"THE SQUARING OF THE CIRCLE."
Eckington, Derbyshire, 15th October 1855. but—When will men ignorant of some of the first principles of mathe- matics cease to weary themselves in search of what the most rigid analysis has pronounced to be unattainable ? The proposition of your correspondent "It. D. S." admits of a very brief refutation ; which, as being more suitable to your.pages than a long mathematical proof, I beg leave to offer. He says, " It is evident that the area of a circle is the same as that of a square ' of the same periphery, or circumference ; in other words, that a wire or string of given length will enclose the same area whatever be the form into which it is bent. Let him bend his wire into a long oval, until the two sides meet if he will, and then say whether the enclosed area is as large as when the wire was circular. Or let hint take a cord of W. attains iu length, and to by actual measurement whether it wall contain the same number of roods when formed into a .square as when formed into a circle. So far from being "'evident" that it is so, he will Snd it utterly incorrect. In the one ease, the square, there will be 3 roods 2,t perches; in the other ease, the circle,. there will be 1 acre 0 mode 23. perches,. or nearly. sr rood more than in the former case. In- like manner,.with regard to a city enclosed by twelve miles of. square, the area would be 9 square miles ; if circular, it would amount to nearly 11[ miles. If the city were oblong, the same length of wall might enclose a much smaller-space; e.g. if two sides wan each 5 miles Thug,. and the other two 1 mile each, the enclosed area would only be 6 square miles. We may safely conclude, therefore, that R. D. S. has hrought.ua no nearer to the squaring-of the circle than we were before..
[The "quadrature of the circle" is tu very old puzzle ; and, taking our correspondent's grave solution of the problem as-a joke for the dead season- that might pair off with Table-turning or Spirit-rapping, which we under- stand to be still a matter of anxiouainvestigation among certain savans-we, perhaps too carelessly, allowed the bagatelle to pass- into our epistolary columns. That the joke was a bad one, must appear from the number and tone-of the answers to "R. D. S." now lying before us;. all very serious, and some of ponderous scientific elaboration. We select one of the least crabbed ; and so take leave of -the subject, with an apology for the trouble our in- advertence has occasioned.-En.]
Previous page
