How to make Archives

Instructions. 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˙6 0.1 6 ˙ hours. Place quadrilaterals on the cooling rack, sprinkle with ε ε kg sugar, leave to cool, then

How to cheat at cards

Now, an in shuffle is given by x ↦ 2x+1 mod 52. x ↦ 2 x + 1 mod 52. That is, multiply by 2, add 1 and take mod 52 (note, not 51 this time). This can be checked in the same way as for the out shuffle. For a binary representation this will just add a 1 to …

How to crochet a fractal

Crocheting a simple fractal. The first step is to draw out a diagram of the triangle you want to create, then trace out a path that goes over all of the lines. Below is an example where the diagram is in blue dots and black lines, and the path has been drawn in red, starting from the top. Next, you need to work out how long you want each side

How to kick a conversion

A larger circle drawn through the posts will give a smaller angle. If a vertical line is drawn which just touches the right of the circle, then the point at which it touches the circle will be the best place on this line to take a kick. This is because any other point on the line will be on a larger circle and so make a smaller angle.

Solutions to recent puzzles

Many a Chalkdust article started life as a puzzle. What’s the intersection of these two lines? How many of these cups would it take to make a sphere? How can I cut my birthday cake? … How else can I cut my birthday cake? Writing and doing puzzles is great but, well, sometimes you don’t feel satisfied unless you’ve got the solution.

7 ways to tell if a number is divisible by 7

and for 22442: 2244+2×5= 2254, 225+4×5 =245, 24+5×5= 49. 2 2 4 4 + 2 × 5 = 2254, 2 2 5 + 4 × 5 = 245, 2 4 + 5 × 5 = 49. If input number is divisible by 7, then the last number after repeating this step enough times is 7 or 49. Please note that instead of …

To share, or not to share

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 …

Catching criminals with maths

A very good example that shows how relevant mathematics can be in cutting crime is the use of highly advanced quantitative applications to improve …

Four ways Photoshop encourages thinking mathematically

Photoshop, the Adobe program for manipulating images, has become the symbol of a digital generation – for some, its use is a feminist issue, for others, a post-truth one. It has also been the means behind plenty of hilarious Twitter threads. (For those who prefer their software free, there have been many similar programs developed such as GIMP which provide some of the important

Taking the (mathematically) perfect picture at the Leaning

Hundreds, perhaps thousands of tourists visit Pisa every day —mainly for its famous leaning tower. They rush from the train station, through the bridges and medieval alleys just to stand near the tower and take that picture they have dreamed of, posing in as many creative (and sometimes ridiculous!) ways as imaginable.

Bend it like Newton: curves in football

Describing a ball’s trajectory: Newton’s second law. In order to describe the path of the football, Newton’s second law is applied. This law simply states that acceleration a a of a body (in our case, the ball) will change when it is subjected to external forces (gravitational, drag and lift). Mathematically speaking, the equation is: ma

Victorian maths tricks with old money

A trick for multiplying shillings. Martin gives two (wordy) methods of multiplying shilling amounts here. The first method (67 × 4s.) instructs you to multiply by half the price (67 × 2 = 134), which you can then convert into pounds by taking the last digit, doubled, as shillings (4 × 2 = 8), and the rest as pounds (giving £13 8s. 0d.).

Is it better to run or walk in the rain

One of the many things affecting us living in the UK is the rain! Especially when we are caught out in it without an umbrella (or when we’re too lazy to dig it out of our bag). Intuitively it seems like a good idea to run, or at least walk faster so we spend less time in the rain, however this means that the rain hits our front at a faster rate.

Hairy balls, cyclones and computer graphics

Because of this, it is possible to comb smoothly the hair on your head and the hairy ball theorem is no excuse for disorderly hair conduct. One possibility is to comb all the hair to one side like a comb-over or to comb all the hair to the back. The hairless parts on the body then prevent the formation of …

The croissant equation

Layers of dough =2r(3s)+1, Layers of dough = 2 r ( 3 s) + 1, which then will go into the oven to form one wonderful piece of baked goodie. Different bakeries make their croissants with different rolls and folds, but most commonly, s= 4 s = 4 and r =4 r = 4, so that the number of layers of dough in a regular croissant is 649.

