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• Squaring_the_circle abstract "Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that the construction would be impossible if pi were transcendental, but pi was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π.The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible.The term quadrature of the circle is sometimes used synonymously or may refer to approximate or numerical methods for finding the area of a circle.".
• Squaring_the_circle thumbnail Squaring_the_circle.svg?width=300.
• Squaring_the_circle wikiPageExternalLink 1.
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• Squaring_the_circle wikiPageExternalLink CircleSquaring.html.
• Squaring_the_circle wikiPageExternalLink Squaring_the_circle.html.
• Squaring_the_circle wikiPageExternalLink sq_circle.shtml.
• Squaring_the_circle wikiPageExternalLink event.asp?PageId=45&EventId=624.
• Squaring_the_circle wikiPageExternalLink Squaring_the_Circle.html.
• Squaring_the_circle wikiPageID "201359".
• Squaring_the_circle wikiPageRevisionID "603862092".
• Squaring_the_circle caption "Some apparent partial solutions gave false hope for a long time. In this figure, the shaded figure is the Lune of Hippocrates. Its area is equal to the area of the triangle .".
• Squaring_the_circle caption "Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge.".
• Squaring_the_circle hasPhotoCollection Squaring_the_circle.
• Squaring_the_circle image "Hipocrat arcs.svg".
• Squaring_the_circle image "Squaring the circle.svg".
• Squaring_the_circle width "250".
• Squaring_the_circle subject Category:Compass_and_straightedge_constructions.
• Squaring_the_circle subject Category:Euclidean_plane_geometry.
• Squaring_the_circle subject Category:History_of_geometry.
• Squaring_the_circle subject Category:Mathematical_problems.
• Squaring_the_circle subject Category:Pi.
• Squaring_the_circle type Abstraction100002137.
• Squaring_the_circle type Attribute100024264.
• Squaring_the_circle type Condition113920835.
• Squaring_the_circle type Difficulty114408086.
• Squaring_the_circle type MathematicalProblems.
• Squaring_the_circle type Problem114410605.
• Squaring_the_circle type State100024720.
• Squaring_the_circle comment "Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.".
• Squaring_the_circle label "Cuadratura del círculo".
• Squaring_the_circle label "Kwadratura koła".
• Squaring_the_circle label "Kwadratuur van de cirkel".
• Squaring_the_circle label "Quadratur des Kreises".
• Squaring_the_circle label "Quadratura del cerchio".
• Squaring_the_circle label "Quadratura do círculo".
• Squaring_the_circle label "Quadrature du cercle".
• Squaring_the_circle label "Squaring the circle".
• Squaring_the_circle label "Квадратура круга".
• Squaring_the_circle label "تربيع الدائرة".
• Squaring_the_circle label "円積問題".
• Squaring_the_circle label "化圓為方".
• Squaring_the_circle sameAs Kvadratura_kruhu.
• Squaring_the_circle sameAs Quadratur_des_Kreises.
• Squaring_the_circle sameAs Τετραγωνισμός_του_κύκλου.
• Squaring_the_circle sameAs Cuadratura_del_círculo.
• Squaring_the_circle sameAs Quadrature_du_cercle.
• Squaring_the_circle sameAs Quadratura_del_cerchio.
• Squaring_the_circle sameAs 円積問題.
• Squaring_the_circle sameAs 원적문제.
• Squaring_the_circle sameAs Kwadratuur_van_de_cirkel.
• Squaring_the_circle sameAs Kwadratura_koła.
• Squaring_the_circle sameAs Quadratura_do_círculo.
• Squaring_the_circle sameAs m.01clw7.
• Squaring_the_circle sameAs Q193394.
• Squaring_the_circle sameAs Q193394.
• Squaring_the_circle sameAs Squaring_the_circle.
• Squaring_the_circle wasDerivedFrom Squaring_the_circle?oldid=603862092.
• Squaring_the_circle depiction Squaring_the_circle.svg.
• Squaring_the_circle isPrimaryTopicOf Squaring_the_circle.