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To share, or not to share

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The Montagues and the Capulets have never been friends and Juliet is quite aware of this. Even at her young age, she knows that her love for Romeo is an impossible dream her father will never accept. So, she designs a strategic plan. She will take a couple of sleeping pills, just enough to make her look like she is dead to trick everyone into thinking that she has passed away. Brilliant! If everything goes right, she will always be happy with Romeo… but if things go wrong… well, you never know. Continue reading

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Should you buy a Valentine’s day present?

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Valentine’s day is just around the corner and you are still not sure whether or not you should buy your beloved one a present.  It’s a tough call. Should you spend money on buying your partner some chocolates and a teddy bear (that no one wants anyway), or will you risk it and bring only a charming smile to your romantic dinner? Continue reading

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21 December

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Welcome to the twenty-first day of the 2016 Chalkdust Advent Calendar. Today, we bring you our final selection of fascinatingT&Cs apply facts, randomly generated by Santa’s elves.  Remember to send us your favourite scientific curiosities via Facebook, Twitter or email and we’ll feature the best in a blog next year.

The number 21

Setter of fiendish conjectures.

Today is the 21st day of the Chalkdust Advent calendar. The numbers 8 and 9 are the only powers of integers ($2^3$ and $3^2$ respectively) that are consecutive. This was conjectured by the Belgian mathematician Eugène Charles Catalan in 1844. It was proved in 2002 by Preda Mihailescu. Unlike Andrew Wiles, who proved Fermat’s last theorem, Mihailescu didn’t shoot to fame. This had absolutely nothing to do with the number 21.

Rudolph the red-nosed she-reindeer

Female. Female. Not male.

Rudolph the red-nosed reindeer is very confused as to why she has a male name. Male reindeers shed their antlers once they’ve finished using them as swords during the mating season in autumn, while females cast them in spring and regrow them in time for Christmas (when they use them as swords to fight other females over holes in the snow). I’m sure she is confused for many other reasons too. Such as why she has a red nose.

Father Christmas and the multiverse

If the multiverse theory is correct, and our universe is just one of an infinite number of universes, there may be one in which Father Christmas was not popularised by Coke adverts of the 1920s.

And that’s that from Santa’s elves. They’re off to find Rudelle.

[Pictures. Eugène Charles Catlan: Public domain; Rudelle: Tristan Ferne, CC BY-2.0]

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14 December

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Welcome to the fourteenth day of the 2016 Chalkdust Advent Calendar.  Today, we bring you some more fascinatingT&Cs apply facts, randomly generated by Santa’s elves.  Remember to send us your favourite scientific curiosities either on Facebook, Twitter or email and we’ll feature the best in a blog next year.

Osiris was ripped into 14 pieces by his brother Set.

The number 14

The numbers fourteen and forty sound very similar. They often get confused when speaking on the telephone. This is a common affliction caused by all teens and I’m sure the reader can think of many more.

 

Pesky bumblebees defying nature

Bumblebees. Obviously capable of flying.

According to an engineer (obviously) a long time ago (probably also obviously), bumblebees can’t fly. This is based on the assumption that the air remains attached as it goes over a bee’s wings and that the same aerodynamics takes place as occurs for flow over aeroplane wings. This leads to the result that a bumblebee would not be able to generate enough lift to stay in the air. Unfortunately, however, they can. This was all quite mysterious until someone had the bright idea to stick some bees in a wind tunnel and see what is going on. It turns out that bumblebees don’t flap their wings just up and down, but forwards and backwards too; and a vortex evolves on the upper side of the wing, allowing the bee to generate more lift. The moral of the story is to never listen to engineers. You can find a cool video of bumblebees in a wind tunnel here.

The computer of the Ancient Greeks

Our forefathers’ computer.

The Antikythera mechanism is the first (analogue) computer, built by the ancient Greeks prior to 100BC. Either that, or it was left behind by alien visitors who decided that our civilisation 2,000 years ago wasn’t worth bothering about. Incorporating much of the mathematical and astronomical knowledge of the Greeks, interlocking gearwheels turned a minimum of seven dials that told celestial time (whatever that means). Presumably we then got bored of making scientific magic and went back to waging war on each other, which meant that we didn’t come up with anything that mind-blowingly intricate until at least the invention of the pocket watch.

The perpetually surprising trapezium rule

The trapezium rule is often used for numerical integration and involves summing up the areas of many many trapeziums. The more trapeziums you use, the more accurate your answer will be. Bizarrely, despite it being just a simple sum, it turns out that in some cases adding more trapeziums allows you to converge exponentially to the right answer. My brain has just exploded.

I’ll be back on the 21st when I’ve picked up all the pieces.

[Pictures: Osiris, public domain; Bumblebees, CC0 license; Antikythera mechanism, CCA-SA 3.0, Marsyas]

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03 December

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Welcome to the third day of the 2016 Chalkdust Advent Calendar.  Today, we bring you some fascinatingT&Cs apply facts, randomly generated by Santa’s elves.  Please send us your favourite scientific curiosities either on Facebook, Twitter or email and we’ll feature the best in a blog next year.

