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Paul Peter Urone 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 formulas 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 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 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. 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. In modern mathematical analysis, it is often instead defined without any reference to geometry; therefore, it also appears in areas having little to do with geometry, such as number theory and statistics. 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: The ratio 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. 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.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 x2 + y2 = 1, as the integral: 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 numbers at which exp z is equal to one is then an (imaginary) arithmetic progression of the form: and there is a unique positive real number π with this property.A variation on the same idea, making use of sophisticated mathematical concepts of topology and algebra, is the following theorem: there is a unique (up to automorphism) continuous isomorphism from the group R/Z of real numbers under addition modulo integers (the circle group), onto the multiplicative group of complex numbers of absolute value one. The number π is then defined as half the magnitude of the derivative of this homomorphism. Irrationality and normality π is an irrational number, meaning that it cannot be written as the ratio of two integers. Fractions such as 22/7 and 355/113 are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value. Because π is irrational, it has an infinite number of digits in its decimal representation, and does not settle into an infinitely repeating pattern of digits. There are several proofs that π is irrational; they generally require calculus and rely on the reductio ad absurdum technique. The degree to which π can be approximated by rational numbers (called the irrationality measure) is not precisely known; estimates have established that the irrationality measure is larger than the measure of e or ln 2 but smaller than the measure of Liouville numbers.The digits of π have no appare.... Discover the Paul Peter Urone popular books. Find the top 100 most popular Paul Peter Urone books.

Best Seller Paul Peter Urone Books of October 2022

Mr. Trouble e-book Download

Mr. Trouble

Nana MaloneAugust 1, 2018Get

Yeah, I'm trouble...so what? Women like it. That and my big...bank account. Not to mention my, ah, silver tongue. I'm the prince of my world, right up until the king gets upset. My f...

Coming Home to Glendale Hall e-book Download

Coming Home to Glendale Hall

Victoria WaltersSeptember 25, 2019Get

'WOW! From the first page I was absolutely hooked ...Would highly recommend to get you in a feel good mood!’ (5 stars) Netgalley reviewer Uplifting and full of heart - this is an utter tre...

The Wonderful Wizard of Oz e-book Download

The Wonderful Wizard of Oz

L. Frank BaumMay 17, 1900Get

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 book? L...

Accidentally Aphrodite e-book Download

Accidentally Aphrodite

Dakota CassidySeptember 24, 2019Get

An apple a day keeps the Goddess in play... Mythology buff Quinn Morris has always wanted to visit Greece, where her inner hardcore romantic envisioned proposing to her boyfriend. And she's ...

Wanna Puck? (Book Two) e-book Download

Wanna Puck? (Book Two)

Layla Valentine & Ana SparksDecember 24, 2021Get

One cool-as-ice veteran player One smoking hot rising star And little old me in the middle All wrapped up in an all-star ménage a trois I've been sent to write a piece on two NHL stars Joel...

The Baltic Run e-book Download

The Baltic Run

Charles WhitingJune 15, 2020Get

From the carnage of war a new hero is born. 1920. The slaughter of World War One is over, but already secret little wars are breaking out all over 'New Europe'. Sub-Lieutenant de Vere Smith ...

Make Me Wilder e-book Download

Make Me Wilder

Serena BellMay 20, 2021Get

She's a city girl. I'm a mountain man. This shouldn't work. So why can't I stay away? Gabe: I promised my dad I’d take care of the Wilder family adventure business, including my rowdy co-w...

The Bangover e-book Download

The Bangover

Lili ValenteOctober 3, 2019Get

Note to Self --Do NOT bang your best guy friend in the limo on the way to the swanky Vegas hotel. I give myself very good advice. Too bad I suck at taking it. If only Colin and I hadn't ...

A Royal Farce e-book Download

A Royal Farce

Laura HeffernanNovember 23, 2021Get

A ROYAL FARCE is the hilarious first book in the Retail to Riches series, which follows a plucky big box store employee on her journey from fighting to pay the bills to discovering she’s m...

The Killing Game (An Alexa Chase Suspense Thriller—Book 1) e-book Download

The Killing Game (An Alexa Chase Suspense Thriller—Book 1)

Kate BoldOctober 15, 2021Get

Alexa Chase, 34, a brilliant profiler in the FBI’s Behavioral Analysis Unit, was too good at her job. Haunted by all the serial killers she caught, she left a stunning career behind to joi...

Someone Else's Daughter e-book Download

Someone Else's Daughter

Linsey LanierOctober 29, 2010Get

Book I of the popular Miranda's Rights Mystery series by bestselling author Linsey Lanier.  A woman can never make herself too tough, too strong, or too street smart.  THE SEARCHIN...

