David Halliday Robert Resnick Jearl Walk Popular Books

David Halliday Robert Resnick Jearl Walk Biography & Facts

The number π (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 7 {\displaystyle {\tfrac {22}{7}}} are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706. The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits. These computations are motivated by the development of efficient algorithms to calculate numeric series, as well as the human quest to break records. The extensive computations involved have also been used to test supercomputers as well as stress testing consumer computer hardware. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres. It is also found in formulae from other topics in science, such as cosmology, fractals, thermodynamics, mechanics, and electromagnetism. It also appears in areas having little to do with geometry, such as number theory and statistics, and in modern mathematical analysis can be defined without any reference to geometry. The ubiquity of π makes it one of the most widely known mathematical constants inside and outside of science. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines. Fundamentals Name The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi. In English, π is pronounced as "pie" ( PY). In mathematical use, the lowercase letter π is distinguished from its capitalized and enlarged counterpart Π, which denotes a product of a sequence, analogous to how Σ denotes summation. The choice of the symbol π is discussed in the section Adoption of the symbol π. Definition π is commonly defined as the ratio of a circle's circumference C to its diameter d: π = C d {\displaystyle \pi ={\frac {C}{d}}} The ratio C d {\textstyle {\frac {C}{d}}} is constant, regardless of the circle's size. For example, if a circle has twice the diameter of another circle, it will also have twice the circumference, preserving the ratio C d {\textstyle {\frac {C}{d}}} . This definition of π implicitly makes use of flat (Euclidean) geometry; although the notion of a circle can be extended to any curve (non-Euclidean) geometry, these new circles will no longer satisfy the formula π = C d {\textstyle \pi ={\frac {C}{d}}} . Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be formally defined independently of geometry using limits—a concept in calculus. For example, one may directly compute the arc length of the top half of the unit circle, given in Cartesian coordinates by the equation x 2 + y 2 = 1 {\textstyle x^{2}+y^{2}=1} , as the integral: π = ∫ − 1 1 d x 1 − x 2 . {\displaystyle \pi =\int _{-1}^{1}{\frac {dx}{\sqrt {1-x^{2}}}}.} An integral such as this was adopted as the definition of π by Karl Weierstrass, who defined it directly as an integral in 1841. Integration is no longer commonly used in a first analytical definition because, as Remmert 2012 explains, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to have a definition of π that does not rely on the latter. One such definition, due to Richard Baltzer and popularized by Edmund Landau, is the following: π is twice the smallest positive number at which the cosine function equals 0. π is also the smallest positive number at which the sine function equals zero, and the difference between consecutive zeroes of the sine function. The cosine and sine can be defined independently of geometry as a power series, or as the solution of a differential equation. In a similar spirit, π can be defined using properties of the complex exponential, exp z, of a complex variable z. Like the cosine, the complex exponential can be defined in one of several ways. The set of complex n.... Discover the David Halliday Robert Resnick Jearl Walk popular books. Find the top 100 most popular David Halliday Robert Resnick Jearl Walk books.

Best Seller David Halliday Robert Resnick Jearl Walk Books of 2024

  • Teased by Fire synopsis, comments

    Teased by Fire

    Molly O'Hare

    From USA Today bestselling author Molly O’Hare comes an enemiestolovers, older brother’s best friend, romantic comedy with a curvy, antisocial, supernaturalobsessed, allyearround h...

  • Silver Santa synopsis, comments

    Silver Santa

    Lacey Silks

    Trapped together on Christmas, their unintended onenight stand becomes a lifechanging encounter amidst the snow. Laura Young's professional role as a security guard at the Sil...

  • Enemies With Benefits synopsis, comments

    Enemies With Benefits

    Roxie Noir

    I don’t love him. I don’t even like him. I just want him. Eli Loveless was my nemesis from the first day of kindergarten until we graduated high school. Everything I did, he had to...

  • The Icing on the Cake synopsis, comments

    The Icing on the Cake

    Linda Seed

    She’s a baker without a kitchen. He’s got a double oven to spare. It’s a recipe for success, until his mother starts stirring up trouble … Cassie Jordan has a sweet dream to open a...

