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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 to mean the same thing as squaring the circle, but it may also refer to approximate or numerical methods for finding the area of a circle.".
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- Squaring_the_circle wikiPageWikiLink Adam_Adamandy_Kochański.
- Squaring_the_circle wikiPageWikiLink Alexander_Pope.
- Squaring_the_circle wikiPageWikiLink Algebraic_number.
- Squaring_the_circle wikiPageWikiLink Anaxagoras.
- Squaring_the_circle wikiPageWikiLink Angle_trisection.
- Squaring_the_circle wikiPageWikiLink Antiphon_(orator).
- Squaring_the_circle wikiPageWikiLink Approximations_of_π.
- Squaring_the_circle wikiPageWikiLink Archimedes.
- Squaring_the_circle wikiPageWikiLink Aristophanes.
- Squaring_the_circle wikiPageWikiLink Arnaut_Daniel.
- Squaring_the_circle wikiPageWikiLink Augustus_De_Morgan.
- Squaring_the_circle wikiPageWikiLink Axiom.
- Squaring_the_circle wikiPageWikiLink Babylonian_mathematics.
- Squaring_the_circle wikiPageWikiLink Benjamin_Bold.
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- Squaring_the_circle wikiPageWikiLink Calculus.
- Squaring_the_circle wikiPageWikiLink Carl_D._Olds.
- Squaring_the_circle wikiPageWikiLink Category:Compass_and_straightedge_constructions.
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- Squaring_the_circle wikiPageWikiLink Category:History_of_geometry.
- Squaring_the_circle wikiPageWikiLink Category:Mathematical_problems.
- Squaring_the_circle wikiPageWikiLink Category:Pi.
- Squaring_the_circle wikiPageWikiLink Circle.
- Squaring_the_circle wikiPageWikiLink Classical_antiquity.
- Squaring_the_circle wikiPageWikiLink Compass-and-straightedge_construction.
- Squaring_the_circle wikiPageWikiLink Constructible_number.
- Squaring_the_circle wikiPageWikiLink Crank_(person).
- Squaring_the_circle wikiPageWikiLink Cut-the-Knot.
- Squaring_the_circle wikiPageWikiLink Dante_Alighieri.
- Squaring_the_circle wikiPageWikiLink Doubling_the_cube.
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- Squaring_the_circle wikiPageWikiLink Euclidean_geometry.
- Squaring_the_circle wikiPageWikiLink Euclidean_space.
- Squaring_the_circle wikiPageWikiLink Eudemus.
- Squaring_the_circle wikiPageWikiLink Ferdinand_von_Lindemann.
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- Squaring_the_circle wikiPageWikiLink Gilbert_and_Sullivan.
- Squaring_the_circle wikiPageWikiLink Gottfried_Wilhelm_Leibniz.
- Squaring_the_circle wikiPageWikiLink Gresham_College.
- Squaring_the_circle wikiPageWikiLink Hekat_(unit).
- Squaring_the_circle wikiPageWikiLink Henry_Oldenburg.
- Squaring_the_circle wikiPageWikiLink Hippocrates_of_Chios.
- Squaring_the_circle wikiPageWikiLink History_of_longitude.
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- Squaring_the_circle wikiPageWikiLink Integral.
- Squaring_the_circle wikiPageWikiLink Isaac_Newton.
- Squaring_the_circle wikiPageWikiLink James_Gregory_(mathematician).
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- Squaring_the_circle wikiPageWikiLink Jean-Étienne_Montucla.
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- Squaring_the_circle wikiPageWikiLink Lewis_Carroll.
- Squaring_the_circle wikiPageWikiLink Lindemann–Weierstrass_theorem.
- Squaring_the_circle wikiPageWikiLink List_of_geometers.
- Squaring_the_circle wikiPageWikiLink Lunar_distance_(navigation).
- Squaring_the_circle wikiPageWikiLink Lune_(geometry).
- Squaring_the_circle wikiPageWikiLink Lune_of_Hippocrates.
- Squaring_the_circle wikiPageWikiLink MacTutor_History_of_Mathematics_archive.
- Squaring_the_circle wikiPageWikiLink Marine_chronometer.
- Squaring_the_circle wikiPageWikiLink Martin_Gardner.
- Squaring_the_circle wikiPageWikiLink MathWorld.
- Squaring_the_circle wikiPageWikiLink Mathematics_of_paper_folding.
- Squaring_the_circle wikiPageWikiLink Metaphor.
- Squaring_the_circle wikiPageWikiLink Meton_of_Athens.
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- Squaring_the_circle wikiPageWikiLink Non-Euclidean_geometry.
- Squaring_the_circle wikiPageWikiLink Numerical_analysis.
- Squaring_the_circle wikiPageWikiLink Numerical_integration.
- Squaring_the_circle wikiPageWikiLink O._Henry.
- Squaring_the_circle wikiPageWikiLink Oenopides.
- Squaring_the_circle wikiPageWikiLink Origami.
- Squaring_the_circle wikiPageWikiLink Perpetual_motion.
- Squaring_the_circle wikiPageWikiLink Pi.
- Squaring_the_circle wikiPageWikiLink Polynomial.
- Squaring_the_circle wikiPageWikiLink Princess_Ida.
- Squaring_the_circle wikiPageWikiLink Professional_wrestling.
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- Squaring_the_circle wikiPageWikiLink Robert_Dixon_(mathematician).
- Squaring_the_circle wikiPageWikiLink Robin_Wilson_(mathematician).
- Squaring_the_circle wikiPageWikiLink Sestina.
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- Squaring_the_circle wikiPageWikiLink Square.