DUBAI: A 3,700-year-old clay tablet analyzed by researchers in Australia has proven that Babylonians, not Greeks, developed trigonometry.
The tablet, known as Plimpton 332, was found in the early 1900s in modern-day southern Iraq but experts at the University of New South Wales, Australia, have only just discovered what the etchings on the tablet mean.
It is the world’s oldest and most accurate trigonometric table and proves that Babylonians developed the mathematic technique some 1,500 years before the Greeks, whose version is still in use today.
However, unlike the modern form of trigonometry, Babylonian mathematics used a sexagesimal system.
“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr. Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science, according to The Telegraph.
“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.
“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education.
“This is a rare example of the ancient world teaching us something new.”
Until now, Greek astronomer Hipparchus, who lived around 120BC, was regarded as the father of trigonometry.
“Plimpton 322 predates Hipparchus by more than 1000 years,” says Wildberger.
The tablet is thought to have come from the ancient Sumerian city of Larsa and has been dated between 1822 and 1762 BC.
Tablet found in modern-day Iraq shows Babylonians, not Greeks, developed trigonometry
Tablet found in modern-day Iraq shows Babylonians, not Greeks, developed trigonometry
Cheating on your spouse is no longer a crime in New York, with the repeal of a little-known 1907 law
Cheating on your spouse is no longer a crime in New York, with the repeal of a little-known 1907 law
ALBANY, N.Y.: New York on Friday repealed a seldom-used, more than century-old law that made it a crime to cheat on your spouse — a misdemeanor that once could have landed adulterers in jail for three months.
Gov. Kathy Hochul signed a bill repealing the statute, which dates back to 1907 and has long been considered antiquated as well as difficult to enforce.
“While I’ve been fortunate to share a loving married life with my husband for 40 years — making it somewhat ironic for me to sign a bill decriminalizing adultery — I know that people often have complex relationships,” she said. “These matters should clearly be handled by these individuals and not our criminal justice system. Let’s take this silly, outdated statute off the books, once and for all.”
Adultery bans are actually law in several states and were enacted to make it harder to get a divorce at a time when proving a spouse cheated was the only way to get a legal separation. Charges have been rare and convictions even rarer. Some states have also moved to repeal their adultery laws in recent years.
New York defined adultery as when a person “engages in sexual intercourse with another person at a time when he has a living spouse, or the other person has a living spouse.” The state’s law was first used a few weeks after it went into effect, according to a New York Times article, to arrest a married man and 25-year-old woman.
State Assemblymember Charles Lavine, sponsor of the bill, said about a dozen people have been charged under the law since the 1970s, and just five of those cases resulted in convictions.
“Laws are meant to protect our community and to serve as a deterrent to anti-social behavior. New York’s adultery law advanced neither purpose,” Lavine said in a statement Friday.
The state’s law appears to have last been used in 2010, against a woman who was caught engaging in a sex act in a park, but the adultery charge was later dropped as part of a plea deal.
New York came close to repealing the law in the 1960s after a state commission tasked with evaluating the penal code said it was nearly impossible to enforce.
At the time, lawmakers were initially on board with removing the ban but eventually decided to keep it after a politician argued that repealing it would make it seem like the state was officially endorsing infidelity, according to a New York Times article from 1965.
Banana taped to a wall sells for $6.2 million in New York
- Chinese-born crypto founder Justin Sun forks over more than six million for the fruit and its single strip of silver duct tape
- Given the shelf life of a banana, Sun is essentially buying a certificate of authenticity that the work was created by Maurizio Cattelan
NEW YORK: A fresh banana taped to a wall — a provocative work of conceptual art by Italian artist Maurizio Cattelan — was bought for $6.2 million on Wednesday by a cryptocurrency entrepreneur at a New York auction, Sotheby’s announced in a statement.
The debut of the edible creation entitled “Comedian” at the Art Basel show in Miami Beach in 2019 sparked controversy and raised questions about whether it should be considered art — Cattelan’s stated aim.
Chinese-born crypto founder Justin Sun on Wednesday forked over more than six million for the fruit and its single strip of silver duct tape, which went on sale for 120,000 dollars five years ago.
“This is not just an artwork. It represents a cultural phenomenon that bridges the worlds of art, memes, and the cryptocurrency community,” Sun was quoted as saying in the Sotheby’s statement.
“I believe this piece will inspire more thought and discussion in the future and will become a part of history.”
The sale featured seven potential buyers and smashed expectations, with the auction house issuing a guide price of $1-1.5 million before the bidding.
Given the shelf life of a banana, Sun is essentially buying a certificate of authenticity that the work was created by Cattelan as well as instructions about how to replace the fruit when it goes bad.
The installation auctioned on Wednesday was the third iteration — with the first one eaten by performance artist David Datuna, who said he felt “hungry” while inspecting it at the Miami show.
Sun, who founded cryptomoney exchange Tron, said that he intended to eat his investment too.
“In the coming days, I will personally eat the banana as part of this unique artistic experience, honoring its place in both art history and popular culture,” he said.