  • Whiskey Girl synopsis, comments

    Whiskey Girl

    Melissa Belle

    They'll do anything for each other…except commit. Logan Wild isn’t just the hottest broncriding cowboy in Texas. He’s also my best friendwith benefits. And that’s all we’ll ev...

  • The Next Girl synopsis, comments

    The Next Girl

    Carla Kovach

    IF YOU ONLY READ ONE BOOK THIS YEAR, MAKE IT THE NEXT GIRL... You thought he’d come to save you. You were wrong. ‘ Absolutely the best thriller I’ve read this year! ’ Goodreads Rev...

  • My Paper Heart synopsis, comments

    My Paper Heart

    Magan Vernon

    One piece of paper can change everything After my parents received the letter I failed out of college, they didn't ask questions. They just sent me to work for my great aunt i...

  • Becoming Lady Dalton synopsis, comments

    Becoming Lady Dalton

    Carrie Lomax

    A dance of desire and deceit... In the glittering world of London's ton, Mrs. Viola Cartwright revels in her newfound freedom as a lady of leisureuntil a series of jewel theft...

  • Think and Grow Rich synopsis, comments

    Think and Grow Rich

    Greg Habstritt & Napoleon Hill

    Think and Grow Rich is one of the most popular success book of alltime, having sold more than 60 million copies since it was first published more than 70...

  • Christmas in Sweetbriar Cove synopsis, comments

    Christmas in Sweetbriar Cove

    Melody Grace

    Celebrate the holidays in Sweetbriar Cove with this festive romance collection, containing two sizzling smalltown holiday stories perfect for fans of Tessa Bailey, Sophie Kinsella...

  • The Art of War synopsis, comments

    The Art of War

    Sun Tzu

    An Apple Books Classic edition. It’s believed that Sun Tzu wrote this Chinese military primer during the 5th century BChundreds of years before the Bible. The book’s 13 chapters ex...

  • Hard Love synopsis, comments

    Hard Love

    Peyton Banks

    He was football royalty. Legendary quarterback. A champion.  Reiner Strickland had led his team to three national championships and playing a knight in shining armor was a...

  • The Stoic Mind synopsis, comments

    The Stoic Mind

    Addy Osmani & GoLimitlesss

    Discover the timeless wisdom of Stoicism in a modern context with "The Stoic Mind," an enlightening visual guide by Addy Osmani and GoLimitlesss. This rich exploration co...

  • Holy Bible synopsis, comments

    Holy Bible

    The Church of Jesus Christ of Latter-day Saints

    The 2013 edition of the Holy Bible contains all of the study aids contained in the 1979 edition and includes revisions to the study aids, several new photos, updated maps, and adju...

  • A Christmas Carol synopsis, comments

    A Christmas Carol

    Charles Dickens

    An Apple Books Classic edition. It’s Christmas Eve in Victorian England. While some families don’t know where their next meal will come from, Ebenezer Scrooge sits in his large hom...

  • A Green Kind of Witch synopsis, comments

    A Green Kind of Witch

    Sierra Cross

    Cinderella crossed with Mean Girls.   That's what Hazel's daily existence feels like. Born to a family of elegant yet shallow Beige Witches, seventeen y...

  • Hot Off the Press synopsis, comments

    Hot Off the Press

    Lexy Timms

    "This is what really happened… reported by a free press, for a free people…" Wes Shaw leads a secret double life. As the secret owner of a billion dollar newspap...

  • All Fired Up synopsis, comments

    All Fired Up

    Kathryn Shay

    Captain Jarek Zenko, a war veteran and firefighter, meets Lacey Roth at a bar one night. They don’t share their real identities, even when they retreat to a hotel. When they meet t...

  • Wuthering Heights synopsis, comments

    Wuthering Heights

    Emily Brontë

    An Apple Books Classic edition. If you’ve only ever seen Wuthering Heights on screen, you may have an image of Catherine and Heathcliff as the ultimate starcrossed lovers. But that...

