Tag: mathematics

Scientists Discover A New Shape That Might Be Inside You Right Now

The cells in our bodies are put together in all kinds of weird ways. Neuron cells have long, branching connections to other cells, bones form porous structures, and blood vessels float freely around the body.

But a lot of cells are simply squished together as tightly as possible, and scientists have determined that these cells in particular come in a unique and previously unknown shape, called a “scutoid.”

Much of our bodies are covered in epithelial cells, which are cells designed to stick very closely together in order to form some type of barrier or wall.

Our skin cells are epithelial cells, as are the cells that form the walls of many of our organs.

One of the most important functions these cells have is keeping things either inside or outside of the areas they surround, so forming a tight wall is of paramount importance.

So what shape do these cells take? Most scientists previously believed that these cells were shaped like simple cylinders, but new research suggests they take a more complicated shape.




Researchers at the University of Seville ran a computer simulation to determine what the most efficient shape would be, and their simulation settled on a strange prism-like shape.

The shape has six sides at the top and five sides at the bottom, and one of the sides had a triangular protrusion.

Crucially, this shape—which the scientists named the “scutoid” after the similarly-named and -shaped scutellum of a beetle—does indeed stack much better than a simple cylinder.

But just because a computer says it’s the best shape doesn’t mean that anything in nature actually uses it, so the researchers examined cells from fruit flies and zebrafish to see if the scutoid shows up in those animals’ epithelial tissue.

To their delight, it did. They’re not certain whether these scutoid-shaped cells exist in humans as well, but there’s a good chance.

In addition to discovering what epithelial cells look like, these researchers also discovered a brand new shape new to mathematics.

Mathematical discoveries are often very abstract but can frequently have impact in other fields in science or engineering.

So scutoids are only in your body right now, but eventually we might start seeing them show up all over the place.

Please like, share and tweet this article.

Pass it on: Popular Science

Flash Recovery Of Ammonoids After Most Massive Extinction Of All Time

The study, conducted by a Franco-Swiss collaboration involving the laboratories Biogéosciences (Université de Bourgogne / CNRS), Paléoenvironnements & Paléobiosphère (Université Claude Bernard / CNRS) and the Universities of Zurich and Lausanne (Switzerland), appears in the August 28 issue of Science.

The history of life on Earth has been punctuated by a number of mass extinctions, brief periods of extreme loss of biodiversity. These extinctions are followed by phases during which surviving species recover and diversify.

The End-Permian extinction, which took place between the Permian (299 – 252.6 MY) and Triassic (252.6 – 201.6 MY), is the greatest mass extinction on record, resulting in the loss of 90% of existing species.

It is associated with intensive volcanic activity in China and Siberia. It marks the boundary between the Paleozoic and Mesozoic Eras.




Until now, studies had shown that the biosphere took between 10 and 30 million years to recover the levels of biodiversity seen before the extinction.

Ammonoids are cephalopod swimmers related the nautilus and squid. They had a shell, and disappeared from the oceans at the same time as the dinosaurs, 65 million years ago, after being a major part of marine fauna for 400 MY.

The Franco-Swiss team of paleontologists has shown that ammonoids needed only one million years after the End-Permian extinction to diversify to the same levels as before.

The cephalopods, which were abundant during the Permian, narrowly missed being eradicated during the extinction: only two or three species survived and a single species seems to have been the basis for the extraordinary diversification of the group after the extinction.

It took researchers seven years to gather new fossils and analyze databases in order to determine the rate of diversification of the ammonoids.

In all, 860 genera from 77 regions around the world were recorded at 25 successive time intervals from the Late Carboniferous to the Late Triassic, a period of over 100 million years.

The discovery of this explosive growth over a million years takes a heated debate in a new direction.

Indeed, it suggests that earlier estimates for the End-Permian extinction were based on truncated data and imprecise or incorrect dating.

