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# Pi Before Pi

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Although our ancestors had managed to invent the wheel millennia prior to the good ol’ days of Ancient Egypt, it wasn't until that civilization arose thousands of years later that the human race began to understand the mysteries behind the circle. Our modern comprehension of pi, or the ratio of a circle’s circumference to its diameter, is a fairly recent development in our history, and the Egyptians were the first on the ball.

The Rhind Mathematical Papyrus (above), excavated in the area surrounding the Memorial Temple of Pharaoh Rameses II in Egypt, constitutes the finest example of ancient Egyptian mathematics, as well as their claim to having discovered pi. Its author, Ahmose, titled the work “Directions for Attaining Knowledge of All Dark Things,” but its contents were much less sinister than its name suggested. Of the 87 problems into which the content of the papyrus was divided, the 48th and 50th were those which suggested genuine insight into things previously unknown.

Problem 48 of the RMP showed a circle inscribed within a square, with hieroglyphic markings denoting its value as 64; problem 50 followed up on this information with a procedure to find “the area of a round field with a diameter of 9 khet.” The steps given call for subtracting 1/9th of the circle’s diameter, leaving 8, then multiplying it by 8, for an area of 64. After some substitution using our contemporary knowledge of the circle area formula as π * r2, the Egyptians seem to have calculated the constant value of pi as 256/81, or 3.16—not bad for a first attempt in 2000 BC.

As human civilization, and consequently the field of mathematics, advanced, great minds of every age tackled the question of pi. In 250 BC, Archimedes calculated the areas of a polygon inscribed within a circle and the polygon in which that same circle was inscribed, knowing that pi must lie between the two, and determined its exact value must be between 3 1/7 and 3 10/71. Chinese astronomer Zu Chongzhi, independently of Archimedes’s findings and approximately 700 years later, carried out a series of painstaking calculations on 24,576-sided polygon to approximate pi as 355/113.

In the early days of computer technology, new machines were put to the test by calculating pi: the amount of its digits that the computer could process served as an easy benchmark for its overall computing power. As technology has improved exponentially in the past few decades, so too has our knowledge of pi: as of September 2010, we know 2,000,000,000,000,000 digits of pi—that’s two quadrillion digits. According to Nicholas Sze, the Yahoo! engineer who used 1000 of the company’s computers and its Hadoop cloud computing app to calculate pi over a period of 23 days, that final (for now) digit is 0.

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25 Royals in the Line of Succession to the British Throne
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Between the Duke and Duchess of Cambridge welcoming their third child on April 23, 2018 and Prince Harry's upcoming marriage to Suits star Meghan Markle in May, the line of succession to the British throne has become a topic of interest all over the world. And the truth is, it’s complicated. Though Queen Elizabeth II, who turned 92 years old on April 21, shows no signs of slowing down, here are the royals who could one day take her place on the throne—in one very specific order.

#### 1. PRINCE CHARLES

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As a direct result of his mother being the world's longest-reigning monarch, Prince Charles—the eldest child of Queen Elizabeth II and Prince Philip—is the longest serving heir to the throne; he became heir apparent in 1952, when his mother ascended to the throne.

#### 2. PRINCE WILLIAM

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At 35 years old, odds are good that Prince William, Duke of Cambridge—the eldest son of Prince Charles and the late Princess Diana—will ascend to the throne at some point in his lifetime.

#### 3. PRINCE GEORGE

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On July 22, 2013, Prince William and Catherine, Duchess of Cambridge welcomed their first child, Prince George of Cambridge, who jumped the line to step ahead of his uncle, Prince Harry, to become third in the line of succession.

#### 4. PRINCESS CHARLOTTE

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On May 2, 2015, William and Catherine added another member to their growing brood: a daughter, Princess Charlotte of Cambridge. Though her parents just welcomed a bouncing baby boy, she will maintain the fourth-in-line position because of the Succession to the Crown Act 2013, which went into effect just a few weeks before her arrival, and removed a long-held rule which stated that any male sibling (regardless of birth order) would automatically move ahead of her.

#### 5. PRINCE OF CAMBRIDGE

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On April 23, 2018, the Duke and Duchess of Cambridge welcomed their third child—a son, whose name has yet to be announced, but who has already pushed his uncle, Prince Harry, out of the fifth position in line to the throne.