As well as his banana work, Cattelan is also known for producing an 18-carat, fully functioning gold toilet called “America” that was offered to Donald Trump during his first term in the White House.
His work is often humorous and deliberately provocative, with a 1999 sculpture of the pope stuck by a meteor titled “The Ninth Hour.”
He has explained the banana work as a critical commentary on the art market, which he has criticized in the past for being speculative and failing to help artists.
The asking price of $120,000 for “Comedian” in 2019 was seen at the time as evidence that the market was “bananas” and the art world had “gone mad,” as The New York Post said in a front-page article.
The banana sold on Wednesday was bought for 35 cents from a Bangladeshi fruit seller on the Upper East Side of Manhattan, according to The New York Times.
Sun has hit headlines in the past as an art collector and as a major player in the murky cryptocurrency world.
He was charged last year by the US Securities and Exchange Commission for alleged market manipulation and unregistered sales of crypto assets, which he promoted with celebrity endorsements, including from Lindsay Lohan.
In 2021, he bought Alberto Giacometti’s “Le Nez” for $78.4 million, which was hailed by Sotheby’s at the time as signaling “an influx of younger, tech-savvy collectors.”
Global art markets have been dropping in value in recent years due to higher interest rates, as well as concern about geopolitical instability, experts say.
“Empire of Light” (“L’Empire des lumieres“), a painting by Rene Magritte, shattered an auction record for the surrealist artist on Tuesday, however, selling for more than $121 million at Christie’s in New York.
Farmer in Argentina gets jail term for killing penguin chicks
- The sheep farmer was found guilty of destroying nests and killing chicks while clearing land along the Punta Tumbo nature reserve
- In his defense, he said he had no choice but to clear the land as the state had failed to set up an access route to his property
BEUNOS AIRES: An Argentinian farmer was given a three-year prison sentence for animal cruelty Wednesday, likely to be commuted, after being found guilty of killing over 100 Patagonian penguin chicks.
The sheep farmer from the southern province of Chubut was found guilty last month of destroying dozens of nests and killing chicks in 2021 while clearing land along the Punta Tumbo nature reserve, home to one of the main colonies of Magellanic penguins on the Atlantic coast.
The farmer is unlikely to be incarcerated as Argentina’s penal code recommends alternatives to prison for a first conviction and sentences up to three years.
Prosecutors had requested a four-year sentence.
Environmental group Greenpeace, the complainant in the case, had welcomed the farmer’s conviction as “an important step for environmental justice.”
The farmer argued there was no choice but to clear the land as the state had failed to set up an access route to his property, or boundaries between his farm and the reserve.
The Magellanic Penguin is listed as a species of “least concern” on the International Union for Conservation of Nature’s Red List, meaning it is not at risk of extinction even though numbers are in decline.
SpaceX fails to repeat Starship booster catch, as Trump looks on
BOCA CHICA: SpaceX’s Starship megarocket blasted off on its latest test flight Tuesday, with President-elect Donald Trump joining Elon Musk to witness the spectacle firsthand in the latest sign of their ever closer ties.
But the Republican leader was deprived of the chance to see the booster stage caught in the launch tower’s “chopstick” arms, an engineering marvel demonstrated by the company last month and one he personally lauded during his election victory speech.
Instead, the colossal Super Heavy first stage made a more subdued splashdown in the Gulf of Mexico. Company representatives cited unmet technical criteria, dampening the triumph of an event attended by a bevy of Trump-world figures, including Donald Trump Jr.
Earlier, Trump greeted Musk warmly on Tuesday afternoon, sporting a red MAGA hat as the pair headed off to watch from the control tower of the company’s Starbase in Boca Chica, Texas, where the rocket blasted off at 4:00 p.m. local time (2200 GMT) on the sixth test flight for Starship.
SpaceX founder and CEO Musk has been a constant presence at Trump’s side since the incoming president’s election victory, joining him at a meeting with Argentina’s President Javier Milei and even at a UFC bout.
Trump’s decision to travel to Musk’s home turf was the latest sign of the growing alliance between the billionaire duo, which has raised questions over possible conflicts of interests given SpaceX’s lucrative contracts with NASA and the Pentagon.
Tuesday’s launch marked the quickest turnaround between test flights for the world’s most powerful rocket, a gleaming, 121-meter-tall (400-foot) stainless steel colossus central to Musk’s ambition of colonizing Mars and making humanity a multiplanetary species.
Musk aims to launch the first uncrewed missions to the Red Planet as early as 2026, coinciding with the next “Mars transfer window” — a period when the journey between Earth and Mars is at its shortest.
NASA is also counting on a specialized version of Starship to ferry astronauts to the lunar surface later this decade under its Artemis program.
Flight six of Starship was seen as a test of whether SpaceX’s first booster catch was pure precision or relied on a stroke of luck after Musk — perhaps inadvertently — disclosed how close the last flight came to disaster.
In a clip posted to X showcasing his gaming chops in “Diablo IV,” sharp-eared fans caught an employee briefing him that the Super Heavy booster was “one second away” from a system failure that could have spelled catastrophe.