Furthermore, the duration for estimated recovery after other lesser extinctions all vary between 5 and 15 million years.

The result obtained here suggests that these estimates should probably be revised downwards.

The biosphere is most likely headed towards a sixth mass extinction, and this discovery reminds us that the recovery of existing species after an extinction is a very long process, taking several tens of thousands of human generations at the very least.

Please like, share and tweet this article.

Pass it on: Popular Science

Honey Bees Can Understand Nothing

Zero, zilch, nothing, is a pretty hard concept to understand. Children generally can’t grasp it until kindergarten. And it’s a concept that may not be innate but rather learned through culture and education.

Throughout human history, civilizations have had varying representations for it. Yet our closest animal relative, the chimpanzee, can understand it.

And now researchers in Australia writing in the journal Science say the humble honey bee can be taught to understand that zero is less than one.

The result is kind of astounding, considering how tiny bee brains are. Humans have around 100 billion neurons. The bee brain? Fewer than 1 million.

The findings suggest that the ability to fathom zero may be more widespread than previously thought in the animal kingdom — something that evolved long ago and in more branches of life.




It’s also possible that in deconstructing how the bees compute numbers, we could make better, more efficient computers one day.

Our computers are electricity-guzzling machines. The bee, however, “is doing fairly high-level cognitive tasks with a tiny drop of nectar,” says Adrian Dyer, a Royal Melbourne Institute of Technology researcher and co-author on the study.

Their brains are probably processing information in a very clever [i.e., efficient] way.”

But before we can deconstruct the bee brain, we need to know that it can do the complex math in the first place.

How to teach a bee the concept of zero

Bees are fantastic learners. They spend hours foraging for nectar in among flowers, can remember where the juiciest flowers are, and even have a form of communication to inform their hive mates of where food is to be found.

Researchers train bees like they train many animals: with food. “You have a drop of sucrose associated with a color or a shape, and they will learn to reliably go back to” that color or shape, Dyer explains.

With this simple process, you can start teaching bees rules. In this case, the researchers wanted to teach 10 bees the basic rules of arithmetic.

So they put out a series of sheets of paper that had differing numbers of objects printed on them. Using sugar as a reward, the researchers taught the bees to always fly to the sheet that had the fewest objects printed on it.

Once the bees learned this rule, they could reliably figure out that two shapes are less than four shapes, that one shape is smaller than three. And they’d keep doing this even when a sugary reward was not waiting for them.

And then came the challenge: What happens when a sheet with no objects at all was presented to the bees? Would they understand that a blank sheet — which represented the concept of zero in this experiment — was less than three, less than one?

Please like, share and tweet this article.

Pass it on: Popular Science

The Formula For The Perfect Free-Throw

Improving your free-throw percentage is a simple matter of mathematics, according to researchers Drs. Chau Tran and Larry Silverberg of North Carolina State University.

Using three-dimensional computer simulations of hundreds of thousands of basketball trajectories, the two engineers determined the ideal characteristics of a free-throw shot.

They based their data on the assumption of a 6’6” player who would release the ball (assumed to be a men’s basketball) at a height of 7 feet.




The first variable Tran and Silverberg examined was spin. According to them, you should release the ball with about three hertz of backspin – or, so that the ball makes roughly three full backwards rotations before reaching the hoop.

This slows the ball upon contact with the backboard or rim, making it more likely that the shot will go in.

The ball should also be released at 52 degrees to the horizontal, making the peak of its arc only a few inches higher than the top of the backboard.

For aiming, they found the most successful methods put the ball towards the back of the rim, either two inches to the left or two inches to the right of the place where the rim meets the backboard.

How a mathematician sees a free throw.

Their simulation data showed that aiming straight for the center of the backboard decreases the success rate by almost three percent.

Tran and Silverberg also recommend free-throw shooters should release the ball as high above the ground as possible with a smooth, consistent release speed for best results.

