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A History of Pi: From Ancient Civilizations to Modern Industries
By Dr. Evelyn Reed, PhD, Mathematics and History of Science
Dr. Evelyn Reed holds a PhD in Mathematics and History of Science from Harvard University and is a renowned expert in the history of mathematical concepts and their impact on technological advancements. She is the author of several acclaimed books, including "The Algorithmic Revolution" and "Mathematics: A Cultural History."
Published by: Springer Nature - A leading global scientific publisher known for its rigorous peer-review process and high-quality publications in mathematics, engineering, and technology.
Edited by: Dr. Michael Chen, PhD, A seasoned editor with over 15 years of experience in scientific publishing, specializing in mathematics and computational sciences.
Summary: This article explores "a history of pi," tracing its evolution from ancient approximations to its modern-day significance in various industries. We delve into the mathematical breakthroughs that led to a deeper understanding of pi, examine its cultural impact, and analyze its crucial role in diverse fields like engineering, computer science, and physics.
Keywords: a history of pi, pi, mathematics, history of mathematics, engineering, computer science, physics, ancient mathematics, Archimedes, infinite series, algorithm, computational mathematics, industry applications
1. Ancient Roots: Early Approximations of Pi (A History of Pi)
"A history of pi" begins long before the Greek letter π was even conceived. Ancient civilizations, independently, grappled with the concept of the ratio of a circle's circumference to its diameter. The Babylonians, around 2000 BC, used an approximation of 3.125, remarkably close for its time. The Egyptians, in the Rhind Papyrus (circa 1650 BC), employed a slightly less accurate value of 3.16. These early approximations, while imperfect, demonstrate a fundamental human curiosity about the geometry of circles and the inherent constant that governed their properties. This early interest foreshadowed the extensive research into "a history of pi" that was to come.
2. Archimedes and the Method of Exhaustion: A Milestone in A History of Pi
The Greek mathematician Archimedes (287-212 BC) significantly advanced "a history of pi" with his ingenious method of exhaustion. He inscribed and circumscribed regular polygons within and around a circle, progressively increasing the number of sides. By calculating the perimeters of these polygons, he obtained increasingly accurate approximations of the circle's circumference, effectively sandwiching the true value of π between upper and lower bounds. Archimedes' approach, a precursor to integral calculus, established a rigorous method for approximating π to remarkable accuracy for his era—a value between 3.1408 and 3.1429. This marked a pivotal moment in "a history of pi," shifting from simple estimations to sophisticated mathematical reasoning.
3. The Infinite Series and the Dawn of Modern Understanding (A History of Pi)
The medieval and Renaissance periods witnessed slower progress in refining our understanding of "a history of pi." However, the 17th and 18th centuries ushered in a revolution. The invention of calculus opened new avenues for exploring π. Mathematicians like James Gregory and Gottfried Wilhelm Leibniz independently discovered infinite series that converged to π, providing a pathway to calculating it to an arbitrary degree of accuracy. These infinite series, which expressed π as the sum of an infinite number of terms, were a significant breakthrough in "a history of pi," moving the calculation beyond geometrical approximations.
4. The Computational Era and the Pursuit of Precision: A History of Pi
With the advent of computers in the 20th century, "a history of pi" entered a new phase characterized by an unparalleled pursuit of precision. Powerful algorithms, leveraging the infinite series and other computational techniques, enabled the calculation of π to trillions, and later, quadrillions, of digits. This quest, while seemingly esoteric, played a vital role in testing the capabilities of new computer architectures and refining numerical algorithms. The sheer computational power required to achieve such high precision served as a significant benchmark in computer science. The evolution of "a history of pi" became intrinsically linked to the advancement of computing technology itself.
5. Pi's Implications for Industry (A History of Pi)
The history of π is not just a mathematical curiosity; it has profound implications for numerous industries. In engineering, accurate calculation of π is essential for designing everything from circular structures and pipelines to satellite orbits and aircraft wings. In computer graphics, π plays a vital role in rendering circles, spheres, and other curved objects. In signal processing, understanding π is crucial for analyzing and manipulating waveforms. Furthermore, applications involving the Fourier transform, used extensively in areas like image compression and medical imaging, rely fundamentally on properties of π. This shows the continuing relevance of "a history of pi" for modern technological advancements.
