Thomas Baxter ( 1732–1740), was a schoolmaster and mathematician who published an erroneous method of

squaring the circle Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty ...

. He was derided as a "pseudo-mathematician" by

F. Y. Edgeworth Francis Ysidro Edgeworth (8 February 1845 – 13 February 1926) was an Anglo-Irish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. From 1891 onward, he was appointed th ...

, writing for the ''

Dictionary of National Biography The ''Dictionary of National Biography'' (''DNB'') is a standard work of reference on notable figures from British history, published since 1885. The updated ''Oxford Dictionary of National Biography'' (''ODNB'') was published on 23 September ...

''. When he was master of a private school at

Crathorne, North Yorkshire Crathorne is a village and civil parish in the Hambleton District of North Yorkshire, England. The parish population was 172 at the United Kingdom Census 2011, 2011 census. The River Leven, North Yorkshire, River Leven flows through the parish. ...

, Baxter composed a book entitled ''The Circle squared'' (London: 1732), published in octavo. The mathematical book begins with the untrue assertion that "if the

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...

of a

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

be unity or one, the

circumference In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to ...

of that circle will be 3.0625", where the value should correctly be pi. From this incorrect assumption, Baxter proves fourteen geometric theorems on circles, alongside some others on cones and

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

s, which Edgeworth refers to as of "equal absurdity" to Baxter's other assertions.

Thomas Gent Thomas Gent (1693–1778) was a printer and writer, born in Ireland, who spent most of his working life in York. He authored several works, mostly histories, but was financially unsuccessful. His poetry and the woodcut illustrations in his pub ...

, who published the work, wrote in his reminisces, in ''The Life of Mr. Thomas Gent'', that "as it never proved of any effect, it was converted to waste paper, to the great mortification of the author". This book has received harsh reviews from modern mathematicians and scholars. Antiquary Edward Peacock referred to it as "no doubt, great rubbish". Mathematician Augustus De Morgan included Baxter's proof among his ''Budget of Paradoxes'' (1872), dismissing it as an absurd work. The work was the reason Edgeworth gave Baxter the epithet, "pseudo-mathematician". Baxter published another work, ''Matho, or the Principles of Astronomy and Natural Philosophy accommodated to the Use of Younger Persons'' (London: 1740). Unlike Baxter's other work, this volume enjoyed considerable popularity in its time.

References

{{DEFAULTSORT:Baxter, Thomas Year of birth missing Year of death missing 18th-century British mathematicians People from Hambleton District Pseudomathematics Squaring the circle Schoolteachers from Yorkshire