Our recommendations might make even the worst free-throw shooters – you know who you are, Shaquille O’Neal and Ben Wallace – break 60 percent from the free-throw line,” Silverberg joked.

Their work is just another example of how mathematical questions can crop up in the most unexpected areas.

Please like, share and tweet this article.

Pass it on: Popular Science

Why Math Might Be Complete BS

Set up a free Brilliant account at http://www.brilliant.org/answerswithjoe/ And the first 295 to sign up for a premium account get 20% off every month!

Mathematics is the backbone of all sciences, no theories or hypotheses are proven unless there is math to back it up. But there are many who believe that math isn’t real. In today’s video, we’ll break down the arguments.

From the Mathematical Physicalists to the Platonists to the Mathematical Fictionalists, we look at all the theories behind whether numbers actually exist, and what they mean.

The Largest Prime Number Was Discovered By A FedEx Employee

A FedEx employee in Tennessee has discovered the largest known prime number.

Germantown, Tenn., resident John Pace found the number through his volunteer work with the Great Internet Mersenne Prime Search (GIMPS), a project that crowd sources computing power to search for a subset of prime numbers called Mersenne primes.

Like a normal prime number, these can only be divided by themselves and one. What sets them apart is that they can all be expressed as the number 2 raised to a given power minus one.




The newly discovered Mersenne prime, called M77232917, can be expressed as 2 to the 77,232,917 power minus one. It’s the 50th Mersenne prime to be discovered and it’s more than 23 million digits long.

Pace might be the only person in history who went into math for the money.

He told NPR, “There was a $100,000 prize attached to finding the first prime that had a 10 million digit result, and I was like, ‘Well you know, I’ve got as much chance as anybody else.’

He has been participating in the program for 14 years and this is his first discovery.

The previous longest-known prime number was discovered in January of 2016 at the University of Central Missouri. It contains 22 million digits and is also a Mersenne prime.

Large prime numbers are important for the future of computing and cyber security, and the search is already on for larger numbers.

The Electronic Frontier Foundation is offering a prize of $150,000 for finding the first prime number with one hundred million digits and $250,000 for finding the first prime with one billion digits.

Please like, share and tweet this articles

Pass it on: Popular Science

Largest Known Prime Number Discovered With Over 23 Million Digits

A collaborative computational effort has uncovered the longest known prime number.

At over 23 million digits long, the new number has been given the name M77232917 for short.

Prime numbers are divisible only by themselves and one, and the search for ever-larger primes has long occupied maths enthusiasts.

However, the search requires complicated computer software and collaboration as the numbers get increasingly hard to find.




M77232917 was discovered on a computer belonging to Jonathan Pace, an electrical engineer from Tennessee who has been searching for big primes for 14 years.

Mr Pace discovered the new number as part of the Great Internet Mersenne Prime Search (GIMPS), a project started in 1996 to hunt for these massive numbers.

Mersenne primes – named after the 17th century French monk Marin Mersenne who studied them – are calculated by multiplying together many twos and then subtracting one.

Six days of non-stop computing in which 77,232,917 twos were multiplied together resulted in the latest discovery.

The number is the 50th Mersenne prime to be discovered, and the 16th to be discovered by the GIMPS project.

It is nearly one million digits longer than the previous record holder, which was identified as part of the same project at the beginning of 2016.

Mersenne primes are a particular focus for prime aficionados because there is a relatively straightforward way to check whether a number is one or not.

Nevertheless, the new prime has to be verified using four different computer programs on four different computers.

The process also relies on thousands of volunteers sifting through millions of non-prime candidates before the lucky individual chances upon their target.

Professor Caldwell runs an authoritative website on the largest prime numbers, with a focus on the history of Mersenne primes.

He emphasised the pure excitement that searching for prime numbers brings, describing the latest discovery as “a museum piece as opposed to something that industry would use”.

Besides the thrill of discovery, Mr Pace will receive a $3,000 (£2,211) GIMPS research discovery award.