#### 6. PRINCE HARRY

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As the second-born son of Prince Charles and Princess Diana, Prince Harry's place in the line is a regularly changing one. It changed earlier this week, when his brother William's third child arrived, and could change again if and when their family expands.

#### 7. PRINCE ANDREW, DUKE OF YORK

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Prince Andrew is a perfect example of life before the Succession to the Crown Act 2013: Though he’s the second-born son of Queen Elizabeth and Prince Philip, he’s actually their third child (Princess Anne came between him and Prince Charles). But because the rules gave preference to males, Prince Andrew would inherit the throne before his older sister.

#### 8. PRINCESS BEATRICE OF YORK

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Because Prince Andrew and his ex-wife, Sarah, Duchess of York, had two daughters and no sons, none of that male-preference primogeniture stuff mattered in terms of their placement. But with each child her cousin Prince William has, Princess Beatrice moves farther away from the throne. If Beatrice looks familiar, it might be because of the headlines she made with the Dr. Seuss-like hat she wore to William and Catherine’s wedding. (The infamous topper later sold on eBay for more than \$130,000, all of which went to charity.)

#### 9. PRINCESS EUGENIE OF YORK

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Though she’s regularly seen at royal events, Prince Andrew and Sarah Ferguson’s youngest daughter spends the bulk of her time indulging her interest in fine art. She has held several jobs in the art world, and is currently a director at Hauser & Wirth’s London gallery.

#### 10. PRINCE EDWARD, EARL OF WESSEX

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Like his older brother Andrew, Prince Edward—the youngest son of Queen Elizabeth and Prince Philip—jumps the line ahead of his older sister, Princess Anne, because of the older rule that put males ahead of females.

#### 11. JAMES, VISCOUNT SEVERN

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James, Viscount Severn—the younger of Prince Edward, Earl of Wessex and Sophie, Countess of Wessex’s two children, and their only son—turned 10 years old on December 17, 2017, and celebrated it as the 10th royal in line of succession. (The birth of the youngest Prince of Cambridge pushed him back a spot.)

#### 12. LADY LOUISE MOUNTBATTEN-WINDSOR

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Because the Succession to the Crown Act 2013 wasn’t enacted until 2015, Lady Louise Mountbatten-Windsor—the older of Prince Edward’s two children—will always be just behind her brother in the line of succession.

#### 13. PRINCESS ANNE, THE PRINCESS ROYAL

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Princess Anne, the Queen and Prince Philip’s second-born child and only daughter, may never rule over the throne in her lifetime, but at least she gets to be called “The Princess Royal.”

#### 14. PETER PHILLIPS

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The eldest child and only son of Princess Anne and her first husband, Captain Mark Phillips, stands just behind his mother in line. Interesting fact: Had Phillips’s wife, Autumn Kelly, not converted from Roman Catholicism to the Church of England before their marriage in 2008, Phillips would have lost his place in line.

#### 15. SAVANNAH PHILLIPS

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On December 29, 2010, Peter and Autumn Phillips celebrated the birth of their first child, Savannah Anne Kathleen Phillips, who is also the Queen’s first great-grandchild. She’s currently 15th in line.

#### 16. ISLA PHILLIPS

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Less than two years after Savannah, Peter and Autumn Phillips had a second daughter, Isla, who stands just behind her sister in line. It wasn’t until 2017 that Savannah and Isla made their Buckingham Palace balcony debut (in honor of their great-grandmother’s 91st birthday).

#### 17. ZARA TINDALL

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Not one to hide in the background, Zara Tindall—Princess Anne’s second child and only daughter—has lived much of her life in the spotlight. A celebrated equestrian, she won the Eventing World Championship in Aachen in 2006 and was voted BBC Sports Personality of the Year the same year (her mom earned the same title in 1971). She’s also Prince George’s godmother.

#### 18. MIA TINDALL

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Zara Tindall’s daughter Mia may just be 4 years old, but she’s already regularly making headlines for her outgoing personality. And though she’s only 18th in line to the throne, her connection to the tippity top of the royal family is much closer: Prince William is her godfather.

