Wednesday, May 23, 2018
Perspective

A Little Perspective: An ancient clay tablet got the angle on Pythagoras by a millennium

Two Australian mathematicians assert that an ancient clay tablet was a tool for working out trigonometry problems, possibly adding to the many techniques that Babylonian mathematicians had mastered.

"It's a trigonometric table, which is 3,000 years ahead of its time," said Daniel F. Mansfield of the University of New South Wales. Mansfield and his colleague Norman J. Wildberger reported their findings in the journal Historia Mathematica.

The tablet, known as Plimpton 322, was discovered in the early 1900s in southern Iraq and has long been of interest to scholars. It contains 60 numbers organized into 15 rows and four columns inscribed on a piece of clay about 5 inches wide and 3.5 inches tall. Based on the style of cuneiform script used for the numbers, Plimpton 322 has been dated to between 1822 and 1762 B.C.

One of the columns on Plimpton 322 is just a numbering of the rows from 1 to 15. The other three columns are much more intriguing. In the 1940s, Otto E. Neugebauer and Abraham J. Sachs, mathematics historians, pointed out that the other three columns were essentially Pythagorean triples — sets of integers, or whole numbers, that satisfy the equation "A squared + B squared = C squared."

This equation — the Pythagorean Theorem — also represents a fundamental property of right triangles, that the square of the longest side, or hypotenuse, is the sum of the squares of the other two shorter sides. That by itself was remarkable given that the Greek mathematician Pythagoras would not be born for another 1,000 years.

Wildberger, who once had proposed teaching trigonometry in terms of ratios rather than angles, wondered if Babylonians took a similar angle-less approach to trigonometry. "You don't make a trigonometric table by accident," Mansfield said. "Just having a list of Pythagorean triples doesn't help you much. That's just a list of numbers. But when you arrange it in such a way so that you can use any known ratio of a triangle to find the other sides of a triangle, then it becomes trigonometry. That's what we can use this fragment for."

A Babylonian faced with a ziggurat word problem may have found it easy to set up: a right triangle with the long side, or hypotenuse, 56 cubits long, and one of the shorter sides 45 cubits. Next, the problem solver could have calculated the ratio 56/45, or about 1.244 and then looked up the closest entry on the table, which is line 11, which lists the ratio 1.25.

From that line, it is then a straightforward calculation to produce an answer of 33.6 cubits. In their paper, Mansfield and Wildberger show that this is better than what would be calculated using a trigonometric table from the Indian mathematician Madhava 3,000 years later.

Kenneth Chang, New York Times

How horses got their hooves

All four-limbed, land-based vertebrates came from a common ancestor with legs that ended in five toes. Over time, many animals lost some of their digits: Hippos, rhinos and camels have four, three and two toes on each leg. But only one living group of animals ended up with a single toe per foot: the group containing modern horses.

A study in Proceedings of the Royal Society B, lends support to existing hypotheses about the dramatic transformation in horses' hooves through history. Namely, as horses evolved and got larger from their ancestral, dog-sized form, it was better to have one very robust toe than several smaller ones to support their increased body mass. Furthermore, having just one toe reduced the weight horses had to carry at the end of each leg, making it easier for them to run and maneuver.

Steph Yin, New York Times

This secret stops honeybees from becoming hive queens

"You are what you eat" is a common adage among humans, but a new study explains why it might be more apt for honeybees.

In a paper in PLOS Genetics, researchers found specific molecules in the pollen and honey mixture that honeybee larvae feed on cause physical changes that determine whether females develop into long-living, reproductive queens or the mostly sterile workers that nourish larvae and collect food.

Researchers have long known that these differences are not determined at birth but rather are a product of diet. Larvae that eat royal jelly, a substance secreted by the glands of nurse bees, develop into queens, while those that feed on a combination of pollen and honey called bee bread become workers.

Previous research focused on the role of the protein and sugar-rich royal jelly in caste development, but this study found a new mechanism: small molecules in plants called microRNA. These molecules can affect the size and colorfulness of plants, and also play a crucial role in bee development. Transferred to a bee through bee bread, the microRNA can affect genes in ways that delay physical development and keep the bees sterile.

"Neither substance is sufficient alone," said Chen-Yu Zhang, co-author of the study and a professor of biochemistry at Nanjing University in China. "The royal jelly and plant microRNA work together to affect caste formation."

Aneri Pattani, New York Times

Solving a prehistoric puzzle of how plesiosaurs swam the oceans

Millions of years ago, when dinosaurs dominated the land, leviathans known as plesiosaurs prowled the oceans. With their long necks and barreled bodies, these marine reptiles — which were not dinosaurs — resembled the mythical Loch Ness monster.

Though not every plesiosaur had a neck like "Nessie," they all had four long flippers. Since the first fossils of this prehistoric sea creature were found about two centuries ago, the two nearly identical pairs of aquatic limbs have puzzled paleontologists.

"Having four big flippers like that is rather strange," said Luke Muscutt, a biomechanist and postdoctoral researcher at the University of Southampton in England. Muscutt spent his thesis decoding how the plesiosaur paddled, which he said is unlike any other living vertebrate that swims in the ocean. Fish and sharks swim by swinging their tails side to side, and whales and dolphins swing theirs up and down. Even other animals with flippers like sea lions and sea turtles do not swim with all four flippers, he said.

A study he published in the journal Proceedings of the Royal Society B provides further evidence that the hind flippers were key to the plesiosaur's underwater moves, and were not just limbs used for steering.

"Plesiosaurs definitely used all four flippers for propulsion and that made them more efficient and effective swimmers," said Muscutt. The findings, he said, could help settle the long-running debate on how the plesiosaur swam. They could also contribute to future designs for underwater drones or submersibles.

Nicholas St. Fleur, New York Times

Casting light on mystery of a star that vanished after 14 days

On March 11, 1437, Korean astronomers scanning the night sky for omens of the future spotted a new star in the cluster of stars they called Wei, and what today's star watchers consider the tail of the Scorpius constellation. Fourteen nights later, it vanished.

Astronomers have now identified the source of that brief brightening — a binary star system a couple of thousand light-years away.

In these systems, one of the stars is a white dwarf, the burned-out but still hot remnant of a star. The powerful gravity of the white dwarf pulls hydrogen away from its companion star and onto its surface, building up pressure until it sets off a thermonuclear explosion, a burst of light known as a nova that is up 1 million times as bright as the sun.

That is what the Koreans saw nearly six centuries ago.

Kenneth Chang, New York Times

Hack a chrysanthemum, and broaden its palette

A blue human is a cold, dead or sad human. We don't want to be blue. And flowers don't appear to either.

Less than 10 percent of 400,000 floral species bear blue flowers. Scientists and horticulturalists have tried to force blueness upon petals, but breeding and genetic engineering haven't worked out.

Now Japanese scientists have finally created a true blue chrysanthemum — one that passes the strict color standards of the Royal Horticulturalist Society.

Naonobu Noda, a plant biologist at the National Agriculture and Food Research Organization in Japan, and his colleagues spliced genes from Canterbury bells and the butterfly pea into the chrysanthemum genome, shifting the plant's pH and altering its color. The researchers confirmed the color as blue by testing its wavelengths in the lab.

Joanna Klein, New York Times

     
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