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# 15-Year-Old Spots a Math Mistake in a Museum Exhibit

The "Mathematica: A World of Numbers...and Beyond" exhibit at the Boston Museum of Science opened in 1981. Until recently, a small error in the equation for the Golden Ratio had gone completely unnoticed—that is, until 15-year-old Joseph Rosenfeld visited the museum.

The high school sophomore from Virginia was in Boston on a family vacation when he noticed that the equation had a minus sign where there should be a plus.

“It was cool,” Rosenfeld told Boston.com. “At first, I wasn’t sure, I thought maybe I had it wrong, but I was excited.”

When Rosenfeld realized he was right about the missing addition symbol, he left a note about the error at the museum's front desk, but didn't include any contact information. His aunts, who had accompanied the teen on his visit, later reached out and informed the museum about who had spotted the mistake. In response, the museum sent Joseph a letter acknowledging their error and promising to address it.

"You are right that the formula for the Golden Ratio is incorrect. We will be changing the – sign to a + sign on the three places it appears if we can manage to do it without damaging the original," Alana Parkes, the museum’s exhibit content developer, wrote in the letter. She noted that changing that particular exhibit would be tricky because the entire thing is considered an artifact. However, by the time the Boston.com story ran, the error had been fixed.

For his contribution, Joseph, who wants to go to MIT one day, was invited back to tour the museum's newest exhibit, The Science Behind Pixar.

UPDATE: As many people have pointed out, in this comment section and others, while Joseph had a point, he wasn't right in saying the museum was wrong.

Technically, the Golden Ratio—which describes the relationship between side lengths of a particularly appealing rectangles—is (√(5)±1)/2, where ± means plus or minus. Typically, it is written with just the plus sign as a way of indicating that the ratio of the whole segment to the longer part is equal to the ratio of the longer part to the shorter part. This number, the one you get if you use addition, is 1.618... going on forever. However, it is equally true to say that the smaller part divided by the larger part equals the larger part divided by the whole—a ratio described by the same formula if you use subtraction instead.

Joseph was expecting to see the plus sign because 1.618 is the number typically associated with the Golden Ratio, a number symbolized by the lowercase Greek phi. The museum, however, had the formula written with the minus sign, or 0.618. As a final point in their favor, earlier in the exhibit, the ratio is symbolized by an uppercase phi, which is used to represent 0.618. So while the museum was unconventional, they were not only correct, they were also consistent.

So the museum wasn't wrong. But neither was Joseph. And when the whole thing was cleared up, the museum had this to say:

Hulton Archive/Getty Images
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Art
Museum Discovers Classic Renaissance Painting Hidden in Its Own Collection
##### Andrea Mantegna circa 1475
Hulton Archive/Getty Images

A long-lost painting by a master artist of the Renaissance was recently rediscovered in the storeroom of an Italian museum near Milan, according to The Art Newspaper and The Wall Street Journal.

The painting in question, Andrea Mantegna’s 15th century The Resurrection of Christ, was found by a curator at an art museum in the city of Bergamo. The Accademia Carrara has been in possession of the Mantegna painting since the 19th century, but long ago discounted it as a copy. While working on a catalogue for the museum in March, Accademia Carrara curator Giovanni Valagussa took note of the tempera-on-panel work and began to investigate its origins.

Count Guglielmo Lochis purchased the painting in 1846, cataloguing it as an original Mantegna; it was bequeathed to the museum as part of his collection after his death in 1859. But decades later, other experts cast doubt on the originality of the work, first re-attributing it to the artist’s son, and later suggesting that it was a copy that was not even made in his workshop. The museum removed it from display sometime before 1912, and it has been in storage for more than a century.

The Resurrection of Christ
Andrea Mantegna, Accademia Carrara

Upon inspecting the painting, Valagussa suspected it was more than just a copy. The painting features a small cross at the bottom of the image that looked disconnected from the rest, and the structure of the back of the painting made it seem like it might be part of a larger work. Valagussa tracked down another Mantegna painting, Descent Into Limbo, that seemed to fit underneath—the paintings are likely two halves of one image that was cut apart.

The Accademia Carrara also conducted an infrared survey of The Resurrection of Christ, discovering that the artist drew nude figures first, then painted over them with images of clothed soldiers, a technique that Mantegna was known for.

