Rainwater Harvesting Ramanujan
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R In desert areas of Rajasthan, there are many khadins Rainwater Harvesting of 20 ha or more, some of them having been first constructed in the fifteenth century AD. In North America, research on the modern potential ARNOLD PACEY of runoff farming methods has been stimulated by the realization that people living in what is now Mexico Throughout history people have lived in areas where and the southwestern United States prior to European there are few rivers and where the direct collection of settlement had methods of directing rainwater from hill- rainwater from roofs, paved courtyards, hillsides, or sides on to plots where crops were being raised, thereby rock surfaces is one of the best available methods for making productive agriculture possible in an otherwise securing a water supply. By extending this principle to unpromising semiarid environment. On lands occupied provide water for crops, early civilizations practiced by the Hopi and Papago peoples in Arizona, fields were agriculture much further into the semidesert areas of predominantly on alluvial valley soils below hillsides Arabia, Sinai, North Africa, India, and Mexico than orgullies from which water could flow to the crops during has been possible in modern times – and this is not rainstorms. Sites were chosen so that only minimal explicable by changes in climate. earthworks were needed to spread the water over the Agriculture in the Old World originated in climatically fields. These were short lengths of bund referred to as dry regions in the Middle East and may have depended spreader dikes. to some degree on rainwater running off nearby slopes almost from the start. Evidence is lacking until a later See also: ▶Irrigation in India period, however, when some of the most striking appli- cations of rainwater harvesting were related to crop production in the Negev Desert between 200 BCE and References AD 700. One technique would be to dig a channel Bradfield, M. The Changing Pattern of Hopi Agriculture. across a hillside to intercept water running downslope London: Royal Anthropological Institute, 1971. during storms. The water would be directed onto Evenari, M., L. Shanan, and N. Tadmor. The Negev: The fields which, in the Negev, were carefully leveled and Challenge of a Desert. 2nd ed. Cambridge, Massachusetts: enclosed by bunds (an embankment or dike). Further Harvard University Press, 1982. Kutsch, H. Principal Features of a Form of Water- west, steeper hillsides were used in Morocco, with Concentrating Culture (in Morocco). Trier: Geographisch cultivation on flat terraces formed behind stone retaining Geselkschaft Trier,1982. walls. In Tunisia, French travelers in the nineteenth Pacey, Arnold and Adrian Cullis. Rainwater Harvesting. century noted fruit trees being grown at the downslope London: Intermediate Technology Publications, 1986. end of small bunded rainwater catchment areas or microcatchments. In India, one common technique is simply to build a bund across a gently sloping hillside, so that runoff Ramanujan flows originating from rainfall collect behind the bund, where water is left standing until the planting date for the crop approaches; then the land is drained, and the BRUCE C. BERNDT crop sown. This land behind the bund which is sea- sonally flooded and then later planted with a crop is Srinivasa Ramanujan was born on 22 December 1887 known as an ahar in Bihar, or a khadin in Rajasthan. in the home of his maternal grandmother in Erode, Although some ahars may be only one hectare in extent India, a small town located about 250 miles southwest with a bund 100 m long, others are very large and of Madras. Soon thereafter, his mother returned with account for 800,000 ha of cultivation in Bihar state. her son to her home in Kumbakonam, approximately 1868 Ramanujan 160 miles south–southwest of Madras. Ramanujan’s many diagnoses made, but a more recent examination of father was a clerk in a cloth merchant’s shop, and his Ramanujan’s symptoms points to hepatic amoebiasis. In mother took in local college students to augment the 1919, he returned to India with the hope that a more family’s meager income. favorable climate and more palatable food would restore Ramanujan’s mathematical talent was recognized his health. However, his condition worsened, and on 26 in grammar school, and he won prizes, usually books April 1920, Ramanujan passed away. of English poetry, in recognition of his mathematical After Ramanujan’s death, Hardy strongly urged that skills. At the age of 15, Ramanujan borrowed G. S. Carr’s Ramanujan’s notebooks be edited and published with Synopsis of Pure Mathematics from the local Govern- his Collected Papers. Two English mathematicians, ment College in Kumbakonam. This unusual book, G. N. Watson and B. M. Wilson, devoted over 10 years written by a Cambridge tutor to teach students, contained to proving the approximately 3,000–4,000 theorems approximately 5,000 theorems, mostly without proofs, claimed by Ramanujan in his notebooks, but