From the exquisite patterns of the Alhambra palace in Spain to a jigsaw puzzle on a rainy day, tessellations (tilings of the plane using shapes with no overlaps or gaps) are everywhere. They are sometimes used for practical reasons: providing durable and water-resistant surfaces, or for efficiencies of space (like hexagons in a honeycomb). And sometimes they are there for aesthetic reasons: tessellations are known to have been used in architecture since at least 4000BC when the Sumerians decorated walls with patterns of clay tiles. Continue reading
Maths is a fickle world. Stay à la mode with our guide to the latest trends.
HOT Issue 10
We’re so excited about releasing issue 10!
NOT Issue 3628800
Wait another 1.8 million years for this one? No thanks.
This issue, Top Ten features the top ten issues of Chalkdust! Then vote here on the top ten pictures of scorpions for issue 11!
After a whole year at number 1, it’s the issue that’s finally been knocked down to number 2: issue 08.
If you model rabbits under ideal circumstances, you may find that the number of pairs of rabbits each month follows the Fibonacci sequence.
In this case, ‘ideal circumstances’ is a euphemism for nonsense, as your assumptions would include blatant untruths such as “rabbits mate once a month every month except their first month alive”, “a pair of rabbits gives birth to exactly one pair of rabbits per month”, and “the hutch is infinitely big (and hence Starsky is very squashed)”.
Fibonacci numbers, however, are not completely absent from nature. They accurately describe a vastly superior animal: the honeybee.
Male bees (drones) come from unfertilised eggs, and so they only have one parent — the queen.
Female bees (workers or queens) come from fertilised eggs and so have two parents — the current queen and a drone.
If you follow a drone’s family tree backwards, you will see that a drone has:
The number of ancestors of a male bee follows the Fibonacci sequence.
Who would’ve expected that?!
You will need
- 4kg butter
- 6kg flour
- $(2+\varepsilon)$kg sugar
- an oven that has been preheated to 220°C
- a rolling pin
- an oven tray
- a cooling rack
- a knife or cookie cutter
- Combine 4kg butter, 6kg flour and 2kg sugar in a large bowl with your hands.
- Roll out the dough on a flat surface.
- Cut the dough into equally shaped quadrilaterals.
- Place quadrilaterals on the baking tray and bake for $0.1\dot6$ hours.
- Place quadrilaterals on the cooling rack, sprinkle with $\varepsilon$kg sugar, leave to cool, then tessellate and eat.
With issue 10 of Chalkdust fast approaching, it’s time to announce the winners of the Chalkdust prize crossnumber #9! Before we reveal the winners, here is the solution of the crossnumber.
The sum of the across clues was 2222222406182591.
There were 100 entries, 66 of which were correct. The randomly selected winners are:
- Matt Hutton, who wins a £100 Maths Gear goody bag,
- George Lambert, who wins a Chalkdust T-shirt,
- Sami Wannell, who wins a Chalkdust T-shirt,
- Deborah Tayler, who wins a Chalkdust T-shirt.
Well done to Matt, George, Sami and Deborah, and thanks to everyone else who attempted the crossnumber. See you shortly in issue 10…
Our original prize crossnumber is featured on pages 54 and 55 of Issue 09.
- Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
- One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
- To enter, enter the sum of the across clues below by 9 September 2019. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 28 September 2019.
Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to firstname.lastname@example.org.
My husband and I have found ourselves in a long-distance relationship. His company offered him a large promotion if he moved to Canada for six months, but it seems now that the position will require more time. I’m not sure that I want to move out there with him, or that I could be happy knowing he had to move back here. Conversation with the time difference is hard as well. Any tips?
— Getting tensor, Four Oaks
Mar 21 – Apr 19
Apr 20 – May 20
May 21 – Jun 20