The Recruiting Trip e-book Download

The Recruiting Trip

Lexy TimmsNovember 19, 2014Get

Aspiring college athlete Aileen Nessa is finding the recruiting process beyond daunting. Being ranked #10 in the world for the 100m hurdles at the age of eighteen is not a fluke, even though...

The School of Starting Over e-book Download

The School of Starting Over

Lisa SwiftMarch 11, 2020Get

‘this was a delight to read …I just can’t recommend it enough. The best romance book I’ve read this year .’ ☆☆☆☆☆ Books and Bookends Nell’s going back to school… but ...

Severance e-book Download

Severance

AnonymousMarch 18, 2022Get

When does the cost of staying silent become greater than the price of speaking up? A desperate woman risks everything to expose the sinister company at the heart of Severance , the thrilling...

The Art of War e-book Download

The Art of War

Sun TzuOctober 4, 2010Get

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

Some Call It Love e-book Download

Some Call It Love

Sarah PeisAugust 20, 2018Get

"The best feel-good romcom you need right now." Goodreads reviewer A mistaken arrest, an unpaid debt, and a trip to Vegas. Living in a small town where everyone knows your business isn't eas...

Become A Better Version of Yourself e-book Download

Become A Better Version of Yourself

Ben LeightonFebruary 22, 2015Get

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& emotional wellbeing, ...

The Lost Siren e-book Download

The Lost Siren

Raven StormMay 16, 2022Get

A human female born into a breeding manor never has a choice…I am a slave, but at least I am alive. When the man with wings and scales gave me a second choice—I took it. I'll do what I m...

The Tanglewood Tea Shop e-book Download

The Tanglewood Tea Shop

Lilac MillsJanuary 31, 2019Get

What happens after your dreams come true? Patisserie-Chef Stevie is stuck in a rut. Her beloved Great Aunt Peggy has passed away and she’s lost both her job and the love of her life. Then ...

Think and Grow Rich e-book Download

Think and Grow Rich

Greg Habstritt & Napoleon HillDecember 23, 2010Get

Think and Grow Rich is one of the most popular success book of all-time, having sold more than 60 million copies since it was first published more than 70 years ago.  It&...

Man Crush Monday e-book Download

Man Crush Monday

Kirsty MoseleyFebruary 3, 2020Get

Perma-single Amy Clarke prides herself on three things: her pink hair, her Converse collection, and her ability to drink copious amounts of margarita without puking. She isn’t looking for ...

The Deal e-book Download

The Deal

Elle KennedyFebruary 24, 2015Get

The international bestseller! Get ready for another binge-worthy romance from New York Times bestselling author Elle Kennedy! She's about to make a deal with the college bad boy… Hannah We...

Lola Is Missing e-book Download

Lola Is Missing

Alison JamesFebruary 7, 2018Get

‘I was hooked from page one and couldn’t put it down until I’d reached the end. The twists and turns just keep coming … will have you gasping in surprise.’  Goodreads Reviewer...

Manifesting Abundance: How to Manifest Your Desires Using the Law of Attraction e-book Download

Manifesting Abundance: How to Manifest Your Desires Using the Law of Attraction

Beau NortonSeptember 26, 2015Get

Did you know that up to 95% of the people that attempt to use the law of attraction to manifest their desires see no noticeable results? The truth is that most people fail to use the law of ...

A Match for the Marine e-book Download

A Match for the Marine

Jess MastorakosMarch 31, 2021Get

Matchmaker Rule #1: Never fall in love with the client. After working my way to the top, I'm in the running to become the CEO of Southern California's premier matchmaking service. All I have...

Moby Dick e-book Download

Moby Dick

Herman MelvilleOctober 17, 1851Get

An Apple Books Classic edition. Herman Melville’s classic begins with one of the most famous opening lines in world literature: “Call me Ishmael.” Moby Dick was a commercial failure wh...

Stop Procrastinating & Overthinking: Learn The Mind Hacks To Cure Your Procrastination Habit And Improve Your Perseverance To Overcome Laziness. Eliminate Negative Thoughts And Stop Worrying e-book Download

Stop Procrastinating & Overthinking: Learn The Mind Hacks To Cure Your Procrastination Habit And Improve Your Perseverance To Overcome Laziness. Eliminate Negative Thoughts And Stop Worrying

Sebastian GoodwinMarch 25, 2021Get

"I TRIED EVERYTHING ELSE, BUT IT'S STILL A NEVER-ENDING BATTLE…" Everybody knows that procrastination is the biggest waste of time – I am talking about those moments when you imagine wha...

A Lot Like Home e-book Download

A Lot Like Home

Kathryn CantrellMay 21, 2018Get

Destiny isn't a thing in her world. Smooth-talking strangers need not apply... Superstition Springs native Havana Nixon is convinced letting a big developer into their tiny Texas oasis is th...

