First we will deal with the area of mathematics. One of the most recognized achievements of the Gupta period was the highly accurate calculation of pi, made by the renowned mathematician Aryabhata. Before this time, pi, the value that explained the relationships between the area, circumference, diameter, radius, and volume of circles and spheres, was frequently represented by Indian mathematicians as three, or the square root of ten. (Although both of these values are far from accurate, the fact that the civilization had a knowledge of geometry and mathematical relationships is proof of scientific advancement, especially when one compares it to Europe, which in the eleventh century still had no knowledge of mathematics.) Aryabhata calculated pi to the fourth decimal place at a value of 3.1416. Aryabhata also studied and improved other concepts of mathematics; for example, he determined the rule for the area of isosceles triangles and researched algebraic identities and intermediate equations. His work can be observed in the Gitikapanda, a book which includes a trigonometrical sine table, rules for extracting square and cube roots, the concepts of spheres, pyramids and other plane figures,
Bibliography: Beck, Roger B. (et al). World History: Patterns of Interaction. McDougal Littel. Boston. 1999. This textbook provided quality information that was relevant to the topic and accurate when compared to other sources. Jaggi, O.P. Dawn of Indian Science: Volume Two. Atma Ram & Sons. Delhi. 1969. The information was irrelevant to the time period as well as inconsistent with the other sources. Jain, Nem Kumar, M. Sc. Science and Scientists in India. Indian Book Gallery. Delhi. 1982. The book was helpful in identifying names of people and their achievements, but had very little information on the topic otherwise. Langer, William L. (ed.). An Encyclopedia of World History. Houghton Mifflin. Boston. 1968. The information was relevant and accurate, but not specific. It did, however, provide some interesting new details that were not known previously. Mookerji, R. K. The Gupta Empire. Shri Jainendra Press. Delhi. 1969. The information was relevant and accurate when compared to other sources. It was well-organized and provided useful information of the topic. Papanek, John L. (ed. et al). Ancient India: Land of Mystery. Time-Life Books. Virginia. 1994. The information was accurate and somewhat relevant to the topic. It was a little difficult to follow, but did provide some good information. Smith, Vincent A. The Early History of India. Oxford University Press. England. 1924. The book was not very relevant to the topic, but helped clarify previous information with dates.