  • A Bookshop to Die For synopsis, comments

    A Bookshop to Die For

    M.P. Black

    Ditching her fiancé at the altar, Alice Hartford bolts to her childhood hometown to reconnect with the last, happy remnant of her past: her mom's old bookstore. But the bookst...

  • School of Potential synopsis, comments

    School of Potential

    W.J. May

    USA Today Bestselling author, W.J. May brings you a continuation of the international bestselling series, The Chronicles of Kerrigan! Come back and enjoy the famous characters, or ...

  • Noxious synopsis, comments

    Noxious

    Lexy Timms

    Stop setting yourself on fire to keep someone else warm. Brady and Levi have been together since high school, since before he became famous and started thinking only about himself....

  • Alpha synopsis, comments

    Alpha

    Sybil Bartel

    Billionaire. Mercenary. Navy SEAL. The Teams trained me to be a killer. War taught me to be ruthless. Then an illfated mission proved I was human. Combat wounded, cut loose by the ...

  • Always Yours synopsis, comments

    Always Yours

    Claire Raye

    Some things are just meant to be... Ellen Somerville and Will McIntyre met by accident and under unusual circumstances. Getting sprayed by a skunk in a parking lot wouldn’t normall...

  • Dream Psychology synopsis, comments

    Dream Psychology

    Sigmund Freud

    An Apple Books Classic edition. Written by the founding father of psychoanalysis, Sigmund Freud’s 1899 book is the definitive text on learning to interpret dreams. Freud’s groundbr...

  • The Adventures of Sherlock Holmes synopsis, comments

    The Adventures of Sherlock Holmes

    Arthur Conan Doyle

    An Apple Books Classic You get not one, not two, but 25 gripping mysteries in Arthur Conan Doyle’s first of five collections of Sherlock Holmes short stories. Follow the brilliant ...

  • The Count of Monte Cristo synopsis, comments

    The Count of Monte Cristo

    Alexandre Dumas

    An Apple Books Classic edition. Alexandre Dumas’ classic paints a portrait of Edmond Dantès, a dark and calculating man who is willing to wait years to exact his perfect plan for r...

  • Awaken Me synopsis, comments

    Awaken Me

    Jenna Jacob

    He was more than a ghost haunting my dreams…he was real. By day, I’m Julianna Garrett …a prim, proper accountant. By night, I’m tormented by dreams of an alpha, ambereyed Adonis wh...

  • You Are Kind synopsis, comments

    You Are Kind

    Michael Gordon

    A little kindness goes a long way. How can you help encourage your kids to be kind from a young age? Teach kindness to preschoolers Acts of kindness can be fun, easy, and make a ...

  • The Scarlet Letter synopsis, comments

    The Scarlet Letter

    Nathaniel Hawthorne

    An Apple Books Classic edition. Hester Prynne lives in infamy. After committing adultery and bearing a child with a man whose name she refuses to divulge, the heroine of Nathaniel ...

  • The Seduction Series Boxset synopsis, comments

    The Seduction Series Boxset

    Roxy Sloane

    “Sensual, thrilling and wild!”   Discover the bestselling series in one collection: THE SEDUCTION, THE BARGAIN, and THE INVITATION. Perfect for fans of Ana Huang, Sierra S...

  • Assisting the Bosshole synopsis, comments

    Assisting the Bosshole

    Kristin MacQueen

    No hot water? Check Missed the train? Check Broke my heel? Check Dropped my coffee? Check My first day of my new job can’t possibly go worse, right? Wrong. When I meet Parker Scott...

  • Eternal synopsis, comments

    Eternal

    W.J. May

    She will fight for what is hers. When the king is murdered, Katerina, his only daughter, must flee for her life. She finds herself on a strange and dangerous path. Alone for the fi...

  • The Wonderful Wizard of Oz synopsis, comments

    The Wonderful Wizard of Oz

    L. Frank Baum

    An Apple Books Classic edition. You’ve seen the iconic 1939 movie, but do you know about the talking field mice, the Winkies, and the Witch of the North that appear in the original...