Savage Prince e-book Download

Savage Prince

Meghan MarchApril 24, 2018Get

Who knew things could get even darker and dirtier in New Orleans?  New York Times  bestselling author Meghan March introduces the  Savage Prince  of the city, the man you...

An Acquired Taste e-book Download

An Acquired Taste

Kelly CainJune 8, 2021Get

May the best chef win... After four years at the country’s top culinary school and several years as head chef in her mother’s restaurant, Rowan Townsend has built a notable reputation. H...

Right Time e-book Download

Right Time

Lexy TimmsFebruary 11, 2022Get

Don't rush on anything.  If the time is right, it will happen. Rae I've always known I was meant to get out of the dead-end side of town where I was born. Trevor is my plan. He's from t...

Just One Night e-book Download

Just One Night

Carly PhillipsApril 20, 2021Get

She’s the woman he can’t live without. The one he can’t risk screwing up their relationship by sleeping with her. Linc Kingston doesn’t accept anything less than perfection. ...

Contract with a SEAL e-book Download

Contract with a SEAL

Kate AsterSeptember 7, 2016Get

Some contracts are meant to be broken... Desperate to shake herself free from the humiliation of a very public divorce, TV financial correspondent Vi Owens makes a deal with a Navy SEAL Comm...

iPad User Guide e-book Download

iPad User Guide

Apple Inc.September 20, 2021Get

Here’s everything you need to know about iPad, straight from Apple. This definitive guide helps you get started using iPad with iPadOS 15 and discover all the amazing things it can do.

Don't Play With Odin e-book Download

Don't Play With Odin

Cynthia EdenJuly 13, 2021Get

Big, bad, and currently out of his element... Odin Shaw thought he’d spend his life on a battlefield. But fate had other plans, and now the former Special Forces operative has just landed ...

Secrets and Scandals e-book Download

Secrets and Scandals

Piper GlendaleMay 5, 2022Get

Emily Delaney, a reporter for one of Hollywood’s hottest gossip magazines, has her world turned upside down when her former journalism mentor dies, and she is called back to the hometown s...

The Chase e-book Download

The Chase

Elle KennedyAugust 6, 2018Get

New York Times bestseller! Get ready for another binge-worthy romance from international bestselling author Elle Kennedy! Everyone says opposites attract. And they must be right, because the...

Liberty Begins e-book Download

Liberty Begins

Leigh JamesFebruary 13, 2015Get

Adventure. Fate. From Rags to Riches… My name is Liberty and I'm a good girl. I come from nothing. I have no one but myself. Sometimes I do things I don't want to -- I do them beca...

Without Mercy (A Dakota Steele FBI Suspense Thriller—Book 1) e-book Download

Without Mercy (A Dakota Steele FBI Suspense Thriller—Book 1)

Ava StrongJune 14, 2022Get

MMA champ-turned-FBI Special Agent and BAU specialist Dakota Steele is as tough as they come—and as brilliant, too, able to crack serial killers that no one else can. But this new case is ...

The Crash e-book Download

The Crash

Skye WarrenJune 14, 2022Get

Carter Morelli works alone, but his orders are clear. Pilot the small aircraft carrying the renowned photographer to a remote island. June Porter wants to stay on solid land. She doesn't...

So Wrong It's Right e-book Download

So Wrong It's Right

Julie JohnsonNovember 2, 2018Get

Shelby Hunt has the perfect life, married to the perfect man. At least, that’s what anyone would think, looking at her. They couldn’t possibly know about the past five years of lonely ni...

Chasing Romeo e-book Download

Chasing Romeo

Sarah ReadyMay 25, 2021Get

A laugh out loud, soul mate chasing rom-com romp, Sarah Ready's Chasing Romeo is a perfect feel-good novel about finding love where you least expect it. Chloe Daniels is a starry-eyed romant...

Jaxon e-book Download

Jaxon

Olivia SandsJune 2, 2019Get

She's his little sister's best friend.  Completely off limits.  And now they're working together. Jaxon Green 's plans to offer a summer camp for kids at his thoroughbred training ...

Love Me Like a Love Song e-book Download

Love Me Like a Love Song

Annmarie BoyleNovember 9, 2020Get

She used to be on top of the music world. He's desperate to get there. Unable to compose since the death of her rock star husband, Grammy award-winning songwriter, Grace O'Connor is terrifie...

Persuasion e-book Download

Persuasion

Jane AustenDecember 31, 1817Get

A woman of no importance, she manoeuvres in her restricted circumstances as her long-time love Captain Wentworth did in the wars. Even though she is nearly thirty, well past the sell-by bloo...

