# Prize crossnumber, Issue 16

Our original prize crossnumber is featured on pages 36 and 37 of Issue 16.

### Corrections

• There was a typo in the clue for 1D: This originally read “One less than 1D”, when it should have been “One less than 1A.. This has been corrected below and in the pdf linked above.

### Rules

• Four of the across clues and four of the down clues are false. All the other clues are true.
• Solvers may wish to use the OEIS, Wikipedia, Python, a slide rule, etc to (for example) obtain a list of cube numbers, but no programming should be necessary to solve the puzzle. As usual, no numbers begin with 0.
• 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, submit the sum of all the digits in the row marked by arrows using this form by 14 April 2023. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 May 2023.

# The big argument: Is Matlab better than Python?

## Yes: Matlab is better, argues Ellen Jolley

while people still think Python is better than Matlab

Whoever said that the best things in life are free had clearly never tried scientific computing.

I have tried coding with Python, and I really wanted it to work out, but everything I wanted to do was always harder in Python than Matlab. Why are vectors called lists? What exactly was unexpected about my indent? Good for you if you are over these conceptual humps but personally I have neither the time nor the interest. I like my coding languages to meet me where I’m at and Matlab does just that.

Learning vector and matrix manipulation in Matlab is an effortless task for a
mathematician—it is effectively written in code just as it is on paper. Not in
Python. Import this, import that, import who, import what?! I just want an easy
life where machines understand what I tell them without me having to do
anything, is that so much to ask?

If you like Python, then truly I am happy for you, and I hope you enjoy all your
fancy jobs and feeling clever by pretending to find counting from zero easier
than counting from one. Oh, and if you’re about to tell me I’ll never get a job if I don’t learn Python… well, I did, with MathWorks, so how do you like that?

end

## No: Python is better, argues Madeleine Hall

for people who think Matlab is better than Python:

There are so many reasons why Python is better than Matlab: [it’s open-source, it has named arguments, it doesn’t think everything is a matrix, …]. As well as all of these obvious ones…

reasons.append(Python is not just simply a scripting language for mathematics. It’s also an imperative and functional language which people can use for anything and everything—from crawling web servers, to controlling external devices, to making UIs. Fun fact: the original Google algorithm was written in Python.)

reasons.append(It indexes from zero which is obviously correct since zero is CLEARLY the first integer.)

reasons.append(I don’t need to LITTER my functions or loops with silly little end statements.)

reasons.append(It’s named after Monty Python which is way more fun than Matlab which is named after `Matrix Laboratory’ (BORING).)

And finally, reasons.append(Python doesn’t give me traumatic flashbacks to my PhD research.)

# Top ten vote issue 16

What is the best mathematical monty?

View Results

# Cryptic crossword, Issue 16

Cryptic #4, set by Humbug: Download as a PDF or read on!

### Across clues

• 1. XL age limit for 4 & 21. (5)
• 3. Advanced zero with FF first embodied #FF0000. (7)
• 7. Confused cats to sing wordless phrases. (4)
• 10. 2.71828 and 9.81, for example. (2)
• 12. He and I gathered around broken kilns. This year’s 4 & 21s were awarded here. (8)
• 13. Information hidden in old Atari. (4)
• 14. Every other alpha’s usually equal to 2. (1,1,1)
• 16. Even split is irrational. (2)
• 17. Smog endlessly enters sky, making it this. (5)
• 18. Representation of most common 50. (5)
• 19. Thanks for the article. (2)
• 20. Opening of Oswestry Hospital’s maternity unit. (3)
• 22. SIAM journal on scientific computing is a bit of quasi-science. (4)
• 24. Confused Paris and East Germany? This is how fast a plane will take you. (8)
• 25. I circle moon. (2)
• 26. Berry hidden in a cairn. (4)
• 28. This analytic number theorist is darn confused after former prime minister. (7)
• 29. Latin manor in a mess. (5)

### Down clues

• 1. The point in Banach’s theorem for first nine Balls. (5)
• 2. Odd rehash should be equal to 14. (1,1,1)
• 4 & 21. 9, 15, 5 & 23, and 28 were awarded this prize for scarecrows?. (6,5)
• 5 & 23. Probability theorist is getting by without gravity after mild uni mess. (7-5)
• 6. They confused last email CC group. (5)
• 8. Mixed CD at Hulk’s magazine. (9)
• 9. She packed spheres by initially zinging ovals against empty Kia. (9)
• 11. Magma blown up by a ray of energy. (5)
• 15. Regularly though, he linked geometry and combinatorics. (3)
• 16. “Perhaps edit parses?” Sophie implied initially. Is this okay?. (5)
• 17. Start moving coefficient of friction up a level. (7)
• 20. Interval without endpoints and centre of interval’s support. (6)
• 21. see 4.
• 23. see 5.
• 27. 1101’s inverse was something in 12 in 2022. (1,1,1)

# Top Ten: Mathematical clothes

This issue, Top Ten features the top ten items of mathematical clothing! Then vote here for your favourite mathematical monty for issue 17!

