Parallelogram 26 • Level 2 • 1 Mar 2024Maths Jokes

• Tackle each Parallelogram in one go. Don’t get distracted.
• Finish by midnight on Sunday if your whole class is doing parallelograms.
• Your score & answer sheet will appear immediately after you hit SUBMIT.
• Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. Maths jokes

It sounds odd, but there are maths jokes. Lots of jokes. In fact, lots of mathematicians are very funny. Some of my favourite comedians (Dara O'Briain, Romesh Ranganathan and Dave Gorman) studied maths at university, and I have written a whole book about the mathematicians who write The Simpsons.

So, how good is your mathematical sense of humour? And how much maths do you know? Below are 4 jokes with 3 possible punchlines each. Can you spot the correct punchline? You will need to know a bit of maths in order to work out the right answer.

0.5 marks

1.3 What does the “B” in Benoit B Mandelbrot stand for?

• Benoit B Mandelbrot
• Binomial
• Breviation
• (Not answered)

This was a tough one. Benoit B Mandelbrot helped develop the mathematics of fractals, which are structures or shapes that appear similar when you zoom in or zoom out. Trees, clouds and certain mathematical shapes are fractals, as shown above. The bit of the tree in the red box looks just like the whole tree… and you can zoom in even further and see more and more micro-replicas of the whole tree.

The following video shows what happens if you zoom into the so-called Mandelbrot Set. You see the same pattern (a sort of seahorse’s tail) reappearing again, and again, and again:

(If you have problems watching the video, right click to open it in a new window)

So, returning to the joke, the B represents Benoit B Mandelbrot, because zooming into the name gives you the whole name again.

0.5 marks

1.4 Why did the chicken cross the Möbius strip?

• To get to the other… er…?
• To reach a finite conclusion
• To integrate itself into the tarmac
• (Not answered)

Another toughie – a Möbius strip is a strange mathematical shape which only has one side, so you can’t get to the other side. As shown here, it is just a loop with a single twist, but if you imagine running your finger along one side of the loop you will find that your finger covers every bit of the loop... so it only has one side. Möbius strips are fantastic, one of my favourite bits of geometry, and we’ll return to them in next year’s Parallelogram series.

2. Mini cross-number

2 marks

2 A cross-number is like a crossword, but with numbers instead of letters. Solve the clues to find the digit x in this cross-number.

Across 1. A cube 3. A cube

Down 1. One less than a cube 2. A number

x = Correct Solution: 4

Show Hint (–1 mark)

–1 mark

1 across, 3 across & 1 down are all cubes (or one less than a cube) and they are all 2-digit numbers, which means they are between 10 and 99. There are not very many cube numbers between 10 and 99, so start by writing them down and then see how they might fit into the grid.

The correct answer is x = 4.

1 across, 3 across & 1 down are all cubes (or one less than a cube) and they are all 2-digit numbers, which means they are between 10 and 99. The only cube numbers between 10 and 99 are 27 and 64. So 1 across and 3 across must be 27 and 64, or 64 and 27. Meanwhile, 1 down must be 26 or 63. The cross-number only works if 1 down is 26, because 3 across can then be 64, which means x = 4.

3. Maryam’s inspiration

You might be surprised to know that there is no Nobel Prize for maths. However, there is an even bigger prize for mathematicians, which is called the Fields Medal. It is only given every 4 years, so it is very rare and precious.

In 2014, Maryam Mirzakhani became the first woman to win a Fields Medal, but tragically she died just three years later. The Iranian-born NASA scientist, Firouz Naderi, wrote: “A light was turned off today, it breaks my heart... gone far too soon.”

Commenting on a piece of research she did alongside mathematician Alex Eskin, Mirzakhani said: “If we knew things would be so complicated, I think we would have given up... I don’t know, actually. I don’t know. I don’t give up easily.”

Mirzakhani was born in Iran and then worked in America, and you can find out about her life and work in the short video below.

Not surprisingly, Maryam talks about some incredibly complex maths, so don’t worry if you find it confusing. In fact, if you think you understand what Maryam is describing, then you probably don’t. Watch it carefully and answer the question below.

Maryam has said that she first became fired up about mathematics when her big brother told her a story about the great mathematician Carl Friedrich Gauss. When Gauss was a schoolboy, his teacher tried to keep the class busy by asking them to add up all the numbers from 1 to 100.

However, before the teacher had even left the room, Gauss’s hand shot up and he announced that the answer was 5,050.

Gauss was right, but how did he add up the first 100 numbers in just a few seconds?

Here is Gauss's trick in three stages:

1. Pair up all the numbers in the following way and add them together: 1 + 100 = 101,
   2 + 99 = 101,
   3 + 98 = 101
   … 50 + 51 = 101
2. So, you have 50 pairs of numbers, which all add up to 101.
3. So, the result is 50 × 101 = 5,050!

Another way to think about this is:

Sum from 1 to n=n2×n+1

• n+1 represents step 1, because you pair up all the numbers, so that all the pairs add up to n+1.
• n2 represents step 2, because the number of pairs is equal to the total number of numbers divided by 2.
• × represents step 3, because you then multiply the sum of each pair by the number of pairs.

Let’s see if you can apply Gauss’s trick.

4. Domino toppling

I watched this terrific video last week. Take a look and answer the question afterwards.

Each domino can knock over a domino that is 1.5 times bigger, which does not seem big, but when this happens over and over again, the dominoes get bigger and bigger very quickly. This is known as exponential growth and we will return to this in a future Parallelogram.

In the meantime, here is an even more extraordinary example of domino toppling where the dominos get bigger and bigger. In fact, it was a world record at the time.

5. Junior Maths Challenge Problem (UKMT)

6. Weird optical illusions

The amazing, mind-warping objects in this video have been created by mathematical artist and engineer Professor Kokichi Sugihara. These incredible illusions literally mess with your brain.

Sometimes the geometry that you study at school might seem ordinary – what could be more ordinary than the angles of a triangle or the symmetry of a square? – but your teachers are really providing you with the first stepping stones towards gaining an understanding of the nature of space, and how you can build the sort of flabbergasting structures in this video.

Before you hit the SUBMIT button, here are some quick reminders:

• You will receive your score immediately, and collect your reward points.
• You might earn a new badge... if not, then maybe next week.
• Make sure you go through the solution sheet – it is massively important.
• A score of less than 50% is ok – it means you can learn lots from your mistakes.
• The next Parallelogram is next week, at 3pm on Thursday.
• Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon.

Additional Stuff

You can read more about mathematician Maryam Mirzakhani in this interview published in the Guardian: 'The more I spent time on maths, the more excited I got'.

This website goes into more detail about ways of adding the numbers from 1 to 100, and is worth looking at.

Credits

• Portrait of Carl Gauss by Christian Albrecht Jensen, 1840 (public domain)
• Image of Maryam Mirzakhani taken from Alchetron