Love in a Small Town e-book Download

Love in a Small Town

Zoe YorkOctober 6, 2020Get

Are they one late-night hayride away from tumbling back into a very bad idea? Olivia Minelli needs a one-way ticket out of Pine Harbour. It's too small for both her and her ex-husband. So wh...

Man In The Water e-book Download

Man In The Water

Jon HillOctober 5, 2021Get

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

Come Back for Me e-book Download

Come Back for Me

Corinne MichaelsJanuary 7, 2020Get

From  New York Times  Bestselling author Corinne Michaels comes a new emotional and riveting standalone love story. One night, eight years ago, she gave me peace. No names. No prom...

The Girl Outside: A Shocking and Gripping Psychological Thriller e-book Download

The Girl Outside: A Shocking and Gripping Psychological Thriller

James CaineJune 22, 2022Get

Her daughter has a dark secret. One that will turn their perfect small town upside down.  Now she's missing. Mandy Knox can't shake the gut wrenching feeling that something sinister hap...

Kissing my Co-worker e-book Download

Kissing my Co-worker

J. SterlingDecember 16, 2021Get

I've had a crush on my co-worker Declan since the day I started working at Rockline Studios. Trust me, if you could see this man, you'd have a crush on him too. It's been two yea...

Best Seller Paul Peter Urone Audio Books of October 2022

The Obstacle Is the Way: The Timeless Art of Turning Trials into Triumph (Unabridged) audiobook
The Obstacle Is the Way: The Timeless Art of Turning Trials into Triumph (Unabridged)Ryan Holiday$12.99

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True Believer (Unabridged) audiobook
True Believer (Unabridged)Jack Carr$16.99

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The Hotel Nantucket audiobook
The Hotel NantucketElin Hilderbrand$16.99

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The Secret (Unabridged) audiobook
The Secret (Unabridged)Rhonda Byrne$12.99

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The Girl Upstairs audiobook
The Girl UpstairsGeorgina Lees$2.99

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Good to Great audiobook
Good to GreatJim Collins$19.99

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The 48 Laws of Power audiobook
The 48 Laws of PowerRobert Greene$19.99

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The 5 Love Languages audiobook
The 5 Love LanguagesGary Chapman$16.99

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Sparring Partners: Novellas (Unabridged) audiobook
Sparring Partners: Novellas (Unabridged)John Grisham$14.99

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The Four Agreements (Unabridged) audiobook
The Four Agreements (Unabridged)Don Miguel Ruiz$10.99

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I'd Like to Play Alone, Please audiobook
I'd Like to Play Alone, PleaseTom Segura$16.99

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Rising Tiger (Unabridged) audiobook
Rising Tiger (Unabridged)Brad Thor$14.99

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Book Lovers (Unabridged) audiobook
Book Lovers (Unabridged)Emily Henry$16.99

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We'll Always Have Summer audiobook
We'll Always Have SummerJenny Han$16.99

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Finding Me audiobook
Finding MeViola Davis$19.99

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The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma (Unabridged) audiobook
The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma (Unabridged)Bessel van der Kolk, M.D.$14.99

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November 9 (Unabridged) audiobook
November 9 (Unabridged)Colleen Hoover$16.99

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Can't Hurt Me: Master Your Mind and Defy the Odds (Unabridged) audiobook
Can't Hurt Me: Master Your Mind and Defy the Odds (Unabridged)David Goggins$21.99

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The Power Of Positive Thinking (Unabridged) audiobook
The Power Of Positive Thinking (Unabridged)Dr. Norman Vincent Peale$19.99

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A Court of Thorns and Roses audiobook
A Court of Thorns and RosesSarah J. Maas$22.99

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How to Change Your Mind: What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence (Unabridged) audiobook
How to Change Your Mind: What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence (Unabridged)Michael Pollan$14.99

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It's Not Summer Without You audiobook
It's Not Summer Without YouJenny Han$16.99

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In the Blood (Unabridged) audiobook
In the Blood (Unabridged)Jack Carr$14.99

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Harry Potter and the Order of the Phoenix audiobook
Harry Potter and the Order of the PhoenixJ.K. Rowling$39.99

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The Wrong Side of Goodbye audiobook
The Wrong Side of GoodbyeMichael Connelly$9.99

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Untamed (Unabridged) audiobook
Untamed (Unabridged)Glennon Doyle$16.99

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You Are a Badass® audiobook
You Are a Badass®Jen Sincero$14.99

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The Subtle Art of Not Giving a F*ck audiobook
The Subtle Art of Not Giving a F*ckMark Manson$16.99

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The Power of One More: The Ultimate Guide to Happiness and Success audiobook
The Power of One More: The Ultimate Guide to Happiness and SuccessEd Mylett$16.99

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Reminders of Him: A Novel (Unabridged) audiobook
Reminders of Him: A Novel (Unabridged)Colleen Hoover$25.99

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