they never and was to serve as Ramanujan’s primary source of completed the task. It was not until 1957 that an mathematical knowledge. unedited photocopy edition of Ramanujan’s notebooks With a scholarship, Ramanujan entered the Govern- was published. In 1977, Berndt, with the help of Watson ment College in Kumbakonam in 1904. However, by and Wilson’s notes, began to devote all of his research this time, he was completely absorbed with mathemat- efforts toward editing the notebooks, and in 1998 he ics and would not study any other subject. Consequent- completed the task with the publication of his fifth ly, at the end of his first year, Ramanujan failed all of volume on the notebooks. In 1976, Andrews discovered his exams, except mathematics. He lost his scholarship a sheaf of 140 pages of Ramanujan’s work, now called and therefore was unable to return to college. the “lost notebook,” in the library at Trinity College, For the next 5 years, working in isolation, Ramanujan Cambridge. In 2005, Andrews and Berndt published devoted himself to mathematics. He worked on a slate, their first volume on Ramanujan’s lost notebook. and because paper was expensive, recorded his Ramanujan made many beautiful discoveries in mathematical discoveries without proofs in notebooks. several areas of number theory and analysis, in During this time, he attempted once more to obtain a particular, the theory of partitions, probabilistic number college education, at Pachaiyappa College in Madras, theory, highly composite numbers, arithmetical func- but his singular devotion to mathematics, and illness, tions, elliptic functions, modular equations, modular deterred him again. forms, q-series, hypergeometric functions, asymptotic Having married Janaki in 1909, Ramanujan sought analysis, infinite series, integrals, continued fractions, employment in 1910. For over a year, he was privately and combinatorial analysis. His influence can be traced supported by Ramachandra Rao, as he gradually to many areas of contemporary mathematics; this is became known in the Madras area for his mathematical evident in the proceedings of major conferences gifts. In 1912, Ramanujan became a clerk in the Madras commemorating Ramanujan on the 100th anniversary Port Trust Office, and this was to be a watershed in his of his birth. Although much of Ramanujan’sworkisquite career, for the manager, S. Narayana Aiyar, and the deep, many of his original discoveries can be understood Chairman, Sir Francis Spring, took a kindly interest in with a background of only high school mathematics. In Ramanujan and encouraged him to write English particular, his several results on solving systems of mathematicians about his work. equations, representing integers as sums of powers, and On 16 January 1913, Ramanujan wrote to the famous approximating π are elementary. In the past few decades, English number theorist and analyst, G. H. Hardy. as more of Ramanujan’s results have been unearthed, He and his colleague J. E. Littlewood examined the his already great reputation has soared even more. approximately 60 mathematical results communicated by Most biographical sketches of Ramanujan’s life Ramanujan and were astounded by his many beauti- rely chiefly on the obituaries written by Seshu Aiyar ful and original claims. Hardy strongly encouraged and Ramachandra Rao, and the writings of Hardy. Ramanujan to come to Cambridge, so that his mathemat- However, Robert Kanigel’s biography is by far the most ical talents could be fully developed. At first, Ramanujan complete and detailed description of Ramanujan’s was reluctant to acceptthe invitation, because of orthodox life. Much can also be learned from Ramanujan’s letters Brahmin beliefs that crossing the seas makes one unclean, to Hardy, his family, and friends. but on 17 March 1914 Ramanujan sailed for England. During the next 3 years Ramanujan achieved References worldwide fame for his mathematical discoveries, some Albert, Robert S. Mathematical Giftedness and Mathematical made in collaboration with Hardy. However, in the Genius: A Comparison of G.H. Hardy and Srinivasa spring of 1917, Ramanujan became ill and was confined Ramanujan. Genius and the Mind: Studies in Creativity to nursing homes for the next 2 years. Tuberculosis, lead and Temperament. Ed. Andrew Steptoe. Oxford: Oxford poisoning, and a vitamin deficiency were among the University Press, 1998. 111–38. Rangoli: Versatile domestic art 1869 Andrews, George E. Simplicity and Surprise in Ramanujan’s finely layered floor. Petals of various flowers, such as ‘Lost’ Notebook. American Mathematical Monthly, 1997. oleanders, cosmos, zinnia, chrysanthemums, and green Andrews, George E., Richard A. Askey, Bruce C. Berndt, K. G. leaves provide the artist with the ability to work out Ramanathan, and Robert A. Rankin. Ramanujan Revisited. Boston: Academic Press, 1988. various patterns and colors. Most of the rangoli designs Andrews, George E. and Berndt, Bruce C. Ramanujan’s Lost are motifs of plants, flowers, leaves such as coconut, Notebook, Part I. New York: Springer, 2005.