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1Construct a square equal in area to a given circle (a problem incapable of a purely geometric solution).
‘The problem of squaring the circle, namely constructing a square with the same area as a given circle using ruler and compasses alone, had been one of the classical problems of Greek mathematics.’
‘While in prison he tried to solve the problem of squaring the circle, that is constructing with ruler and compasses a square with area equal to that of a given circle.’
‘One of the mathematical problems which ibn al-Haytham attacked was the problem of squaring the circle.’
‘He is best remembered for his work in the history of mathematics, in particular he wrote a major article on squaring the circle and he also wrote biographies of mathematicians.’
‘We do know some details of this method of squaring the circle and, despite the criticisms of Aristotle, it was an important step forward in the development of mathematics.’
‘He claimed that the search for truth was equal to the task of squaring the circle.’
‘In the following years he worked on mathematical topics, in particular trying to solve the classical Greek problem of squaring the circle.’
‘This was the age when people were still optimistic of squaring the circle by a geometrical construction.’
‘It is usually claimed that Dinostratus used the quadratrix, discovered by Hippias, to solve the problem of squaring the circle.’
‘Three geometric construction problems from antiquity puzzled mathematicians for centuries: the trisection of an angle, squaring the circle, and duplicating the cube.’
1.1Do something that is considered to be impossible.
‘This is a direct result of social services having to square the circle of increased demand and reduced resources.’
‘The reconciliation of a global economic system based on ‘free trade and shareholder value’ with social needs is equivalent to squaring the circle.’
‘The author of Fear Of Flying - a mother who regrets having only one child and a veteran of four marriages who has spent her life trying to square the circle of feminism, career and family - is scared by what she sees around her.’
‘Despite the apparent chasm between the parties, the Prime Minister's spokesman was optimistic that the governments would be able to square the circle.’
‘In the run-up to the 2001 election, I wrote suggesting that the Tories could square the circle of higher spending on health and education with the tax cuts that had been in the party's DNA since 1979.’
‘When the original idea of foundation hospitals emerged, it was a genuinely bold attempt to square the circle of a taxpayer funded health service, entrepreneurialism, efficiency and patient choice.’
‘House builders have to square the circle of complying with government policy yet meeting customer demands for larger properties in peaceful locations.’
‘In other words, the government's task is to square the circle: to win an electoral constituency for policies that are entirely incompatible with the interests of the majority of the population.’
‘He attempted to square the circle by stating what we instinctively know already: that the international and domestic agendas are now two sides of the same coin.’
‘This is clearly an attempt to square the circle as regards corporate clients; they want predictable, more sedate releases while Microsoft needs more frequent releases in order to get new technologies into the market.’