#### 19. DAVID ARMSTRONG-JONES, 2ND EARL OF SNOWDON

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David Armstrong-Jones, the eldest child of Princess Margaret, isn’t waiting around to see if the British crown ever lands on his head. The 56-year-old, who goes by David Linley in his professional life, has made a name for himself as a talented furniture-maker. His bespoke pieces, sold under the brand name Linley, can be purchased through his own boutiques as well as at Harrods.

#### 20. CHARLES ARMSTRONG-JONES, VISCOUNT LINLEY

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David Armstrong-Jones’s only son, Charles, may be 20th in line to the throne, but the 18-year-old is the heir apparent to the Earldom of Snowdon.

#### 21. LADY MARGARITA ARMSTRONG-JONES

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Lady Margarita Armstrong-Jones, the youngest child of David Armstrong-Jones and his only daughter, is also the only granddaughter of Princess Margaret. Now 15 years old (she'll turn 16 in June), Lady Margarita made headlines around the world in 2011 when she served as a flower girl at the wedding of Prince William and Catherine Middleton.

#### 22. LADY SARAH CHATTO

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Lady Sarah Chatto, Princess Margaret and Anthony Armstrong-Jones’s only daughter, is the youngest grandchild of King George VI and Queen Elizabeth the Queen Mother. In addition to serving as a bridesmaid to Princess Diana, she is Prince Harry’s godmother.

#### 23. SAMUEL CHATTO

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The first-born son of Lady Sarah Chatto and her husband, Daniel, has a long way to go to reach the throne: He’s currently 23rd in line.

#### 24. ARTHUR CHATTO

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For better or worse, Sarah and Daniel Chatto’s youngest son Arthur has become a bit of a social media sensation. He's made headlines recently as he regularly posts selfies to Instagram—some of them on the eyebrow-raising side, at least as far as royals go.

#### 25. PRINCE RICHARD, DUKE OF GLOUCESTER

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At 73 years old, Prince Richard, Duke of Gloucester is the youngest grandchild of King George V and Queen Mary. Formerly, he made a living as an architect, until the 1972 death of his brother, Prince William of Gloucester, put him next in line to inherit his father’s dukedom. On June 10, 1974, he officially succeeded his father as Duke of Gloucester, Earl of Ulster, and Baron Culloden.

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10 Fascinating Facts About Ella Fitzgerald
Library of Congress (LOC), Public Domain, Wikimedia Commons

Today marks what would have been the 101st birthday of Ella Fitzgerald, the pioneering jazz singer who helped revolutionize the genre. But the iconic songstress’s foray into the music industry was almost accidental, as she had planned to show off her dancing skills when she made her stage debut. Celebrate the birthday of the artist known as the First Lady of Song, Queen of Jazz, or just plain ol’ Lady Ella with these fascinating facts.

#### 1. SHE WAS A JAZZ FAN FROM A YOUNG AGE.

Though she attempted to launch her career as a dancer (more on that in a moment), Ella Fitzgerald was a jazz enthusiast from a very young age. She was a fan of Louis Armstrong and Bing Crosby, and truly idolized Connee Boswell of the Boswell Sisters. “She was tops at the time,” Fitzgerald said in 1988. “I was attracted to her immediately. My mother brought home one of her records, and I fell in love with it. I tried so hard to sound just like her.”

#### 2. SHE DABBLED IN CRIMINAL ACTIVITIES AS A TEENAGER.

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Fitzgerald’s childhood wasn’t an easy one. Her stepfather was reportedly abusive to her, and that abuse continued following the death of Fitzgerald’s mother in 1932. Eventually, to escape the violence, she moved to Harlem to live with her aunt. While she had been a great student when she was younger, it was following that move that her dedication to education faltered. Her grades dropped and she often skipped school. But she found other ways to fill her days, not all of them legal: According to The New York Times, she worked for a mafia numbers runner and served as a police lookout at a local brothel. Her illicit activities eventually landed her in an orphanage, followed by a state reformatory.