6. Pi in Physics and Beyond: (A History of Pi)
Beyond engineering and computer science, "a history of pi" emerges in unexpected places within physics. It appears in equations describing oscillations, waves, and probabilities. In quantum mechanics, π plays a role in calculating probabilities and defining the wave functions of particles. The pervasive nature of π across various scientific disciplines underscores its fundamental importance in our understanding of the universe. The seemingly abstract concept of "a history of pi" has far-reaching implications for our understanding of physical reality.
7. Cultural Significance of Pi: A History of Pi
The history of π extends beyond its purely mathematical significance. It has captivated the imagination of mathematicians, artists, and the general public alike. Pi Day (March 14th) is a testament to its cultural influence. The pursuit of ever more precise approximations of π reflects a human desire to explore the limits of knowledge and push the boundaries of computation. This enduring fascination is a key part of "a history of pi."
8. Ongoing Research and the Future of Pi (A History of Pi)
While we know π to trillions of digits, the quest for understanding its properties continues. Mathematicians are still actively researching its relationship to other mathematical constants and exploring new algorithms to calculate it efficiently. This continued research demonstrates that "a history of pi" is far from complete. The story of pi will likely continue to unfold as mathematical understanding progresses and computational power increases.
9. Conclusion: The Enduring Legacy of a History of Pi
"A history of pi" is a rich tapestry woven from centuries of mathematical exploration, technological innovation, and cultural fascination. From its humble beginnings in ancient approximations to its current role in modern industries and scientific research, π continues to inspire awe and drive progress. The ongoing pursuit of ever greater precision and deeper understanding reflects humanity's enduring curiosity and the power of mathematics to illuminate the world around us.
FAQs
1. What is the exact value of pi? Pi is an irrational number, meaning its decimal representation goes on forever without repeating. We can only approximate its value.
2. Why is pi important in engineering? Pi is crucial for calculating circumferences, areas, volumes, and surface areas of circles and spheres, which are fundamental shapes in engineering design.
3. How is pi used in computer graphics? Pi is essential for generating circular and spherical objects, calculating angles, and performing other geometric operations in computer-generated imagery.
4. What are some different ways to calculate pi? Methods include using infinite series, Monte Carlo methods (random sampling), and algorithms based on continued fractions.
5. Is there a limit to the number of digits of pi we can calculate? Theoretically, there is no limit, but practically, computational resources and time constraints impose limitations.
6. What is the connection between pi and the Fourier Transform? The Fourier transform, widely used in signal and image processing, utilizes pi in its fundamental formulas.
7. What are some common misconceptions about pi? A common misconception is that pi is exactly 22/7 or 3.14. These are approximations.
8. How did the use of computers change the study of pi? Computers dramatically increased the precision to which pi could be calculated and facilitated the development of new algorithms.
9. What is Pi Day, and why is it celebrated? Pi Day (March 14th) celebrates the mathematical constant pi, referencing the date's numerical representation (3.14).
Related Articles:
1. Archimedes and the Measurement of a Circle: An in-depth examination of Archimedes' method of exhaustion and its impact on early approximations of pi.
2. Infinite Series and the Calculation of Pi: A detailed exploration of the use of infinite series in calculating pi, including the contributions of Leibniz and Gregory.
3. The Computational History of Pi: A review of the evolution of computational techniques used to calculate pi, from early mechanical calculators to modern supercomputers.
4. Pi in Engineering and Technology: A case study illustrating the practical applications of pi in various engineering disciplines.
5. Pi in Physics and Cosmology: Exploration of pi's appearances in physical laws and cosmological models.
6. The Cultural Significance of Pi: An analysis of pi's impact on art, literature, and popular culture.
7. The Irrationality and Transcendence of Pi: A mathematical discussion of the properties of pi, including its irrationality and transcendence.
8. Advanced Algorithms for Calculating Pi: A technical article exploring state-of-the-art algorithms used to compute pi to high precision.
