Mathematicians end decades-long quest to find elusive ‘vampire einstein’ shape

Published

2 years ago

June 7, 2023

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What has 14 sides, is full of curves, and can perfectly cover a surface with no gaps or overlaps? It’s not a riddle — it’s a “vampire einstein.”

In March, a retired printing technician named David Smith stumbled upon a remarkable discovery in the world of mathematics. He found a 13-sided shape that could completely tile a surface without ever repeating. The shape, nicknamed “the hat” for its vaguely fedora-like shape was the culmination of decades of hunting by mathematicians around the world.

Since 1961 mathematicians had wondered if such a shape could exist. At first, mathematicians found a set of 20,426 shapes that could tile together while creating a pattern that never repeats (in contrast to the tiles on a kitchen floor, which do create a repeating pattern). Eventually, mathematicians found a set of 104 shapes that could create such a never-repeating tiling.

The middle and right shapes are examples of ‘Spectres’ — 14-sided shapes that can be tiled infinitely without ever creating a repeating pattern. (Image credit: Smith et al.)

Then in the 1970’s physicist and Nobel prize winner Roger Penrose found a pair of shapes that together created anon-repeating tiling. And for decades since, mathematicians continued to wonder if the same trick could be done with only a single shape. That semi-mythical shape, known formally as an aperiodic monotile, came to be known as “the einstein,” which means “one stone” in German.

But for all the celebration around Smith’s discovery of an einstein tile, there was one small fly in the ointment. In order to create the non-repeating tiling, the “hat” had to work with its mirror image. Technically it’s the same shape, just flipped, but some argued that Smith hadn’t really found a true einstein.

Now, however, Smith and his colleagues have laid those objections to rest: they’ve found a shape that can tile a surface without repeating or being flipped. They described the new shape May 28 in a paper published to the preprint database arXiv, though it has not yet been peer reviewed.related stories—Mathematicians make rare breakthrough on notoriously tricky ‘Ramsey problem’

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The team named their shape the “Spectre,” an homage to vampires that can’t see their own reflections and thus don’t need a mirror.

“In plane tiling, it is completely standard that tiles may be reflected; nevertheless, some people were dissatisfied that the aperiodic hat monotile requires reflections to tile the plane,” co-author Joseph Samuel Meyers wrote on Mastodon. “In our new preprint, we present the Spectre, the first example of a vampire einstein: an aperiodic monotile that tiles the plane without reflections.”

To find the ghostly shape, the team started with the original “hat” shape and added an extra side to it. That new shape still required its mirror image to fully tile, but the researchers discovered that by transforming the 14-sided shape’s straight edges into curved ones, they could dispense with mirror images and work with just the one shape.

Business

Honeymoon couple unable to access their money online as Barclays suffers major IT glitch

Published

45 mins ago

February 1, 2025

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Honeymoon couple unable to access their money online as Barclays suffers major IT glitch

A newlywed couple say they have been locked out of their bank accounts while on their honeymoon as Barclays suffered a major IT glitch.

Read latest on Barclays glitch:
Bank tells customers to contact family or foodbanks

People were unable to access money overnight after the issue struck on what was payday for many British workers.

Hundreds of customers reportedly claim they are experiencing interrupted services and missing funds, with some alleging they have had no access to their cash for nearly 24 hours.

David Marsh and his wife, from Cumbria, told Sky News they’ve been experiencing problems accessing their money while on holiday in Australia to celebrate their marriage.

“I’m unable to receive money for my honeymoon into my current account or use my current account to clear my credit card before departing,” he said.

“My message to Barclays is: I’ve been a current account holder with Barclays since 1986. The day I return to the UK, I will be moving my current account to another provider and leaving them.”

What has Barclays said?

Barclays has apologised to customers, saying the company is facing ongoing technical issues.

It warned that some people may see an outdated balance, and payments made or received may not show.

“We will ensure that no customer is left out of pocket,” the bank said in a statement on Saturday.

Mum ‘unable to buy milk’

A mother claimed she was unable to buy milk for her baby due to the IT glitch.

“My four-month-old is out of milk powder and screaming for a feed and I still haven’t been paid,” she said.

She added: “I’ve been in tears for hours.”

‘Money never arrived in my account’

Karen Bannister, 52, from Wakefield, West Yorkshire, told Sky News: “I had transferred all my money into Barclays to cover paying for gas, electric, rent, petrol, food etc. The money never arrived in my Barclays account.

She added: “My card got declined at the supermarket which was completely embarrassing and by 9pm I was without heating because my gas had run out.”

“Yesterday was awful. Barclays need to pay compensation to those affected. People were without salary and some couldn’t pay their tax before the deadline.

“Following this, I’m leaving Barclays – and I’ve been a customer for 40 years.”

Frustrated customers have also been reaching out to Barclays support via social media.

“Due to you Barclays I’m left without money had a food shop due for delivery this morning which now will get cancelled, leave my four kids with no food it’s a joke as (it is) my money,” one X user claimed.

Another added: “How can I eat and keep warm if I can’t get to my funds?”

A third person claimed: “Well I’ve just had to put all my shopping back in Tesco never been so embarrassed in my life .. as can’t access my own money.”

The Down Detector tracker has shown more than 1,600 reports of outages for Barclays banking services since Friday.

In its statement on Saturday, Barclays said: “We’re incredibly sorry for the ongoing technical issues that are impacting our customers’ accounts.

“Some may see an outdated balance, and payments made or received may not show.

“We’re working hard to fix this issue, and customers should not try to make the payment again.”

Politics

Wall Street is betting on $30T RWA tokenization market prospects

Published

45 mins ago

February 1, 2025

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Wall Street is betting on T RWA tokenization market prospects

Wall Street giants are betting on the projected $30 trillion RWA tokenization market as the industry sees explosive growth and widespread adoption across TradFi institutions.

US

Trump says US airstrikes have ‘killed many’ ISIS terrorists

Published

45 mins ago

February 1, 2025

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Trump says US airstrikes have 'killed many' ISIS terrorists

Donald Trump has said “many” ISIS terrorists have been killed in caves by US airstrikes he ordered this morning.

Posting on his social media site Truth Social, the US president said: “This morning I ordered precision Military air strikes on the Senior ISIS Attack Planner and other terrorists he recruited and led in Somalia.

“These killers, who we found hiding in caves, threatened the United States and our Allies.

“The strikes destroyed the caves they live in, and killed many terrorists without, in any way, harming civilians.”

Mr Trump did not name any of the people targeted in the strikes or give further details about the location.

He said the US military had targeted the attack planner for years, but former president Joe Biden “and his cronies wouldn’t act quickly enough to get the job done”.

“I did! The message to ISIS and all others who would attack Americans is that “WE WILL FIND YOU, AND WE WILL KILL YOU!”

US special forces killed a senior ISIS leader and 10 other militants in a raid on a mountain cave complex in a remote part of northern Somalia in 2023, in an operation ordered by Mr Biden.

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