#### 3. SHE MADE HER STAGE DEBUT AT THE APOLLO THEATER.

In the early 1930s, Fitzgerald was able to make a little pocket change from the tips she made from passersby while singing on the streets of Harlem. In 1934, she finally got the chance to step onto a real (and very famous) stage when she took part in an Amateur Night at the Apollo Theater on November 21, 1934. It was her stage debut.

The then-17-year-old managed to wow the crowd by channeling her inner Connee Boswell and belting out her renditions of “Judy” and “The Object of My Affection.” She won, and took home a \$25 prize. Here’s the interesting part: She entered the competition as a dancer. But when she saw that she had some stiff competition in that department, she opted to sing instead. It was the first big step toward a career in music.

#### 4. A NURSERY RHYME HELPED HER GET THE PUBLIC’S ATTENTION.

Not long after her successful debut at the Apollo, Fitzgerald met bandleader Chick Webb. Though he was initially reluctant to hire her because of what The New York Times described as her “gawky and unkempt” appearance, her powerful voice won him over. "I thought my singing was pretty much hollering," she later said, "but Webb didn't."

Her first hit was a unique adaptation of “A-Tisket, A-Tasket,” which she helped to write based on what she described as "that old drop-the-handkerchief game I played from 6 to 7 years old on up."

#### 5. SHE WAS PAINFULLY SHY.

Though it certainly takes a lot of courage to get up and perform in front of the world, those who knew and worked with Fitzgerald said that she was extremely shy. In Ella Fitzgerald: A Biography of the First Lady of Jazz, trumpeter Mario Bauzá—who played with Fitzgerald in Chick Webb’s orchestra—explained that “she didn't hang out much. When she got into the band, she was dedicated to her music … She was a lonely girl around New York, just kept herself to herself, for the gig."

#### 6. SHE MADE HER FILM DEBUT IN AN ABBOTT AND COSTELLO MOVIE.

As her IMDb profile attests, Fitzgerald contributed to a number of films and television series over the years, and not just to the soundtracks. She also worked as an actress on a handful of occasions (often an actress who sings), beginning with 1942’s Ride ‘Em Cowboy, a comedy-western starring Bud Abbott and Lou Costello.

#### 7. SHE GOT SOME HELP FROM MARILYN MONROE.

“I owe Marilyn Monroe a real debt,” Fitzgerald said in a 1972 interview in Ms. Magazine. “It was because of her that I played the Mocambo, a very popular nightclub in the ’50s. She personally called the owner of the Mocambo and told him she wanted me booked immediately, and if he would do it, she would take a front table every night. She told him—and it was true, due to Marilyn’s superstar status—that the press would go wild. The owner said yes, and Marilyn was there, front table, every night. The press went overboard … After that, I never had to play a small jazz club again. She was an unusual woman—a little ahead of her times. And she didn’t know it.”

Though it has often been reported that the club’s owner did not want to book Fitzgerald because she was black, it was later explained that his reluctance wasn’t due to Fitzgerald’s race; he apparently didn’t believe that she was “glamorous” enough for the patrons to whom he catered.

#### 8. SHE WAS THE FIRST AFRICAN AMERICAN WOMAN TO WIN A GRAMMY.

William P. Gottlieb - LOC, Public Domain, Wikimedia Commons

Among her many other accomplishments, in 1958 Fitzgerald became the first African American woman to win a Grammy Award. Actually, she won two awards that night: one for Best Jazz Performance, Soloist for Ella Fitzgerald Sings the Duke Ellington Songbook, and another for Best Female Pop Vocal Performance for Ella Fitzgerald Sings the Irving Berlin Songbook.

#### 9. HER FINAL PERFORMANCE WAS AT CARNEGIE HALL.

On June 27, 1991, Fitzgerald—who had, at that point, recorded more than 200 albums—performed at Carnegie Hall. It was the 26th time she had performed at the venue, and it ended up being her final performance.

#### 10. SHE LOST BOTH OF HER LEGS TO DIABETES.

In her later years, Fitzgerald suffered from a number of health problems. She was hospitalized a handful of times during the 1980s for everything from respiratory problems to exhaustion. She also suffered from diabetes, which took much of her eyesight and led to her having to have both of her legs amputated below the knee in 1993. She never fully recovered from the surgery and never performed again. She passed away at her home in Beverly Hills on June 15, 1996.

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