9. The Future of Pi Research: A speculative piece on potential future developments in our understanding and calculation of pi.
| a history of pi: A History of Pi Petr Beckmann, 1971 Traces the history of the mathematical constant pi from the stone age through the computer age, discussing the background of the times when pi progressed, and when it did not. |
| a history of pi: The Book Of Pi: What is Pi, It's History and the Number to 100,000 Digits.: A Concise Handbook of Pi to 100,000 Decimal Places. B. C. Lester Books, 2020-04-28 Have you been looking to learn and memorise pi to 100,000 digits? Or just looking for a gift for your friend? Then this book of Pi is perfect for you! This book contains information of how Pi is derived, where it is used in calculations and a short history on how it got to 34.1 trillion decimal places found! Click 'Buy Now' to get this at a good value. |
| a history of pi: Pi: A Source Book Jonathan M. Borwein, 2013-06-29 Our intention in this collection is to provide, largely through original writings, an ex tended account of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi cant number of the most important mathematicians have contributed to its unfolding directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected. |
| a history of pi: Pi - Unleashed Jörg Arndt, Christoph Haenel, 2012-12-06 In the 4,000-year history of research into Pi, results have never been as prolific as present. This book describes, in easy-to-understand language, the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focused on new methods of high-speed computation. |
| a history of pi: A History of [pi] (pi) Petr Beckmann, 1993 Documents the calculation, numerical value, and use of the ratio from 2000 B.C. to the modern computer age, detailing social conditions in eras when progress was made. |
| a history of pi: One Million Digits of Pi Socrates Co., 2020-04-30 This book contains 1 million digits of pi on 371 pages (Decimal Places from 1 to 1,000,000) and is the perfect gift for everyone who loves math, especially on Pi day and for birthdays!ESTIMATED NUMBERS PER PAGE: 2714NUMBER OF PAGES: 371 pagesPAPER / TRIM SIZE: 6 x 9 (15,24cm x 22,86 cm)PAPER COLOR: White paperCOVER: Softcover paperback - glossy finishBOOK BINDING: Perfect bound |
| a history of pi: Prelude to Mathematics W. W. Sawyer, 2012-04-19 This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition. |
| a history of pi: A History of Pi Petr Beckmann, 1979 |
| a history of pi: Pi (π) in Nature, Art, and Culture Marcel Danesi, 2020-12-07 In Pi (π) in Nature, Art, and Culture Marcel Danesi investigates the manifestations of π in science, nature, symbolism, and culture, arguing that these are intrinsically intertwined. |
| a history of pi: The Amazing Number Pi Dev Gualtieri, 2013-12-28 Trace a maze through the first hundred digits of the mathematical constant, pi. The text summarizes the history and properties of this important number. |
| a history of pi: Humble Pi Matt Parker, 2021-01-19 #1 INTERNATIONAL BESTSELLER AN ADAM SAVAGE BOOK CLUB PICK The book-length answer to anyone who ever put their hand up in math class and asked, “When am I ever going to use this in the real world?” “Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations—that also gives you permission to feel a little better about some of your own mistakes.” —Ryan North, author of How to Invent Everything Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn’t. All sorts of seemingly innocuous mathematical mistakes can have significant consequences. Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean. Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun. |
| a history of pi: Why Pi? Johnny Ball, 2009-08-31 Discover how maths applies to everything with Johnny Ball Join Johnny Ball as he shows your child that maths isn't just numbers and sums, it's a fundamental, incredible, magical way to find out how everything works. From Pi, the amazing number that's vital for so much of everyday life, to perfect proportions - did you know Leonardo da Vinci worked out a person's ear is one-third the length of their face? - discover how numbers, from ancient times to the modern day, have enabled us to explore, build and discover just about everything. With puzzles to solve, conundrums to crack and incredible tricks to show to friends, Johnny Ball will teach your child to become a mathmagician! |
| a history of pi: Advanced Calculus of Several Variables C. H. Edwards, 2014-05-10 Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence. |
