Niches in the hall of fame

Niches in the hall of fame.

The symbol p used by the early English mathematicians William Oughtred, Isaac Barrow, and David Gregory to designate the circumference, or periphery-, of a circle. The first to use the symbol for the ratio of the circumference to the diameter was the English writer William Jone 1675-1749), in a publication in 1706. The symbol was not general]-.- used in this sense, however, until Euler adopted it in 1737.

The symbol n!, called factorial n, to represent the product

(1) (2) (3). . .(n-2) (n-l ) (n),

was introduced in 1808 by Christian Kramp (1760-1826) or Strasbourg. He chose the symbol so as to circumvent printing dilly'' ties incurred by a previously used symbol.

Of the considerable mathematical writings and contributions of Jones and Kramp, the above are undoubtedly the only by which they will, to any degree, be remembered by posterity.

It is interesting to remark here that Kramp's use of exclamation point in connection with factorial n, led to the adoption e. an associated symbol in combinatorial mathematics. In 1878, introduced subfactorial n, defined by

n![1 - 1/1! + 1/2! - . . . + (—l)ⁿ/n!].

It represents the number of derangements of a sequence of n objects in which no one of the n objects occupies its original positions.

A belated recognition. An outstanding get Metrical problem of the last half of the nineteenth century was to discover her a linkage mechanism for drawing a straight line. A solution was finally found in 1864 by a French army officer, A. Peaucellier (1832-1913,) and an announcement of the invention was made by A. Mannheim (1831-1906), a brother officer of engineers and inventor of the so-called Mannheim slide rule, at a meeting of the Paris Philomathic Society in 1867. But the announcement was little heeded until Lipkin, a young student of the celebrated Russian mathematician Chebyshev (1821-1894), independently reinvented the mechanism in 1871. Chebyshev had been trying to demonstrate the impossibility of such a mechanism. Lipkin received a substantial reward from the Russian government, whereupon Peaucellier's merit was finally recognized and he was awarded the great mechanical prize of the Institut de France.

Peaucellier's instrument contains seven bars. In 1874 Harry Hart (1848-1920) discovered a five-bar linkage for drawing straight lines, and no one has been able since to reduce this number of links or to prove that a further reduction is impossible. It has been proved that there exists a linkage mechanism for drawing any given algebraic curve, but that there cannot exist a linkage mechanism for drawing any transcendental curve.