How do calculators do trigonometry

During the all-too-brief reign of the analogue calculator, you could effectively do this electro-mechanically by measuring the induction in a coil of wire angled $40^circ$ out of phase with another coil — but unless your calculator was salvaged from the navigation computer of a 50s Boeing bomber aircraft, this is not how your calculator does it.

Is there a perfect maths font

Say aaaaaaaa. When designing a typeface, you design not just one font but many: you need an italic, a bold, a bold-italic, and maybe more: a typeface is a family of fonts.In maths, matters of style require that certain types of variables are typed in a certain way. For example, the international standard suggests that. variables should be italic,; functions should be upright (roman),

Creating hot ice

This summer we decided to create some hot ice, a substance that is just as exciting as it sounds.Hot ice has a really cool property: it can be easily supersaturated. If you don’t know what it means, don’t worry!

Tupper's self-referential formula

In Tupper’s formula, ‘mod’ refers to modular arithmetic — mod ( a,b a, b) is the remainder when a a is divided by b b. The other funny bit of the formula is the floor function. This is the half square bracket symbol, and returns the largest integer that is less than or equal to the input. If you plot Tupper’s inequality over squares 0

Reproduce or die

Conclusion. The Reproduce or die 2/4 variation does have its moments of oscillators, gliders, guns, collisions and explosions, with some amazing kaleidoscopic patterns to delight the eyes. The downside is that there are far too many uncontrolled population growths that swamp and destroy the more interesting order.

Cracking the Guess Who

Having the cost for each branch and its probability of occurring allows us to compute the expected number of questions we have to ask if, for example, we begin by asking ‘big mouth‘ or ‘earrings‘.If we begin with ‘big mouth‘ we expect to ask roughly 4.8 questions, but if we begin with ‘earrings‘ we expect 5.7 questions, so we should better start with ‘big mouth‘.

The wonders of mathematical crochet

A particularly impressive mathematical crochet feat is this model of the Lorenz manifold, created by researchers at the University of Auckland. The complexity and curvature of this surface means it is very difficult to create physically, but once again the flexibility of crochet came to the rescue. Crochet model of Lorenz Manifold.

The mathematics of brewing

Qm =Qs =msHs Q m = Q s = m s H s. where Qs Q s is the energy contained in the steam water, ms m s is the quantity of steam water or water to be used and Hs H s is the energy needed to evaporate or condensate the water, depending if we are considering a heating or cooling process. The values of Qm Q m (calculated before) and Hs H s (reported in

Modelling in a heartbeat

We’ll take a step back from considering the blood flow and turn our attention to heartbeats. We know that there is a certain rhythm to heartbeats and a sequence in which the different chambers of the heart contract.

How to make: Christmas Special

Instructions. Measure all the ingredients into a mixing bowl. Mix all the ingredients until the mixture forms a dough. Put the ball of dough on a floured surface. Use a rolling pin to roll the mixture out then cut out some triangles. Use a drinking straw to poke holes in the corners of the gingerbread.

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Counting Countdowns

Rachel Riley puts the last of the six numbers on the rack and presses the button to generate a random target. The host—whoever the host is now, I haven’t really watched Countdown since Richard Whiteley died—says a few words and starts a 30-second timer. And the contestant thinks, ‘Now I need to combine those numbers to make the target.

What can you do with this space

The modern way to construct a space-filling curve is as a limit of a family of curves that are more straightforward to define. This is not how Peano originally constructed his curve, which was defined by giving a formula based on a way of writing numbers using a base 3 variant of decimals.

Why do Afro-Caribbean pupils underachieve in education

The most important thing that we can do as a community to improve the level of attainment in education for the Afro-Caribbean community is positively reinforce the younger generation to focus on what they enjoy. This starts in the home, with parents providing positive support for their children from a young age.

Binary magic card trick

This post was part of the Chalkdust 2016 Advent Calendar.. Ah, the Christmas holidays. A time to be spent hiding from the cold, wearing pyjamas, eating too much food and solving integro-differential equations.

