the age of genius

[...]...x The Age of Genius To the faculty and administration of Merrimack College, who created the Faculty Sabbatical Program and the Faculty Development Grant Program, both of which provided me with time to read and write INTRODUCTION he Age of Genius, the second volume of the Pioneers in Mathematics set, profiles the lives of 10 mathematicians who lived between 1300 and 1800 c.e These five centuries... unified theory of calculus that impacted the development of mathematics and the methods of scientific investigation In the 18th century, mathematicians formalized the theoretical basis of calculus and expanded its techniques Swiss mathematician Leonhard Euler was one of many mathematicians who contributed to the development of algebra, geometry, calculus, and number theory and applied the techniques of. .. degree) These tables specified each value to four sexagesimal (base-60) digits, the standard astronomical system of notation in which a number of the form 0: a, b, c, d represented the fractional value The section on 4 The Age of Genius spherical astronomy included a collection of tables that accurately allowed astronomers to track the locations of the Sun, the Moon, the planets, and the stars within the. .. 8 of a cube”) for cube root With these notations, L64 = represented the length of the side of a square having an area of 64, = 4 gave the length of the edge of a cube having and LC64 = a volume of 64 These notations, together with Viète’s concepts of genus and homogeneity, showed the strong influence geometry exerted on the development of his algebraic methods, terminology, and symbolism Theory of. .. ¯ of the law of cosines known in French-speaking countries as al-Kashı ’s theorem ¯ ¯ Al-K ashı also presented a formula for determining the length of ¯ ¯ a chord, the line segment joining two points on the circumference of a circle His formula specified that in a circle of radius r, a central Labeling angle of θ would cut off a chord of length the center of the circle as C and the endpoints of the. .. the first book, he presented three tables of trigonometric functions, a table of values giving the integer lengths of the sides of selected right triangles, a table of products of the 18 The Age of Genius m·n form — — for all integers 0 < m < n < 60, and a table of values re60 lated to calculations with the Egyptian calendar The second book described the computational methods he used to construct the. .. set of tables provided the means to convert from ecliptic coordinates of the celestial sphere to coordinates measured from the Earth’s equator, while other tables gave the longitudinal motion of the Sun, the latitudinal motion of the Moon and the planets, predictions of parallaxes and eclipses, and schedules for the phases of the Moon A geographical section listed the latitudes and longitudes of 516... al¯ t-i rasd (Treatise ¯a on the explanation of observational instruments), he described the construction of eight astronomical instruments The most well known of these was the armillary sphere, a sophisticated three-dimensional model of the universe with movable and stationary rings to represent the orbits of the planets and the locations of the stars He also described the Fakhrı sextant, a ¯ large,... centuries witnessed the end of a culturally rich period of mathematical and scientific innovation in China, India, and the Arabic countries and a renewal of intellectual life throughout Europe and the Western Hemisphere Although mathematical innovation had stagnated in Europe after the fall of the Roman Empire, scholars in southern Asia and the Middle East preserved the mathematical writings of the Greeks and... seas The final section of the book included tables cataloging the locations and magnitudes of the 84 brightest fixed stars, listing the distances of each planet from the center of the Earth, and providing information for astrologers In January 1416, al-K ashı completed a short work on astro¯ ¯ nomical instruments dedicated to Sultan Iskandar of the Turkoman dynasty, a different ruler than the one of the . Age of Genius, the second volume of the Pioneers in Mathematics set, profiles the lives of 10 mathematicians who lived between 1300 and 1800 c.e. These five centuries witnessed the end of a. governmental official. As the title indicated, this work gave estimates for the sizes of the Sun, the Moon, and the planets as well as approximations for their distances 2 The Age of Genius from the. the General Binomial Theorem 73 Method of Fluxions Introduces the Formal Theory of Calculus 75 Additional Mathematical Treatises 79 A New Theory of Light 80 Laws of Motion and the Principle of