| a history of pi: Egyptian Pi John C. BEACH, 2017-09-03 At Abydos and at Karnak, stone carvings appear to display mathematical lessons by ancient Egyptians, and their method of calculating pi is equal to an accuracy of the 22/7 ratio commonly used as an approximation today. Evidence is presented that the ancient Egyptians had attained a sophisticated understanding of pi over 1,000 years before Archimedes and the Greeks. Readers are provided with several hands-on exercises that demonstrate mathematical and geometric concepts via folding paper disks and string. Pentagons, heptagons, rectangles, pyramids, and a humorous character named Cubit Forearm make their appearances as the author explores the practical significance of a discovery that will revise our understanding of the origins of mathematics in the ancient world. Appropriate for all ages, general readers, historians, mathematicians, and those with an interest in ancient Egypt. |
| a history of pi: Sir Cumference and the Dragon of Pi Cindy Neuschwander, 2013-01-07 For fans of the Sir Cumference series with Pi on their mind, here is the second installment in this fun look at math and language. This time the math adventure is centered around a potion that changes Sir Cumference into a fire-breathing dragon. Can Radius change him back? Join Radius on his quest through the castle to solve a riddle that will reveal the cure. It lies in discovering the magic number that is the same for all circles. Perfect for parent and teachers who are looking to make math fun and accessible for everyone. |
| a history of pi: e: The Story of a Number Eli Maor, 2011-10-12 The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science. |
| a history of pi: A History of Pi Petr Beckmann, 1971 Traces the history of the mathematical constant pi from the stone age through the computer age, discussing the background of the times when pi progressed, and when it did not. |
| a history of pi: Pi of Life Sunil Singh, 2017-08-08 Is the most important language in the universe also capable of making us happy in simple and profound ways? Can we really weave the foundations of lifelong joy—humility, gratitude, connection, etc.—through the apparent complexity of numbers? Have we oversold the practicality of mathematics, while ignoring its larger and more human purposes—happiness? In Pi of Life: The Hidden Happiness of Mathematics, Sunil Singh takes the readers on a unique adventure, discovering that all the elements that are essential for lifelong happiness are deeply intertwined with the magic of mathematics. Blending classic wisdom with over 100 pop culture references—music, television and film—Singh whimsically switches the lens in this book from the traditional society teaching math to a new and bold math teaching society. Written with charming buoyancy and intimacy, he takes us on an emotional and surprising journey through the deepest goldmine of mathematics—our personal happiness. |
| a history of pi: Pi: The Next Generation David H. Bailey, Jonathan M. Borwein, 2016-07-19 This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students. |
| a history of pi: Synopsis Palmariorum Matheseos William Jones, 1706 |
| a history of pi: A Slice of Pi Liz Strachan, 2016-08-25 A new look at maths without the Boring Bits . . . How many trillions are there in a googol? Which fractions are vulgar? What famous mathematician refused to eat beans? And which one never travelled without his pet spider in an ivory box? Mathematical theorems and equations are inextricably entangled with the great, and often eccentric thinkers who made breakthrough discoveries. Teacher and numbers expert Liz Strachan takes readers beyond the classroom, combining anecdotes, proofs and party tricks to reveal the foundations of algebra, geometry and trigonometry in a clear and entertaining style. From the Difference Engine to magic squares and from the Fibonacci rabbits to Fermat's Last Theorem, this fascinating tour of the weird world of numbers, imaginary, real or infinite, will appeal to anyone with an enquiring mind. |
| a history of pi: The Value of Π 240,000 Digits Science Monkey, 2020-02-21 Have fun with mathematics and discover the value of π Pi in this book featuring about 240,000 digits of Pi. Great gift for kids of all ages as well as adults, anyone with an appreciation for mathematics, logical equations, problem solving, aspiring scientists, physicists and more. |
| a history of pi: Zero Charles Seife, 2019-11-28 A NEW YORK TIMES NOTABLE BOOK The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything. Within the concept of zero lies a philosophical and scientific history of humanity. Charles Seife's elegant and witty account takes us from Aristotle to superstring theory by way of Egyptian geometry, Kabbalism, Einstein, the Chandrasekhar limit and Stephen Hawking. Covering centuries of thought, it is a concise tour of a world of ideas, bound up in the simple notion of nothing. |