Thinking outside the box

On the left, a square, so there’s 90° 90 ° inside, and on the right, the (360−90)=270° ( 360 − 90) = 270 ° outside each vertex. This isn’t a surprise and nor is the internal angle at each vertex ( 360/4 360 / 4) being 90° 90 °. What we want to know is the angle outside each vertex. With the total at a vertex being 360° 360 ° and

On the cover: Apollonian packing

So for example, given three points which don’t lie on the same line, there is exactly one circle which passes through all three. The case which interests us at present is when we are given three circles, each of which is tangent to the other two.

In conversation with Eugenia Cheng

It’s clear that Cheng’s research has influenced the way she approaches her other passions, which include food, music, and teaching. An avid baker, Cheng’s first book, How to Bake Pi, begins each chapter with a recipe for the reader to try.This method mirrors the conversations that introduce chapters in Douglas Hofstadter’s seminal work Gödel, Escher, Bach: An Eternal Golden …

Analogue computing: fun with differential equations

The two triangular elements with the rectangles on their left denote integrators; while the single triangle on the right is a summer. It should be noted that for technical reasons all of these computing elements perform an implicit change of sign, so the leftmost integrator actually yields $-dot{y}$ instead of $dot{y}$ as in our thought experiment above, while the summer with the one input

Seven things you didn't notice in Issue 04

With just a few days to go until we launch issue 05, we thought it’d be fun to share a few bits and pieces that we hid around issue 04.If this gets you excited for issue 05, why not come to the launch party on Tuesday?!. Scorpions. Since we published the horoscope in issue 03, scorpions have been running around all over Chalkdust HQ. Three of them managed to sneak into issue 04.

Maths and music, together in harmony

Here, the black dots represent the 1s, and the white dots represent the 0s. The pattern has several interesting mathematical properties. To begin with, the 7 beats are distributed as uniformly as possible over the 12 slots.

Too good to be Truchet

The tiles Lawrence talked about are not, strictly speaking, due to Truchet. In 1704, Sébastien Truchet published A Memoir On Combinations, in which he discusses squares split diagonally into triangles (pictured right), giving four possible orientations for each tile. It’s an interesting read.

Origami tesseract

The image on the right, which appears frequently in pop culture, is the perspective projection.The cube is projected away into 4D space and diminishes in volume just as the rear face of a cube appears to have a smaller area.

Names for large numbers

The words bymillion and trimillion were first recorded in 1475. Subsequently, the French mathematician and chief notation-creator Nicolas Chuquet wrote in his book, Triparty en la science des nombres, Chuquet’s first mention of million, billion, trillion, and so on (starting top line, in French).

Interstellar travel: the mathematics of wormholes

Last year Christopher Nolan’s blockbuster film Interstellar featured a wormhole as its key plot device, and recently won an Oscar for its visual depiction of them. The film centres around a crew of astronauts travelling through a rip in space and time in the hope of …

Constructing the cover of Issue 10

Ever since Chalkdust Issue 10 was released in October we’ve been admiring the beautiful cover, which features artwork created by Samira Mian.Samira is inspired by patterns from Islamic geometry, which use simple compass and ruler constructions to create intricate tiles that can be repeated in a variety of ways.

Adopt a polyhedron

A polyhedron is a geometrical object bounded by a finite number of polygons. In other words, a polyhedron is a three-dimensional object, whose faces are polygons, whose edges are the straight line segments where two such faces meet, and whose vertices are points where three or more faces meet. One of the simplest (and most famous) polyhedra is

The magnetic pendulum

Using this recipe, we discover a rather striking pattern (see fig. 1). Regions around the origin appear relatively simple. There are large single-colour lobes which indicate that variations in $mathbf{x}_0$ tend to have little impact on which magnet wins.

The kind of problems black mathematicians wish didn't need

The kind of problems black mathematicians wish didn’t need solving. Stories that illustrate the barriers that black mathematicians have faced in recent history. The lighthouse at Alexandria, Egypt, which was an ancient centre of learning. Image: public domain.