squaring the circle

(redirected from Square the circle)
Also found in: Idioms.

squaring the circle:

see geometric problems of antiquitygeometric problems of antiquity,
three famous problems involving elementary geometric constructions with straight edge and compass, conjectured by the ancient Greeks to be impossible but not proved to be so until modern times.
..... Click the link for more information.
The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Squaring the Circle


the problem of finding a square equal in area to a given circle. To square a circle is to construct a square whose area is equal to that of the circle or to compute the area of the circle with given accuracy.

The attempt was made initially to exactly square the circle with compass and straightedge. The mathematicians of antiquity knew a number of cases when, with the help of these instruments, a curvilinear figure could be transformed into a rectilinear figure of the same area (for example, the lune of Hippocrates). Attempts to square the circle, which continued for thousands of years, were invariably unsuccessful. In 1775 the Paris Academy of Sciences, and later other academies as well, refused to consider work devoted to squaring the circle. Only in the 19th century was a scientific basis given for this refusal: the insolubility of the problem of squaring the circle with compass and straightedge was rigorously established.

If the radius of a circle is equal to r, then the side of the square of the same area is equal to x = rSquaring the Circle. Thus, the problem reduces to that of graphic multiplication of a given segment (r) by a given number (Squaring the Circle). However, the graphic multiplication of a segment by a number can be accomplished with compass and straightedge only if the number involved is the root of an algebraic equation with integral coefficients, which is solvable by square roots. Thus, the problem of squaring the circle is equivalent to the problem of determining the arithmetical nature of the number π.

At the end of the 18th century, the irrationality of the number π was established by the German mathematician J. Lambert and the French mathematician A. Legendre. In 1882 the German mathematician F. Lindeman proved that the number π (and that also means Squaring the Circle) is transcendental, that is, does not satisfy any algebraic equation with integral coefficients. Lindeman’s theorem put an end to attempts to solve the problem of squaring the circle using a compass and straightedge. The problem of squaring the circle becomes solvable if the means of construction are broadened. It was already known to Greek geometers that squaring the circle could be accomplished using transcendental curves; the first solution of the problem of squaring the circle was accomplished by Dinostratus (fourth century B.C.) with the help of a special curve—the quadratrix. On the problem of finding an approximate value for the number π, see the article pi.


O kvadrature kruga (Arkhimed, Giuigens, Lambert, Legendre). Sprilo-zheniem istorii voprosa, 3rd ed. Moscow-Leningrad, 1936. (Translated from German.)
Struik, D. J. Kratkii ocherk istorii matematiki, 2nd ed. Moscow, 1969. (Translated from German.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

squaring the circle

[′skwer·iŋthə ′sər·kəl]
For a circle with a specified radius, the problem of constructing a square that has the same area as the circle.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
How do you square the circle in a situation where your business globally depends on the free flow of information and one (side) restricts that " Joerg Wuttke, president of the European Union Chamber of Commerce in China, told Reuters of Google s retreat.
He added that the policy had been reviewed by the Intelligence and Security Committee, the group of MPs and peers who are supposed to oversee the activities of Britain's intelligence agencies, and that the ISC was able to "square the circle between secrecy and accountability".
Hippocrates tries to square the circle, and succeeds in squaring the lune.
In Written Lives, however, Javier Marias--a brilliant novelist, with one foot in the Trollopian pre-modern and the other in perfect strangeness--has managed, simply and offhandedly, to square the circle of literary biography: noting the tendency of much modern fiction to edge towards the status of the essay (Guy Davenport, Alexander Kluge, Enrique Vila-Matas), he treats the twenty-six famous (and not-so-famous) writers in this collection as fictional characters ("which may well be how all writers ...
I am now looking for some of these fresh ideas and if you have some to help square the circle on infrastructure for our region then I would be delighted to hear from you.
There's some great old footage and interviews with people like Bob Geldoff and Chrissie Hynde, and the film was made by a Mormon so it covers that angle pretty heavily, which makes it somewhat bizarre (the notable absence of swearing throughout, for example, or the attempt to square the circle of a cross-dressing, drug-gobbling rock star with his new faith-filled white-bread persona), but a good flick nonetheless.
It will nevertheless be difficult to square the circle on the two sides' conflicting demands.
In reviewing previous literature, Cohn roundly criticizes modern historians who ignore contradictions in order to "square the circle" between medieval and modern plague.
Now, to square the circle, it only remains for the erstwhile Magnificent Seven to return to Parkhead on Champions League duty with his new team and gun down the Hoops.
The passage that most impressed Smith in On Growth and Form is Thompson's discussion of "close-packing," with its brilliant exposition of the bee's hexagon as a space-saving device, a product of natural forces striving to square the circle, so to speak (having to grow within a limited surface, circular cells will of necessity become hexagonal because this represents the maximal possibility of expansion).
No imaginable social order can square the circle. If I wish to be associated with someone who does not desire my company, then necessarily one of us will be disappointed.
Speculation is rife as to how Chen will phrase his words May 20 in a bid to "square the circle" of trying to keep China happy and at the same time not budging on the sovereignty issue.