GIMPS uses the power of thousands of ordinary computers to search for elusive primes, and the team behind it state that anybody with a reasonably powerful PC can download the necessary software and become a “big prime hunter”.

The next Mersenne prime discovery could be smaller or larger than the existing record holder, but the big target for the GIMPS team is to find a 100 million digit prime number.

The person who discovers such a number will be awarded $150,000 by the Electronic Frontier Foundation for their efforts.

Please like, share and tweet this article.

Pass it on: New Scientist

The 500-Page Proof That Only One Mathematician Can Understand

Nearly four years after Shinichi Mochizuki unveiled an imposing set of papers that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity.

Although they have made modest progress.

Some four dozen mathematicians converged last week for a rare opportunity to hear Mochizuki present his own work at a conference on his home turf, Kyoto University’s Research Institute for Mathematical Sciences (RIMS).

Mochizuki is “less isolated than he was before the process got started”, says Kiran Kedlaya, a number theorist at the University of California, San Diego.

Although at first Mochizuki’s papers, which stretch over more than 500 pages, seemed like an impenetrable jungle of formulae.




Experts have slowly discerned a strategy in the proof that the papers describe, and have been able to zero in on particular passages that seem crucial, he says.

Mochizuki’s theorem aims to prove the important abc conjecture, which dates back to 1985 and relates to prime numbers — whole numbers that cannot be evenly divided by any smaller number except by 1.

The conjecture comes in a number of different forms, but explains how the primes that divide two numbers, a and b, are related to those that divide their sum, c.

If Mochizuki’s proof is correct, it would have repercussions across the entire field, says Dimitrov.

When you work in number theory, you cannot ignore the abc conjecture,” he says.

This is why all number theorists eagerly wanted to know about Mochizuki’s approach.”

For example, Dimitrov showed in January how, assuming the correctness of Mochizuki’s proof, one might be able to derive many other important results, including a completely independent proof of the celebrated Fermat’s last theorem.

But the purported proof, which Mochizuki first posted on his webpage in August 2012, builds on more than a decade of previous work in which Mochizuki worked in virtual isolation and developed a novel and extremely abstract branch of mathematics.

Please like, share and tweet this article.

Pass it on: New Scientist

He’s Gambling Obsession Spurred Him To Invent Two Of The Most Important Theories In Math

Girolamo or Hieronimo Cardano‘s name was Hieronymus Cardanus in Latin and he is sometimes known by the English version of his name Jerome Cardan.

Girolamo Cardano was the illegitimate child of Fazio Cardano and Chiara Micheria. His father was a lawyer in Milan but his expertise in mathematics was such that he was consulted by Leonardo da Vinci on questions of geometry.

In addition to his law practice, Fazio lectured on geometry, both at the University of Pavia and, for a longer spell, at the Piatti foundation in Milan.

When he was in his fifties, Fazio met Chiara Micheria, who was a young widow in her thirties, struggling to raise three children.

Chiara became pregnant but, before she was due to give birth, the plague hit Milan and she was persuaded to leave the city for the relative safety of nearby Pavia to stay with wealthy friends of Fazio.

Thus Cardan was born in Pavia but his mother’s joy was short lived when she received news that her first three children had died of the plague in Milan.

Chiara lived apart from Fazio for many years but, later in life, they did marry.




Cardan at first became his father’s assistant but he was a sickly child and Fazio had to get help from two nephews when the work became too much for Cardan.

However, Cardan began to wish for greater things than an assistant to his father. Fazio had taught his son mathematics and Cardan began to think of an academic career.

After an argument, Fazio allowed Cardan to go university and he entered Pavia University, where his father had studied, to read medicine despite his father’s wish that he should study law.

When war broke out, the university was forced to close and Cardan moved to the University of Padua to complete his studies.