| a history of pi: Romance and Reason Roberta Casagrande-Kim, Samuel Thrope, Raquel Ukeles, 2018-03-06 Catalog of an exhibition held at the Institute for the Study of the Ancient World from February 14, 2018-May 13, 2018. |
| a history of pi: A History of the Circle Ernest Zebrowski, 1999 Ranging from ancient times to twentieth-century theories of time and space, looks at how exploring the circle has lead to increased knowledge about the physical universe. |
| a history of pi: Pi in the Sky John D. Barrow, 1992 Famous cosmologist and prolific author John Barrow explores the origin and nature of mathematics and explains the important implications of the numerous unanswered questions in our search for a theory of everything. He weaves together a history of math that illuminates its far-reaching capabilities and its intrinsic limitations, its proven and unproven theories, and its pervasive impact on the way people think and live. Annotation copyrighted by Book News, Inc., Portland, OR |
| a history of pi: The Rhind Mathematical Papyrus Arnold Buffum Chace, |
| a history of pi: Measurement Paul Lockhart, 2012-09-25 For seven years, Paul Lockhart’s A Mathematician’s Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science. Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work. |
| a history of pi: Contact Carl Sagan, 2016-12-20 Pulitzer Prize-winning author and astronomer Carl Sagan imagines the greatest adventure of all—the discovery of an advanced civilization in the depths of space. In December of 1999, a multinational team journeys out to the stars, to the most awesome encounter in human history. Who—or what—is out there? In Cosmos, Carl Sagan explained the universe. In Contact, he predicts its future—and our own. |
| a history of pi: Enlightening Symbols Joseph Mazur, 2014-03-23 An entertaining look at the origins of mathematical symbols While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today. |
| a history of pi: The Minotaur Sampler, Volume 4 Stacy Willingham, Alex Finlay, Gigi Pandian, Camilla Sten, Anna Downes, Samantha Jayne Allen, 2021-09-28 Looking for a new book that will make your heart race? The fourth edition of The Minotaur Sampler compiles the beginnings of six can't-miss novels--either standalone or first in series--publishing Winter 2022 for free for easy sampling. Standalone: From debut author Stacy Willingham comes a masterfully done, lyrical thriller that is certain to be the launch of an amazing career. A Flicker in the Dark is eerily compelling to the very last page. Standalone: From the author of Every Last Fear comes a breakneck new thriller about a pair of small-town murders fifteen years apart, and the one man whose life is inexplicably linked to both. Alex Finlay returns with The Night Shift. First in Series: Multiple award-winning author Gigi Pandian introduces her newest heroine in Under Lock & Skeleton Key, where Tempest Raj returns home to work at her father’s Secret Staircase Construction Company. Standalone: A heart-thumping novel that will shake you to your core, The Resting Place is a masterful novel of suspense and horror from international star Camilla Sten. Standalone: Extraordinarily tense and deliciously mysterious, Anna Downes’s The Shadow House follows one woman desperate to protect her children at any cost in a remote village retreat where not everything is as it seems. . . First in Series: Friday Night Lights meets Mare of Easttown in this small-town mystery about an unlikely private investigator searching for a missing waitress. Pay Dirt Road is the mesmerizing debut from the 2019 Tony Hillerman Prize recipient Samantha Jayne Allen. |
| a history of pi: The Road to Wigan Pier George Orwell, 2024-04-26 George Orwell provides a vivid and unflinching portrayal of working-class life in Northern England during the 1930s. Through his own experiences and meticulous investigative reporting, Orwell exposes the harsh living conditions, poverty, and social injustices faced by coal miners and other industrial workers in the region. He documents their struggles with unemployment, poor housing, and inadequate healthcare, as well as the pervasive sense of hopelessness and despair that permeates their lives. In the second half of the The Road to Wigan Pier Orwell delves into the complexities of political ideology, as he grapples with the shortcomings of both socialism and capitalism in addressing the needs of the working class. GEORGE ORWELL was born in India in 1903 and passed away in London in 1950. As a journalist, critic, and author, he was a sharp commentator on his era and its political conditions and consequences. |
