling of Euclidean.
If (#92;alpha#95;1,#92;dots,#92;alpha#95;n) is an orthonormal basis of a euclidean space V, then for all #92;alpha,#92;beta in V#92;alpha#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)#92;alpha#95;i#92;quad#92;text#123;and#125;#92;quad(#92;alpha#92;vert#92;beta)#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)(#92;beta#92;vert#92;alpha#95;i).We turn now to a somewhat more profound matter. Suppose that we partially order by inclusion the collection of all orthonormal sets of vectors in a euclidean space V. A maximal element of this set is called a maximal orthonormal set.
Thesaurus
Synonyms
adjective — relating to geometry as developed by Euclid
Antonyms
Idioms & Phrases
Example Bank
401
If (#92;alpha#95;1,#92;dots,#92;alpha#95;n) is an orthonormal basis of a euclidean space V, then for all #92;alpha,#92;beta in V#92;alpha#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;
Wiktionary02
The surface of a balloon is not an Euclidean space, and therefore does not follow the rules of Euclidean geometry.
Tatoeba · #37862703
The Euclidean algorithm serves not only to determine the greatest common divisor between two whole numbers, but also to solve Diophantine equations.
Tatoeba · #912011904
The Euclidean algorithm serves not only to determine the greatest common divisor between two integers, but also to solve Diophantine equations.
Tatoeba · #9174243Usage Notes
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