What does "euclidean" mean?

Adhering to the principles of traditional geometry, in which parallel lines are equidistant.

How do you pronounce "euclidean"?

Pronounced //juːˈklɪd.i.ən//.

Common synonyms include: algebraic euclidean property, classical geometry, division domain property, euclid geometry, euclid's geometry, euclidian.

/juːˈklɪd.i.ən/ adj

adj ·Uncommon ·Advanced level

Adjective

1
Adhering to the principles of traditional geometry, in which parallel lines are equidistant. not-comparable
2
Of or relating to Euclidean zoning. not-comparable
3
Alternative spelling of Euclidean. alt-of, alternative, not-comparable, rare
"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."
4
Of or relating to Euclid's Elements, especially to Euclidean geometry. not-comparable

Adjective

"The surface of a balloon is not an Euclidean space, and therefore does not follow the rules of Euclidean geometry."

Etymology 1

Named after Euclid, who established the principles of plane geometry.

Etymology 2

Named after the landmark U.S. Supreme Court case Village of Euclid v. Ambler Realty Co., which in turn refers to the city of Euclid, Ohio.