History
Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by which some of these numbers could be derived was invented circa 850 by Thābit ibn Qurra (826-901). Other Arab mathematicians who studied amicable numbers are al-Majriti (died 1007), al-Baghdadi (980-1037), and al-Fārisī (1260–1320). The Iranian mathematician Muhammad Baqir Yazdi (16th century) discovered the pair (9363584, 9437056), though this has often been attributed to Descartes. Much of the work of Eastern mathematicians in this area has been forgotten.
Thābit's formula was rediscovered by Fermat (1601–1665) and Descartes (1596–1650), to whom it is sometimes ascribed, and extended by Euler (1707–1783). It was extended further by Borho in 1972. Fermat and Descartes also rediscovered pairs of amicable numbers known to Arab mathematicians. Euler also discovered dozens of new pairs. The second smallest pair, (1184, 1210), was discovered in 1866 by a then teenage B. Nicolò I. Paganini, having been overlooked by earlier mathematicians.
As of 1946 there were 390 known pairs, but the advent of computers has allowed the discovery of many thousands since then. Exhaustive searches have been carried out to find all pairs less than a given bound, this bound being extended from 108 in 1970, to 1010 in 1986, 1011 in 1993, and to a bound well over that today.
In 2007, there were almost 12,000,000 known amicable pairs.
Read more about this topic: Amicable Numbers
Famous quotes containing the word history:
“When the landscape buckles and jerks around, when a dust column of debris rises from the collapse of a block of buildings on bodies that could have been your own, when the staves of history fall awry and the barrel of time bursts apart, some turn to prayer, some to poetry: words in the memory, a stained book carried close to the body, the notebook scribbled by hand—a center of gravity.”
—Adrienne Rich (b. 1929)
“As History stands, it is a sort of Chinese Play, without end and without lesson.”
—Henry Brooks Adams (1838–1918)
“History has neither the venerableness of antiquity, nor the freshness of the modern. It does as if it would go to the beginning of things, which natural history might with reason assume to do; but consider the Universal History, and then tell us,—when did burdock and plantain sprout first?”
—Henry David Thoreau (1817–1862)