16 THE SEVEN FOLLIES OF SCIENCE 



a more accurate determination of the ratio. Among the 

 Hindoos, as early as the sixth century, the now well-known 

 value, 3.1416, had been obtained by Arya-Bhata, and a 

 little later another of their mathematicians came to the 

 conclusion that the square root of 10 was the true value 

 of the ratio. He was led to this by calculating the perim- 

 eters of the successive inscribed polygons of 12, 24, 48, 

 and 96 sides, and finding that the greater the number of 

 sides the nearer the perimeter of the polygon approached 

 the square root of 10. He therefore thought that the 

 perimeter or circumference of the circle itself would be the 

 square root of exactly 10. It is too great, however, being 

 3.1622 instead of 3.14159. . . The same idea is attrib- 

 uted to Bovillus, by Montucla. 



By calculating the perimeters of the inscribed and cir- 

 cumscribed polygons, Vieta (1579) carried his approxima- 

 tion to ten fractional places, and in 1585 Peter Metius, 

 the father of Adrian, by a lucky step reached the now 

 famous fraction -||J, or 3.14159292, which is correct to the 

 sixth fractional place. The error does not exceed one part 

 in thirteen millions. 



At the beginning of the seventeenth century, Ludolph 

 Van Ceulen reached 35 places. This result, which " in his 

 life he found by much labor," was engraved upon his 

 tombstone in St. Peter's Church, Leyden. The monu- 

 ment has now unfortunately disappeared. 



From this time on, various mathematicians succeeded, 

 by improved methods, in increasing the approximation. 

 Thus in 1705, Abraham Sharp carried it to 72 places; 

 Machin (1706) to 100 places; Rutherford (1841) to 208 

 places, and Mr. Shanks in 1853, to 607 places. The 

 same computer in 1873 reached the enormous number of 

 707 places. 