Starship’s upper stage will make a partial orbit of Earth, reenter the atmosphere and splash down in the Indian Ocean a little over an hour later, but this time in the daylight, providing clearer visuals for analysis.
Key milestones include reigniting Starship’s Raptor engines for the first time in space and trialing new heat shield materials. The flight also carries Starship’s first ever payload — a stuffed banana — and serves as a swan song for the current generation of Starship prototypes.
With twice the thrust of the Saturn V rockets that powered Apollo missions, Starship is the most powerful rocket ever built. Musk has already teased that its successor, Starship V3, will be “3X more powerful” and could take flight within a year.
The flight comes as Musk is riding high on Trump’s November 5 White House win, having campaigned extensively for the returning Republican leader, as well as donating staggering sums from his own fortune to the cause.
His loyalty has paid off. Musk has been tapped to co-lead a new “Department of Government Efficiency” — or DOGE, a cheeky nod to the meme-based cryptocurrency Musk loves to promote.
That in turn has led to concerns Musk could engage in “self-dealing” as the CEO is poised to straddle the line between government insider and corporate titan.
Critics worry he could sway regulatory decisions to benefit his six companies, including SpaceX and its marquee Starship program, which has faced launch delays linked to an environmental review the company called “superfluous.”
Stray dogs in Giza become tourist draw after ‘pyramid puppy’ sensation
- Apollo became an overnight sensation last month after being filmed scaling the Great Pyramid of Khafre
- As news of Apollo’s daring climb spread worldwide, interest grew in the dogs who have long made their homes among the ancient stones
CAIRO: Beneath the blazing Egyptian sun, crowds at the Giza Pyramids gazed up at the ancient wonders, but some had their eyes peeled for a new attraction.
“There he is,” one Polish tourist told his wife as they spotted a scrappy dog perched on one of the stones.
They were talking about Apollo, a stray who became an overnight sensation last month after being filmed scaling the Great Pyramid of Khafre, one of the seven wonders of the world.
The viral footage, captured by American paragliding enthusiast Alex Lang and shared online by his friend Marshall Mosher, showed Apollo fearlessly climbing the 136-meter monument, barking at birds from the summit.
“He was acting like a king,” Lang told AFP.
As news of Apollo’s daring climb spread worldwide, interest grew in the dogs who have long made their homes among the ancient stones.
“He is climbing over there,” said Arkadiusz Jurys, a tourist from Poland, craning his neck for a better view.
“It is unusual,” he added, describing Apollo as surveying the picture-snapping crowd from above.
Another visitor, Diego Vega from Argentina, felt a special bond with the dogs.
“Connecting with them feels like connecting with the pharaohs,” he said, while petting a member of Apollo’s pack.
Apollo’s newfound fame has even inspired local guides to include him and his pack in their stories for tourists.
“This is Anubis,” one tour guide told two American tourists, comparing Apollo, now known as the “pyramid puppy,” with the ancient Egyptian god of the dead, often depicted as a man with a jackal’s head.
“He and his pack are now part of our tour conversations,” said Sobhi Fakhry, another tour guide.
Businesses around the Giza plateau are also seeing a boost.
Umm Basma, a 43-year-old woman selling souvenirs near the Khafre pyramid, reported an increase in sales thanks to the influx of tourists eager to meet the so-called pyramid dogs.
“We’ve always seen these dogs climbing the pyramids, but we never thought they would become a blessing for us,” she said.
One pyramid guard, who preferred to remain anonymous, also said that some celebrities had paid for permits to have their own dogs photographed with Apollo.
Apollo, a three-year-old Baladi dog, is part of a pack of about eight that has made their home among the ancient ruins.
The dogs, a local breed, are known for their resilience, intelligence and ability to survive in Egypt’s harsh climate.
Ibrahim el-Bendary, co-founder of the American Cairo Animal Rescue Foundation, which monitors the pyramid dogs, described Apollo as the pack’s “alpha male.”
“He is the bravest and strongest in his pack,” he said.
Apollo was born in a rocky crevice within the Khafre pyramid where his mother, Laika, found shelter. Sadly, some of Apollo’s siblings did not survive the site’s perilous heights.
A sympathetic guard eventually relocated Laika to a safer spot where Apollo now stands out with his distinctive curled tail and confident nature.
The initial focus of Lang and Marshall was the daring canine climber, but their visit led to a deeper connection with Cairo’s stray dogs.
Intrigued by the challenges they face, Mosher decided to adopt a puppy from the pack: Anubi, who is Apollo’s daughter.
Anubi will join Marshall in the US after she receives the dedicated care she needs in Egypt to grow up healthy.
At the pyramids, local animal care groups are now working with the government in order to set up food and water stations for the strays, as well as for other animals including camels and horses.
A permanent veterinary center will be established at the pyramids with staff set to receive animal care training, said Egypt’s tourism minister.
Vicki Michelle Brown, the other co-founder of the American Cairo Animal Rescue Foundation, believes that Apollo’s story can make a difference.
“It sheds so much light on the dogs and cats that are here,” Brown said.
“I definitely believe him (Apollo) climbing the pyramids can help all of the dogs in Egypt to have a better life.”