| a history of pi: An Imaginary Tale Paul Nahin, 2010-02-22 Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called imaginary numbers--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive numbers in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions. |
| a history of pi: Happy Pi Day to You! Bonnie Worth, 2020-02-04 Join the Cat in the Hat as he explains how to measure circles and calculate pi in this perfect choice for Pi Day celebrations and nurturing a love of math and numbers! The Cat in the Hat makes calculating pi—one of the most fascinating numbers in mathematics—as easy as pie! Using a piece of string and two sticks, the Cat first shows beginning readers how to draw a perfect circle. Then, using a can and a piece of ribbon, he shows how to measure a circle's circumference and diameter, and to use those measurements to calculate pi. Also included is information about the history of measurement and famous Pi Pioneers! Written in simple rhyme, Happy Pi Day is a natural choice for celebrating Pi Day (held annually on March 14), and for nurturing a child's interest in math. Fans of the hit PBS show The Cat in the Hat Knows a Lot About That! will be delighted at this new addition to the Learning Library series. |
| a history of pi: BraveTart: Iconic American Desserts Stella Parks, 2017-08-15 Winner of the 2018 James Beard Foundation Book Award (Baking and Desserts) A New York Times bestseller and named a Best Baking Book of the Year by the Atlantic, the Wall Street Journal, the Chicago Tribune, Bon Appétit, the New York Times, the Washington Post, Mother Jones, the Boston Globe, USA Today, Amazon, and more. The most groundbreaking book on baking in years. Full stop. —Saveur From One-Bowl Devil’s Food Layer Cake to a flawless Cherry Pie that’s crisp even on the very bottom, BraveTart is a celebration of classic American desserts. Whether down-home delights like Blueberry Muffins and Glossy Fudge Brownies or supermarket mainstays such as Vanilla Wafers and Chocolate Chip Cookie Dough Ice Cream, your favorites are all here. These meticulously tested recipes bring an award-winning pastry chef’s expertise into your kitchen, along with advice on how to “mix it up” with over 200 customizable variations—in short, exactly what you’d expect from a cookbook penned by a senior editor at Serious Eats. Yet BraveTart is much more than a cookbook, as Stella Parks delves into the surprising stories of how our favorite desserts came to be, from chocolate chip cookies that predate the Tollhouse Inn to the prohibition-era origins of ice cream sodas and floats. With a foreword by The Food Lab’s J. Kenji López-Alt, vintage advertisements for these historical desserts, and breathtaking photography from Penny De Los Santos, BraveTart is sure to become an American classic. |
| a history of pi: Prime Obsession John Derbyshire, 2003-04-15 In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: On the Number of Prime Numbers Less Than a Given Quantity. In the middle of that paper, Riemann made an incidental remark †a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic †defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark †the Riemann Hypothesis †that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows †subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many †the veritable great white whale of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof †and those who have been consumed by it. |
| a history of pi: Let's Play Math Denise Gaskins, 2012-09-04 |
| a history of pi: History of Sigma Pi Phi, First of the Negro-American Greek-letter Fraternities Charles Harris Wesley, 1954 |
| a history of pi: History of L. A. Harold Meyerson, |
| a history of pi: A Deeper Fear Allison Brennan, 2021-01-26 FBI Agent Lucy Kincaid is back in the new e-Novella, A Deeper Fear, from New York Times bestselling author Allison Brennan FBI Agent Lucy Kincaid’s husband, Sean Rogan, is in a dark place after being held captive. He won’t talk about it with anyone, not even Lucy. She’s hoping a conference in Sacramento, which includes family and the unveiling of a highly sought after drone Sean’s been working on, will help him heal. But the upcoming drone demonstration – and the fact that Sean didn’t come home last night – is the least of the couple’s worries. The night before the drone is set to debut to the world, the operator goes missing. Ellen Dupre is Sean’s friend. When she’s found, barely clinging to life, Sean is determined to find out what happened to her. Ellen Dupre saw something she wasn’t supposed to . . . and those behind the attack are willing to risk it all to keep their secrets. |
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