What scares a triskaidekaphobe? The United (much smaller) States. And an incredibly cool new shape. Enjoy these fascinating facts about the number 13.

## Modern Einstein solves an 'infinite' problem!

After 60 years of some of the smartest mathematical minds of all time wrestling with an ‘infinite’ problem, it looks like it has finally been solved … by a complete amateur!
**Picture this:** A pattern of four-sided tiles (i.e. squares and/or rectangles) can be easily used to cover a large wall without leaving any gaps or open spaces in between.

Now, as that wall grows infinitely larger in size, the pattern will simply continually repeat itself. This means if we slide them one square down, or two rectangles to the left, the new tiling perfectly covers the old one. (Such patterns are commonly employed for brickwork, or kitchen or bathroom wall tiling.)

**Now consider this:** Since at least 1961, mathematicians have tried to devise a set of tiles that could cover an infinite plane in a pattern that never repeated itself. (We call this ‘aperiodic’ or ‘without period (repetition)’.)

The history of this quest is fascinating and I thoroughly recommend you read about it __here__

**Fast forward to 2023:** Congratulations to 64-year-old Englishman Dave Smith, who enjoys a tinker with graphics software and did okay in high school maths, but who has no formal mathematics training whatsoever!!!

Smith discovered a gorgeous 13-sided shape (pictured below) that tiles the infinite plane all by itself – in a non-repeating repeating pattern. This means that you cannot slide a copy of this tiling into a new place and cover all the tiles exactly! It’s been named an ‘einstein’ not in honour of the great physicist, but from the German word for ‘one stone’.

And making maths even sexier, Smith has since gone on to discover an infinite number of einsteins – each of which can tile the infinite plane forever in all directions, again without repetition!!!

## Trisky business

In Western culture the number 13 is considered unlucky, possibly because it denotes the number of people that attended the biblical Last Supper.

People who fear this number suffer 'triskaidekaphobia'. Friday the 13th is a spooky date for some. In many hotels and casinos there is no 13th floor!

Conversely, Australian cricketers were said to be positively superstitious about being on the batting score 87 (the devil’s number - just 13 short of a century).

However, when stats guru Ric Finlay crunched the numbers, it turns out batters have been dismissed more often for 85, 86, 88 and 89 compared to the comparatively “lucky” 87.

## Did you know? Enjoy these nerdy numerical facts about 13!

**Syncing with the sun**

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Ethiopia follows a 13-month calendar known as Bahere Asab. This includes 12 months of 30 days each and a 13th intercalary month called Pagume of 5-6 epagomonal days to sync the year with the rotation of the Earth around the sun. Ancient Egyptians and Coptics observed a similar calendar.

**O.G. USA**

The original flag of the United States of America had 13 stripes and, after it removed the Union Jack, 13 stars. These represented the original 13 British colonies that declared their independence in 1776. Can you name them all? Hint: They’re all states clustered on the eastern seaboard __(jump to answer)__.

**Let’s go ***koto*

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Japan’s national instrument is the 13-stringed, plucked zither koto. Almost 2 metres long, it’s thought to have derived from the Chinese guzheng and se. Similar instruments exist across cultures, including Mongolia’s yatga, Korea’s gayageum and ajaeng, Vietnam’s đàn tranh, Indonesia’s kacapi, and Kazakhstan’s jetigen. Some variants have 17 strings. __Let me know if I’ve missed any others!__

## It’s sexy prime time!

Thirteen is the 6th prime number. Remember that while a composite number like 6 can be written as the product 6 = 2 x 3, a prime number like 13 can only be written as 13 = 1 x 13; we can’t break it into any smaller factors.

Because its immediate odd neighbour 11 is also prime, we call 11 and 13 ‘twin primes’. And because 13 and 17 differ by just 4 we call them ‘cousin primes’ (almost as close as twins!). And because 13 and 19 differ by 6, or ‘sex’ in Latin, we call 13 and 19 ‘sexy primes’.

So, 13 is an example of a sexy twin cousin prime. Well, there you go!

## Winners of Neil deGrasse Tyson maths joke competition

In number 012, I offered a pretty cool prize of tickets to see astrophysicist extraordinaire Neil deGrasse Tyson and me during his __‘Cosmic Perspectives on Civilisation’ tour__ of Australia next month.

I asked you to submit your best mathematics joke. And I guess the result was to be expected. A flurry of funny, not-quite-so-funny and ‘um, pretty sure we can’t print that Uranus-themed joke in a family EDM’ offerings.

Anyway, I am very happy to announce the following four winners…

A photon is going through the airport. Customs officer - “Anything to declare?” Photon - “No, I’m travelling light!” - Jesse Cahill (9 years old)

Q: What’s the funniest number? A: 101 (lol) - Nick McGrath

Q: Why did Brett quit his job cleaning the bathrooms in a hotel with 288 rooms? A: 288 rooms – that’s two gross! - Peter Degotardi

Q: Why did 7 eat 9? A: Because 7 heard you are supposed to have 3 square meals each day! Hahaha 😃 - Maree Timms

Now while Jesse, Nick, Peter and Maree have their seats sorted to see the one and only __Neil deGrasse Tyson__ for an evening of cosmology, astrophysics and belly laughs as he tours Perth, Adelaide, Brisbane, Sydney and Melbourne, why not join in the fun too and book your own ticket __here__

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*The answer to which original 13 British colonies declared their independence from the USA in 1776 is: **Connecticut, Delaware, Georgia, Maryland, Massachusetts, New Hampshire, North Carolina, New Jersey, New York, Pennsylvania, Rhode Island, South Carolina, and Virginia*

Yours in numbers,

Adam

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