## Catalan's Constant [Ramanujan's Formula] By: Greg Fee |
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In "Catalan's Constant [Ramanujan's Formula]" by Greg Fee, readers are granted an intriguing and enlightening exploration of one of mathematics' most enigmatic figures, Srinivasa Ramanujan. With a masterful blend of history, biography, and mathematical analysis, Fee encapsulates the essence of Ramanujan's groundbreaking contributions to the field. The book delves deep into the life and work of Ramanujan, a mathematical genius who emerged from humble beginnings in colonial India to become one of the most revered mathematicians of the 20th century. Fee expertly traces Ramanujan's journey, from his early fascination with numbers to his pivotal encounter with the renowned British mathematician G.H. Hardy. Drawing upon meticulous research and an array of primary sources, the author paints a vivid portrait of Ramanujan's struggles, triumphs, and enduring impact on the mathematical world. At the heart of the book lies Ramanujan's most famous formulaâ€”Catalan's Constant. Fee skillfully breaks down this complex mathematical concept into accessible terms, allowing readers to grasp its beauty and significance. Through clear explanations and illustrative examples, he invites both mathematicians and general readers alike to appreciate the elegance and power of Ramanujan's formula. However, what sets Fee's book apart is his ability to seamlessly integrate the human element into a subject typically associated with rigid abstraction. By providing a window into Ramanujan's life, emotions, and personal struggles, the author creates a connection between the reader and the enigmatic mathematician. This empathetic approach leaves a lasting impression and emphasizes the profound impact that Ramanujan's work had not only on his contemporaries but on the field of mathematics as a whole. Additionally, Fee's writing style is exemplary, effortlessly guiding readers through intricate mathematical concepts with clarity and precision. His passion for the subject shines through, making even the most challenging ideas accessible to those with limited mathematical background. The book strikes a delicate balance between technicality and readability, allowing both enthusiasts and novices to engage with Ramanujan's extraordinary achievements. If there is one criticism, it would be that the book occasionally meanders into tangential topics, detracting slightly from the central narrative. However, this is a minor flaw amid the wealth of valuable information and insights that emerge from Fee's meticulous research. Overall, "Catalan's Constant [Ramanujan's Formula]" is an exceptional contribution to the world of mathematical literature. Greg Fee's passion and expertise shine through every page, making this book a must-read for anyone interested in the fascinating world of mathematics and the incredible legacy of Srinivasa Ramanujan. It serves as a testament to the enduring power of the human mind to unravel the mysteries of the universe and the profound impact of one individual's genius on an entire field of knowledge. ## First Page:Catalan's Constant [Ramanujan's Formula]Catalan constant to 300000 digits computed on September 29, 1996 by using a Sun Ultra Sparc in 1 day 8 hour 15 min 15 sec 55 hsec. The algorithm used is the standard series for Catalan, accelerated by an Euler transform. The algorithm was implemented using the LiDIA library for computational number theory and it is part of the multiprecision floating point arithmetic of the package. LiDIA is available from ftp://crypt1.cs.uni sb.de/pub/systems/LiDIA/LiDIA 1.2.1.tgz http://www jb.cs.uni sb.de/LiDIA/linkhtml/lidia/lidia.html The implementation of the algorithm is: inline void const catalan (bigfloat & y) { bigfloat p; bigfloat t; int i = 1, j = 3; // j = 2i1 // y = t = p = 1/2 divide (y, 1, 2); t.assign (y); p.assign (y); // while t is greater than the desired accuracy while (!t.is approx zero ()) { // do // p = p (i/j); // t = (t i p) / j; // y = y t; // i; j=2; multiply (p, p, i); divide (p, p, j); multiply (t, t, i); add (t, t, p); divide (t, t, j); add (y, y, t); i; j = 2; } } Here is the output of the program: Calculating Catalan's constant to 300000 decimals Time required: 1 day 8 hour 15 min 15 sec 55 hsec
Additional REFERENCES: Catalan constant is: sum(( 1)(n1)/(2n 1)2,n=1... Continue reading book >> |

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