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Triangle vs Ideal - What's the difference?

triangle | ideal |

As a proper noun triangle

is the area comprising the cities of used with "the" except when attributive.

As a noun ideal is

ideal (perfect standard).

triangle

English

Noun

(en noun)
  • (geometry) A polygon with three sides and three angles.
  • (music) A percussion instrument made by forming a metal rod into a triangular shape which is open at one angle. It is suspended from a string and hit with a metal bar to make a resonant sound.
  • (cue sports) A triangular piece of equipment used for gathering the balls into the formation required by the game being played.
  • A love triangle.
  • * 2009 , Neil McDonald, Quadrant , November 2009, No. 461 (Volume LIII, Number 11), Quadrant Magazine Limited, page 104:
  • One of the writers' most pleasing inventions was to treat the triangle love story as comedy.
  • (systemics) The structure of systems composed with three interrelated objects.
  • A draughtsman's square in the form of a right-angled triangle.
  • (historical) A frame formed of three poles stuck in the ground and united at the top, to which soldiers were bound when undergoing corporal punishment.
  • Synonyms

    * (polygon) trigon (rare) * (love triangle) love triangle, * See also

    Derived terms

    * acute-angled triangle * acute triangle * anal triangle * Bermuda Triangle * black triangle * circular triangle * cyclic triangle * Devil's Triangle * equilateral triangle * eternal triangle * femoral triangle * golden triangle * Golden Triangle * isosceles triangle * love triangle * North Atlantic Triangle * obtuse-angled triangle * obtuse triangle * Pascal's triangle * Polynesian Triangle * pubic triangle * Reuleaux triangle * right-angled triangle * right triangle * scalene triangle * set triangle * Sierpinski triangle * spherical triangle * star-triangle relation * Sunni Triangle * triangle choke * triangle inequality * triangle offense * triangle piercing * triangle test * triangle wave * triangular * triangular distribution * triangular function * triangular prism * triangulate * triangulation

    Anagrams

    * * * * ----

    ideal

    English

    Adjective

    (en adjective)
  • Optimal; being the best possibility.
  • Perfect, flawless, having no defects.
  • * Rambler
  • There will always be a wide interval between practical and ideal excellence.
  • Pertaining to ideas, or to a given idea.
  • Existing only in the mind; conceptual, imaginary.
  • * 1796 , Matthew Lewis, The Monk , Folio Society 1985, p. 256:
  • The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —
  • * 1818 , , [[s:Frankenstein/Chapter 4, Chapter 4],
  • Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.
  • Teaching or relating to the doctrine of idealism.
  • the ideal theory or philosophy
  • (mathematics) Not actually present, but considered as present when limits at infinity are included.
  • ideal point
    An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

    Synonyms

    * See also

    Noun

    (en noun)
  • A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
  • Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny -
  • (mathematics, order theory) A non-empty]] lower set (of a partially ordered set) which is [[closure, closed under binary suprema (a.k.a. joins).[http://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem#Prime_ideal_theorems]
  • If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal .
  • (for example, algebra) A subring closed under multiplication by its containing ring.
  • Let \mathbb{Z} be the ring of integers and let 2\mathbb{Z} be its ideal of even integers. Then the quotient ring \mathbb{Z} / 2\mathbb{Z} is a Boolean ring.
    The product of two ideals \mathfrak{a} and \mathfrak{b} is an ideal \mathfrak{a b} which is a subset of the intersection of \mathfrak{a} and \mathfrak{b}. This should help to understand why maximal ideals' are prime ' ideals . Likewise, the union of \mathfrak{a} and \mathfrak{b} is a subset of \mathfrak{a + b}.

    Antonyms

    * (order theory) filter

    Derived terms

    * left ideal * right ideal * two-sided ideal * principal ideal

    Anagrams

    * ----