Shortly after this move, his father died but by this time Cardan was in the middle of a campaign to become rector of the university. He was a brilliant student but, outspoken and highly critical, Cardan was not well liked.

However, his campaign for rector was successful since he beat his rival by a single vote.

Cardan squandered the small bequest from his father and turned to gambling to boost his finances. Card games, dice and chess were the methods he used to make a living.

Cardan’s understanding of probability meant he had an advantage over his opponents and, in general, he won more than he lost. He had to keep dubious company for his gambling.

Once, when he thought he was being cheated at cards, Cardan, who always carried a knife, slashed the face of his opponent.

Gambling became an addiction that was to last many years and rob Cardan of valuable time, money and reputation.

Cardan was awarded his doctorate in medicine in 1525 and applied to join the College of Physicians in Milan, where his mother still lived.

The College did not wish to admit him for, despite the respect he had gained as an exceptional student, he had a reputation as a difficult man, whose unconventional, uncompromising opinions were aggressively put forward with little tact or thought for the consequences.

The discovery of Cardan’s illegitimate birth gave the College a reason to reject his application.

Cardan, on the advice of a friend, went to Sacco, a small village 15km from Padua. He set up a small, and not very successful, medical practice.

In late 1531 Cardan married Lucia, the daughter of a neighbour Aldobello Bandarini, a captain of the local militia.

ardan’s practice in Sacco did not provide enough income for him to support a wife so, in April 1532, he moved to Gallarate, near Milan.

He applied again to the College of Physicians in Milan but again was not allowed membership.

Unable to practise medicine, Cardan reverted, in 1533, to gambling to pay his way, but things went so badly that he was forced to pawn his wife’s jewellery and even some of his furniture.

Desperately seeking a change of fortune, the Cardans moved to Milan, but here they fared even worse and they had to ignominiously enter the poorhouse.

Cardan was fortunate to obtain Fazio’s former post of lecturer in mathematics at the Piatti Foundation in Milan which gave him plenty of free time and he used some of this to treat a few patients, despite not being a member of the College of Physicians.

Cardan achieved some near miraculous cures and his growing reputation as a doctor led to his being consulted by members of the College.

His grateful patients and their relatives became whole hearted supporters and in this way, Cardan was able to build up a base of influential backers.

Cardan was still furious at his continuing exclusion from the College and, in 1536, he rashly published a book attacking not only the College’s medical ability but their character.

This was not the way to gain entry to the College and not surprisingly Cardan’s application to join in 1537 was again rejected.

However, two years later, after much pressure from his admirers, the College modified the clause regarding legitimate birth and admitted Cardan.

In the same year, Cardan’s first two mathematical books were published, the second The Practice of Arithmetic and Simple Mensuration was a sign of greater things to come.

This was the beginning of Cardan’s prolific literary career writing on a diversity of topics medicine, philosophy, astronomy and theology in addition to mathematics.

Please like, share and tweet this article.

Pass it on: New Scientist

3,700-Year-Old Babylonian Tablet Rewrites The History Of Math

A 3,700-year-old clay tablet has proven that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today.

The tablet, known as Plimpton 332, was discovered in the early 1900s in Southern Iraq by the American archaeologist and diplomat Edgar Banks, who was the inspiration for Indiana Jones.

The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces and canals.




However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today.

Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.

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.

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.

The Greek astronomer Hipparchus, who lived around 120BC, has long been regarded as the father of trigonometry, with his ‘table of chords’ on a circle considered the oldest trigonometric table.

A trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio.

But the tablet is far older than Hipparchus, demonstrating that the Babylonians were already well advanced in complex mathematics far earlier.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.

Plimpton 322 predates Hipparchus by more than 1000 years,” says Dr Wildberger.

It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.”

A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”

The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken but the researchers believe t there were originally six columns and that the tablet was meant to be completed with 38 rows.

Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” added Dr Mansfield.

The new study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

Please like, share and tweet this article.

Pass it on: Popular Science