A world expert on Mantegna, the Metropolitan Museum of Art’s Keith Christiansen, did his own analysis and believes the painting in Bergamo to be an authentic, high-quality Mantegna. That means that the Accademia Carrara’s forgotten wood panel, previously insured for around \$35,000, is probably worth between \$25 million and \$30 million.

The museum hopes to one day bring the two parts of the painting, The Resurrection of Christ and the privately owned Descent Into Limbo, together in an exhibition in the future.

[h/t The Art Newspaper]

Collection of Pedro Corrêa do Lago
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History
New Museum Exhibition Shows Off Rare Handwritten Letters From History’s Most Famous Figures
##### An autographed letter from 7-year-old Victoria, future queen of England, to her uncle, 1826.
Collection of Pedro Corrêa do Lago

There’s something special about seeing the handwriting of one of your heroes. Just ask anyone who has gotten a celebrity’s autograph. The unique power a signature holds is at the center of an upcoming exhibition at the Morgan Library and Museum in New York City, The Magic of Handwriting: The Pedro Corrêa do Lago Collection.

As part of the display, the museum features drawings, signed photos, and rare letters from figures throughout history—from line drawings Michelangelo used to order marble for the facade of a basilica he was contracted to build in Florence to a previously unpublished, signed photo of Rasputin.

Michelangelo Buonarroti (1475–1564). Pen and ink drawing with autograph instructions for a marble order for the facade of San Lorenzo, [Florence, 1518]. Collection of Pedro Corrêa do Lago.

The materials on display are just part of the collection of Pedro Corrêa do Lago, a Brazilian art historian and author who started writing to prominent celebrities when he was 12 years old, asking for their autographs. Over the next 50 years, he assembled a massive collection of autographs, manuscripts, and other handwritten materials that date back to 1140. The 140 items on display at the Morgan make up just a tiny fraction of the 100,000 autographs he owns.

The items are divided up into several different categories: art, history, literature, science, music, and entertainment. Many of them have never been shown before in a public exhibition.

Albert Einstein (1879–1955). Autograph mathematical manuscript, ca. 1940s. Collection of Pedro Corrêa do Lago.

The exhibition includes treasures like a 12th century papal bull signed by four different medieval popes (three were cardinals at the time of signing) and a Catholic saint, Guarinus of Palestrina. There are documents and letters signed by royalty, including Richard III and Elizabeth I of England and Mary, Queen of Scots; there is a rare letter from Leon Trotsky to Frida Kahlo, written as the two were ending their affair; and an autographed draft of a letter Jean-Paul Sartre wrote to the Swedish Academy in 1964, asking them not to give him the Nobel Prize (they awarded it to him anyway). There is a draft of a poem William Butler Yeats wrote on the back of a letter, and a signed mathematical manuscript from Albert Einstein.

Below is a handwritten bill for 20 therapy sessions with Sigmund Freud. Freud charged American neurologist Roy Grinker 100 Austrian schillings per hour, or the equivalent of \$20 or \$25 at that time, for psychoanalysis sessions.

Sigmund Freud (1856–1939). Autograph invoice signed, to Roy Grinker, written on a personal correspondence card, Vienna, 30 June 1934. Collection of Pedro Corrêa do Lago.

Artist René Magritte sent this letter to photographer and filmmaker Francis Lee, suggesting Lee make use of the sequence of drawings included (of a man removing his gloves, hat, and head) in a film:

René Magritte (1898–1967). Autograph letter signed, to Francis Lee, Brussels, 22 January 1946. Collection of Pedro Corrêa do Lago. © 2018 C. Herscovici / Artists Rights Society

This is one of two surviving letters from Oscar Wilde to Bram Stoker. Wilde wanted Stoker, who worked at London’s Lyceum Theatre, to set aside a ticket for him that night:

Oscar Wilde (1854–1900). Autograph letter signed, to Bram Stoker, London, [1879 or 1880]. Collection of Pedro Corrêa do Lago.

This draft of the opening of Swann's Way differs slightly from what Proust eventually published. Notably, it doesn't include what would become the first sentence: “For a long time I used to go to bed early."

Marcel Proust (1871–1922). Swann’s Way (Du côté de chez Swann), autograph manuscript draft of the opening passage, ca. March–April 1913. Collection of Pedro Corrêa do Lago. Image used with permission of the Proust Estate.

The Magic of Handwriting: The Pedro Corrêa do Lago Collection will run from June 1 to September 16, 2018 at the Morgan Library and Museum in New York City.

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