The number 3

The Tre Cime di Lavaredo, iconic symbols of the Italian Dolomites

Today is the third day in your advent calendar. Three is the largest number that, when written in Roman numerals (III), requires the same number of strokes as the number itself. Less interestingly, it is the first odd prime number. More interestingly, it is the only number that is both a Fermat prime (can be written as $2^{2^n} + 1$) and a Mersenne prime ($2^n-1$). It is also the only prime that is one less than a perfect square. Prove it.


Feeling blue

cover_01The ancient Greeks had no word for the colour blue. Despite, presumably, the sky being as blue back then as it is now (due, by the way, to Rayleigh scattering: blue wavelengths of light are scattered more widely by the oxygen and nitrogen molecules in the air, meaning that more blue reaches our eyes). The pigment blue was, however, incredibly hard to make (although those clever folk in Egypt cracked it) and, in a dramatic modern non-twist, creating blue LEDs proved to be beyond the skills of humanity until the 1990s. The scientists who succeeded won the Nobel prize in 2014 and, more impressively, were featured on our very first On the cover. We have unfortunately been unable to ascertain whether the first ancient Egyptians to make blue dye ever had the equivalent honour.


Pub crawler

dublin_castle-interior_cropped

Next stop: that way!

In one of the most impressive and useful pieces of research carried out over the last couple of years, a team of mathematicians led by Professor William Cook at the University of Waterloo (Canada), mapped the shortest possible route between 24,727 pubs in the UK. Its length: over 45,000km. Longer than the circumference of the Earth. This is an example of the travelling salesman problem. Or the very drunk travelling salesman problem.


The average you

The average human has one testicle and one ovary. The standard deviation, however, is huge.  And on that note, I leave you.  Until next time!


[Pictures. Tre Cime di Lavaredo: Federico Galber, used with permission; Chalkdust Issue 1 cover: Chalkdust and Anthony Lee; Pub: The Dublin Castle, picture by the author, used with permission from himself]

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Hooke’s Monument

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A little over 350 years ago, on the night between Saturday 1 and Sunday 2 September 1666, Thomas Farynor, well-known baker, lay in bed in his home above his bakery. Maybe he was staring at the ceiling, worrying, as he did every night, as to whether he had completely put out the fire in his ovens. Or maybe he was just asleep. It had, after all, been a long day.

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John Forbes Nash: the legacy

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When describing John Forbes Nash, Jr (13 June 1928 – 23 May 2015), it’s hard to be more succinct than Richard Duffin, a professor at the Carnegie Institute of Technology, who wrote, in his letter of recommendation to Princeton, that ‘this man is a genius’. It was 1948: Nash, having abandoned a degree in Chemical Engineering for one in Mathematics, was only just embarking on a journey that would ultimately make him one of the most famous mathematicians of the 20th Century. Despite the interest of Harvard University, Nash eventually decided to pursue his graduate studies at Princeton and it was there that he published the 317 word paper, Equilibrium points in N-person games, that introduced the Nash Equilibrium and won him the Nobel Prize for Economics (jointly with Reinhard Selten and John Harsanyi) in 1994. As a result of this work in game theory, Nash was appointed to the RAND Corporation, which applied this relatively young field to the pressing policy issues of the time: nuclear weapons, the space race, the Cold War.

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Ace

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Jeu_de_paumeUnder a (probably) cloudy sky the eyes of a silent, expectant crowd – sated with Pimms and strawberries and cream – fixed on the ball as it was gently tossed from the server’s hands and arced in a gentle parabola; the whisper of a collective intake of breath broken by a sharp ‘toc’ as the tennis ball made contact with the onrushing racket and went hurtling towards the opponent. People have been watching a similar sight since real tennis came into being in the Middle Ages, derived from the French racket-less game of jeu de paume (which also gave rise to handball). One such person was Sir Isaac Newton, who in a paper written in 1672, wondered why it was that a tennis ball was able to follow ‘such a curveline’ as it went from its origin to its destination.
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Maths for money: The Longitude Prize

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The question “why do you do maths?” sparks a flurry of emotions. The mind struggles to formulate an explanation that feels even remotely adequate; and the final answer leaves a lingering buzz of frustration as the eyes of the questioner remain unlit by the same fire that burns within you.

There are, of course, earthly, comprehensible, easy-to-describe reasons that drive us. There is no Nobel Prize in Mathematics, but Cédric Villani’s Birth of a Theorem speaks of the author’s obsession with winning its mathematical equivalent: the Fields Medal.

Then, occasionally, monetary prizes are offered for the solution of mathematical problems.

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The statistics of a squeaky bum

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Football, for a fan, often feels like a week of torture followed by 90 minutes of hell but never more so than when your team is involved in the play-offs. This Bank Holiday weekend sees the League 2, League 1 and Championship play-off finals take place at Wembley, prompting Sir Alex Ferguson to announce that it’s “squeaky bum time” and football commentators around the country to confidently proclaim that “it all boils down to this,” where ‘this’ is a tumbling maelstrom of apprehension; a cacophony of swirling butterflies; a mind electrified, distracted, unable to hold onto any thought that does not involve ‘this’. With only two days to go, with nerves drawing closer to a Himalayan precipice, the fan is liable to search for straws ever more frantically and clutch at them ever more possessively, taking solace in the company of similarly-afflicted supporters of the same team and football’s blurred lines of fact and myth.

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