Week 2Romantic Mathematics

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteaux word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.

Welcome to the second of our Parallelograms designed for Year 9 students, a collection of mathematical challenges designed to stretch your brain and make your neurons more squiggly.

These challenges are a random walk through the mysteries of mathematics. Be prepared to encounter all sorts of weird ideas, including some questions that have nothing to do with mathematics.

  • Tackle each Parallelogram in one go. Don’t get distracted.
  • When you finish, remember to hit the SUBMIT button.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.

IMPORTANT – it does not really matter what score you get, because the main thing is that you think hard about the problems... and then look at the solution sheet to see where you went wrong, and then next time you’ll know what to do.

1. Is 1 a prime number?

Dr James Grime on the Numberphile channel tells you about the whether or not 1 is a prime number... and why.

Just to summarise, “the fundamental theorem of arithmetic” (also known as the “unique-prime-factorization theorem”) states that every integer greater than 1 is either:
(a) a prime number itself, or
(b) can be represented as the product of prime numbers (in only one way).

1 mark

1.1. Is 1 a prime number?

  • Yes
  • No

Watch the video again if you got this question wrong.

2 marks

1.2. If you factorise 2,176 into primes, which is the biggest prime factor?

Correct Solution: 17

17 is the largest prime factor. The best way to find it would have been to divide 2,176 by 2 over and over again, because 2 is the only other prime factor.

3 marks

1.3. If you factorise 1,144 into primes, which is the biggest prime factor?

Correct Solution: 13

13 is the largest prime factor. The best way to find it would have been to begin by dividing 1,144 by 2, and then by 2 again, and continuing until it can't divide by 2 any more, which results in 143.

Unfortunately, 143 is not prime, so by trial and error you would have to work out that 143 = 11 x 13.

2. Statistically I Love You

This is a nerdy love song by physics graduate Helen Arney.

There are no questions, but you can enter a competition. Just write a list of all the maths references in the song. Then email your list to prizes@parallel.org.uk – in the subject header, just write the number of references. The main rule is that no repetitions are allowed. Also a term like “vulgar fraction” counts as one reference, i.e., don’t enter vulgar separate from fraction and have two entries. The names of mathematicians count as mathematical references. The best entry wins a signed copy of "The Simpsons and Their Mathematical Secrets" written by me. Most importantly of all, the judge’s decision is final.

3. Intermediate Maths Challenge Problem

If you are a Year 9 student, then it is likely that you will be taking part in the United Kingdom Maths Trust (UKMT) competition known as the Intermediate Maths Challenge (IMC). If you do particularly well, you might earn yourself a gold, silver or bronze certificate, but you will have to work hard as you will be competing against Year 9, Year 10 and Year 11 students from across the country.

Your teachers will help you prepare for this national maths competition, but in each week's Parallelogram we will always include one UKMT Junior Maths Challenge question.

3 marks

3.1 To find the diameter in mm of a Japanese knitting needle, you multiply the size by 0.3 and add 2.1.

What is the diameter in mm of a size 5 Japanese knitting needle?

  • 3.6
  • 7.4
  • 10.8
  • 12
  • 17.1

We need to work out 5 x 0.3 + 2.1. This gives 1.5 + 2.1 = 3.6 as the answer.

If you missed the first Parallelogram, then try to go back and complete it. After all, you can earn reward points and badges by completing each Parallelogram. Find out more by visiting the Rewards Page after you hit the SUBMIT button.

There will be another Parallelogram next week, and the week after, and the week after that. So check your email or return to the website on Thursday at 3pm.

In the meantime, you can find out your score, the answers and go through the answer sheet as soon as you hit the SUBMIT button below.

It is really important that you go through the solution sheet. Seriously important. What you got right is much less important than what you got wrong, because where you went wrong provides you with an opportunity to learn something new.

Cheerio, Simon.