At 10, it’s a jumper.

At 9, it’s A Pair of Geometry Set Earrings by The Pogues. (etsy.com/shop/Bojanglies)

8, it’s a wearable version of everyone’s favourite one-sided shape: a Möbius scarf.

At 7, it’s a wearable version of everyone’s favourite one-sided shape: a Klein bottle hat.

At 6, it’s great for doing quick calculations on your paper skirt: a pencil skirt.

At 5, it’s A Pair of Pi Earrings by The Pogues. (etsy.com/shop/Bojanglies)

At 4, it’s A Pair of Mathematical Socks by The Pogues. (etsy.com/shop/Bojanglies)

At 3, it’s no one’s favourite LaTeX package: \usepackage{realhats}.

At 2, it’s A Pair of Curly Braces by The Pogues.

Topping the pops this issue, it’s the only item you need in your wardrobe: a Chalkdust T-shirt.

# What’s hot and what’s not, Issue 16

Maths is a fickle world. Stay à la mode with our guide to the latest trends.

### HOT Artwork by artificial intelligence

Not to brag, but we got priority access to Dall.E

### NOT Artwork that makes any sense

“I need you to draw a badly-assembled ham sandwich being cut in half so that all layers are cut equally… got it?”

### NOT Shooting for the moon

“Nasa ground control to Artemis… we’re going to have to delay this launch by a few days…”

### HOT Landing among the stars

See our page 3 model

### HOT Dropping a new paper in front of 30 people

A great turnout to witness the outcome of your many years of academic work

### NOT Dropping paper in front of 30 million people

Ah well, it’s hardly a cardinal sin… (he’s C of E)

### HOT Chalkdust slowly becoming more and more like Cosmo

Issue 17 is full of sexy numbers, interviews with theorems and ‘LaTeX: expectation vs reality’

### NOT Chalkdust slowly becoming more and more like Cosmo

At least they haven’t given Prof Dirichlet’s slot to Scott Mills yet #lovetheshow

### HOT Pipe ﬂow

The hosepipe ban is still in force down south, after a punishingly hot summer

### NOT Miss Flo

At least Holly & Phil will be pleased we moved on

# Page 3 model: Why don’t stars collapse?

Since ancient times, humans have gazed up at the night sky and seen much the same picture—a constant amid the turmoil down on Earth. We now know that chaos lies behind that calm persona: stars are in fact massive, hot balls of turbulent gas, continuously forging new elements through nuclear fusion. Given everything they have going on behind the scenes, have you ever wondered why they seem so… stable?

Of course, as with all the beautiful things in the universe, we ultimately have maths to thank for this. Stars are held together by just two simple differential equations:

$\displaystyle\frac{\mathrm{d}P}{\mathrm{d}r}=-\rho\frac{GM_r}{r^2}$

and

$\displaystyle \frac{\mathrm{d}M_r}{\mathrm{d}r}=4\pi r^2\rho$,

where $r$ represents the distance of a given point to the centre of the star.

Image attribution: Adam Block, CC BY-SA 3.0

The first equation is a statement of hydrostatic equilibrium: the pressure force of the gas pushing the star apart must exactly match the gravitational forwards pulling it in on itself. $P$ is the pressure, $M_r$ is the mass of the sphere contained by the radius $r$, and $\rho$ is the (non-constant) density of the star. The left-hand side, therefore, represents pressure force, while the right-hand side is the gravitational force (familiar perhaps from Newton’s law of gravitation).

The second equation effectively just defines $M_r$ (the right-hand side is simply the surface area of a sphere, multiplied by the density).

In fact, with only two more differential equations (and an equation of state, such as the ideal gas law), we can describe a star’s full structure, including temperature and luminosity:

$\displaystyle\frac{\mathrm{d}T}{\mathrm{d}r}=-\frac3{4ac}\frac{\kappa\rho}{T^3}\frac{L_r}{4\pi r^2},$
$\displaystyle\frac{\mathrm{d}L_r}{\mathrm{d}r}=4\pi r^2\rho\varepsilon.$

These have a bit more physics involved but they express the principles of thermal equilibrium and energy equilibrium. Isn’t it amazing that we can break such a massive, complex, intimidating structure down to just a few lines with a bit of mathematical modelling?

# Dear Dirichlet, Issue 16

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

### Dear Dirichlet,

When I was growing up, I really enjoyed being part of the Girl Guides, so I’ve recently signed my eight-year-old daughter up to the local unit for under-10s. I think she’s having lots of fun but now I can’t stop her wandering off randomly every time we go out. She’s not very quick but I’m just worried she’s going to get herself seriously lost… aren’t they supposed to be learning orienteering or something?

— Sasha Badges, Tamworth