  • Never Enough synopsis, comments

    Never Enough

    Lexy Timms

    Be good enough never is... Anthony Accardi is a man on a mission: make his father's watch company a success while bringing in millions of dollars. To do that, he needs an assi...

  • Dracula synopsis, comments

    Dracula

    Bram Stoker

    An Apple Books Classic edition. Few characters have seized readers’ imaginations quite like Count Dracula of Transylvania, the hero of Bram Stoker’s classic. The 1897 novel put vam...

  • His Girl Next Door synopsis, comments

    His Girl Next Door

    Khardine Gray

    From USA Today Bestselling author Khardine Gray comes a sizzling hot single dad romance you won't want to miss. No strings attached fun with the ubergorgeous single d...

  • Teach Me synopsis, comments

    Teach Me

    Cassandra Dean

    From awardwinning author Cassandra Dean comes a tale where lessons of pleasure between a curious, sunshine widow and a dissolute, grumpy earl leads to passion and allconsuming love...

  • Rogue Alpha synopsis, comments

    Rogue Alpha

    Kimber White

    One touch made her crave him. But the pull of fate could be the path to ruin. College student Laura Prince lands a plum internship deep in the Michigan wilderness. When she discove...

  • Nothing to Hide synopsis, comments

    Nothing to Hide

    Scarlett Finn

    Prize of a lifetime: travel the world with a celebrity billionaire. Come to LA with us, Roxie… It will be so much fun! We have tickets for a latenight talk show! What could possibl...

  • Saltwater Cove synopsis, comments

    Saltwater Cove

    Amelia Addler

    Second chances...and the secrets that sabotage them. At 48 years old, Margie Clifton never expected to be starting her life all over again. But when her brother gifts her a propert...

  • Get Lucky synopsis, comments

    Get Lucky

    Lila Monroe

    Fall for the hot and hilarious romcom spin on 'The Hangover', perfect for fans of Tessa Bailey, Ali Hazelwood, and Emily Henry! What happens when you wake up in a hotel s...

  • Silenced Girls synopsis, comments

    Silenced Girls

    Roger Stelljes

    “ Wow wow wow!  Grips you in a choke hold and  does not let go … Oozes suspense and  bonechilling twists and turns .  Astonishing … One of those...

  • Good Guy synopsis, comments

    Good Guy

    Kate Meader

    He's a Special Forces veteran making his pro hockey debut. She's a dogged sports reporter determined to get a scoop. She's also his best friend's widow . . . Fa...

  • Death at Hazel House synopsis, comments

    Death at Hazel House

    Betty Rowlands

    ‘Riveting, can't put it down! I love this story… a wonderfully twisted tale of a crime that has more twists than I thought possible... fantastic.’ Goodreads Reviewer, 5 stars ...

  • Inception of Gold synopsis, comments

    Inception of Gold

    Lexy Timms

    Things are not as bad as they seem. They are worse. Being the personal assistant to a narcissistic actress who just happens to own the key to my family's undoing isn't ex...

  • The Four Loves synopsis, comments

    The Four Loves

    C. S. Lewis

    The Four Loves summarizes four kinds of human loveaffection, friendship, erotic love, and the love of God. Masterful without being magisterial, this book's wise, gentle, candi...

  • Man In The Water synopsis, comments

    Man In The Water

    Jon Hill

    An attempted murder. A missing spouse. And an international conspiracy that could change the world. Jack Green has always been skeptical of socalled facts. Though he's forced ...

  • Become A Better Version of Yourself synopsis, comments

    Become A Better Version of Yourself

    Ben Leighton

    This ebook contains golden nuggets on how to motivate, inspire and improve your current situation. It encompasses the holistic view of self improvement from mental& emotion...

  • Salvation synopsis, comments

    Salvation

    Meghan O'Flynn

    If you like mouthy detectives, serial killers, and suspenseful mysteries that don't quit, this chilling and actionpacked hardboiled detective series has you covered! Try this ...