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On the cover: Apollonian packing

What can you do with this space? So asks Andrew Stacey. ‘Fill it’ is the prompt reply, but fill it with what? Maybe like Andrew you want to use a single curve, but I want to use circles. If you do this in the way shown above in blue, the result is called an Apollonian packing, a variant of which can be seen on the cover of this issue.

Here we shall explore the history of this entrancing object, which spans over 2000 years, and percolates into a surprising variety of mathematical disciplines. Starting in the familiar world of Euclidean geometry, Apollonian packings extend into fractal geometry and measure theory; Möbius transformations and the hyperbolic plane; and then on into the distant reaches of geometric group theory, number theory, orbital mechanics, and even ship navigation. Continue reading

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Top Ten: pictures of scorpions

This issue, Top Ten features the top ten pictures of scorpions! Then vote here on the top ten maths-themed days out for issue 12!

At 10, it’s Wind of Change by The Scorpions.
At 9, it’s scorPioneers by Bloc Party.
At 8, it’s scorpIonisation, Edgard Var&egrace;se’s work that features only percussion instruments.
At 7, it’s scorpiOne by U2.
At 6, it’s sCorpus Christi Carol by Jeff Buckley.
At 5, it’s scorpiOnce in a Lifetime by The Talking Heads.
At 4, it’s scorpiOn The Road Again by Willie Nelson.
At 3, it’s scorpiOne of These Days by Camper Van Beethoven.

At 2, it’s I Write Sins Not Tragedies by Panic! at the Discorpion.
Topping the pops this issue, it’s the album Scorpion by Drake.
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Chalkdust issue 11 puzzle hunt #1

The day is finally here: issue 11 is out now! To help you celebrate launch day in style, we’ve set a puzzle hunt: throughout the day, we are posting a series of puzzles. The answers to these puzzles form clues to the four-digit code for the door to let you into the Chalkdust issue 11 secret backstage lounge.

The first puzzle is set by Matthew Scroggs. You can see the puzzle below, or download it as a pdf.

Be sure to come back at 11am when the second puzzle will be posted.

Scroggs’s puzzle

Each row and column of this grid contains the letters W, E, T, C, O, I, N, and S exactly once.

Each column and the first 7 rows contain the words given by the clues below in some position. For example, if a row contains the word `WET’, then the row could be WETCOINS,
NOWETSIC, ONSWETCI, or many other things.

Once the puzzle has been completed, the final row will contain a number. This number is one of the digits of the code.

Across

  • 1 Conic ___. (7)
  • 2 A charged atom or molecule. (3)
  • 3 0 seconds in the future. (3)
  • 4 315°. (2)
  • 5 3D shape with volume $\pi r^2h/3$. (4)
  • 6 225°. (2)
  • 7 $\{2,3\}$ or $\emptyset$. (3)

Down

  • 1 Can be found on page 65 of issue 11. (3)
  • 2 $\in$. (2)
  • 3 A baby’s favourite trig function (abbrev). (3)
  • 4 adjacent ÷ hypotenuse (not abbreviated). (6)
  • 5 135°. (2)
  • 6 $\sqrt{100}$. (3)
  • 7 ___ primes. (4)
  • 8 adjacent ÷ hypotenuse (abbrev). (3)
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Crossnumber winners, issue 10

Hello everyone! It’s time to announce the winners of the Chalkdust prize crossnumber #10! Before we reveal the winners, here is the solution of the crossnumber.

1 0 8 9 0 2 2 2 2 2 2 2 2 2
1 9 5 2 8 6 7 5
1 0 8 9 5 2 5 8 6
1 9 7 5 4 3 2 0 4 1 2
0 0 5 4 1 1 9 1 0
0 1 0 7 9 6 7 8 9 6 3 0 1
4 2 1 9 8 1 0
8 9 1 8 7 1 6 5 1 4 3 1 2 1 1
1 4 7 2 0 1 0
7 4 5 6 3 4 1 2 3 5 9 4 9
8 4 5 5 5 9 4 9 9
8 9 1 2 6 1 8 1 6 9 9
2 4 9 5 1 1 0 8 9
8 5 2 4 9 9 8 0
2 2 2 2 2 2 2 2 2 1 0 8 9 0

The sum of the across clues was 891873821817653.

There were 40 entries, 37 of which were correct. The randomly selected winners are:

  1. Laurence, who wins a £100 Maths Gear goody bag,
  2. Robert Hannan, who wins a Chalkdust T-shirt,
  3. James, who wins a Chalkdust T-shirt,
  4. Thomas Smith, who wins a Chalkdust T-shirt.

Well done to Laurence, Robert, James and Thomas, and thanks to everyone else who attempted the crossnumber. See you shortly in issue 11…

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Prize crossnumber, Issue 10

Our original prize crossnumber is featured on pages 48 and 49 of Issue 10.

Rules

  • 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 2 February 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 14 March 2020.

Correction: Clue 13A has been corrected to “49A reversed” instead of “49D reversed”.
Correction: Clue 38D has been corrected to “33A less than 39D” instead of “33A less than 39A”.
Clarificiation: The triangle in 6D is a right-angled triangle.
Continue reading

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Dear Dirichlet, Issue 10

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

Dear Dirichlet,

Boy, am I in a world of woes! In the coming months, I have to go into surgery six times for a whole host of illnesses. To its credit, the hospital has allowed me to arrange my own schedule. In your doctoral opinion, which procedures should I undergo first?

— Under the weather, Cambridge

Continue reading