Parallelogram 14 Year 8 9 Jan 2020Ma and Pa Kettle

This is a preview of Parallel. You have to login or create an account, to be able to answer questions and submit answers.

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.
  • 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. Einstein’s π

Watch this clip from Night at the Museum 2 (Battle of the Smithsonian) and listen carefully to the references to π.

Although Einstein has no problem remembering the digits of π, most of the rest of us find it tricky. 3.14 is about as good as many of us can manage.

As you might know, the digits of π go on forever, so you will never memorise all of π, but there are tricks called mnemonics (pronounced NEM-ON-ICK) that can help you remember quite a few digits.

For example, take the phrase:

“How I wish I could calculate pi.”

If you count the number of letters in each word, then you obtain the digits 3.141592.

“Can I have a small container of coffee?” leads to 3.1415926.

Alternatively, you can remember π with the fraction 22/7.

1 mark

1.1. How much does 22/7 differ from the true value of π? You will need to start by finding the difference between the two number, then dividing by π, then converting to a percentage.

  • 0.04%
  • 0.1%
  • 2%
  • 3%
  • 4.2%

22/7 = 3.14286
π = 3.14159

Inaccuracy is (22/7 – π ) / π = 0.00127 / 3.14159 = 0.0004 = 0.04%

An even better approximation is 355/113 (which is easy to remember, because you just have to remember to repeat the first three odd numbers and then split the result in the middle (113355)).

1 mark

1.2. How much does 355/113 differ from the true value of π?

  • 0.0000000008%
  • 0.00000008%
  • 0.000008%
  • 0.0008%
  • 0.08%

Because π cannot be written as a fraction with perfect accuracy it is labelled an irrational number, but it is not the only irrational number. The golden ratio, often represented as φ (pronounced phi), is the number 1.61803398874...

1 mark

1.3. How much does 13/8 differ from the true value of φ?

  • 0.1%
  • 0.2%
  • 0.4%
  • 0.6%
  • 0.8%

2. Junior Maths Challenge Problem (UKMT)

In 2007, the world record for the largest coin was broken by the Royal Canadian Mint. The coin is 99.999% pure gold and has a mass of 100 kg. A standard British £1 coin has mass of 10g.

2 marks

2.1. What sum of money in £1 coins would weigh the same as the record-breaking coin?

  • £100
  • £1,000
  • £10,000
  • £100,000
  • £1,000,000

We have to work out how many £1 coins, each weighing 10 g, we need to get a total weight of 100kg. Now 1kg = 1000g, and so 100kg = 100,000g. So we need 100,000/10 = 10,000 of these coins. That is, £10,000 in money.

(In fact, the current (2019) record for the world's biggest coin is held by the Perth Mint. The coin weighs one tonne and is made of 99.99% pure gold.)

3. Junior Maths Challenge Problem (UKMT)

2 marks

3.1. All old Mother Hubbard had in her cupboard was a Giant Bear chocolate bar. She gave each of her children one-twelfth of the chocolate bar. One third of the bar was left. How many children did she have?

  • 6
  • 8
  • 12
  • 15
  • 18

One third of the bar was left, so Mother Hubbard’s children ate two-thirds of the bar. Since they ate one-twelfth of the bar each, Mother Hubbard had

4. Ma and Pa Kettle

Ma and Pa Kettle were characters in an American TV show in the 1940s. The characters featured in nine films, which grossed $35 milllion, which was a huge amount of money back then. In fact, without Ma and Pa Kettle, Universal Studios would have gone bankrupt, and without Universal there would be no Jurassic Park, no Despicable Me, no Jaws, and no Fast and Furious franchise.

In this clip, Ma and Pa Kettle wrestle with some maths while trying to discuss a contract in which 25% has to be divided among 5 people. See if you can understand how and why they think 25/5 = 14.

2 marks

4.1 Using the mistaken approach of Ma and Pa Kettle, what is 3 × 16? You might need to watch video again.

Correct Solution: 21

5. Pi mnemonic song

Andrew Huang has created a song which is a mnemonic for the first 100 decimal places of π. It is quite charming, apart from the occasional mentions of "ZERO". There must be a better way to deal with zero, rather than just saying "ZERO" - for example, you could pick a letter, and then any word that starts with that letter (regardless of its length) represents zero.

Anyway, see what you make of it, and maybe make up your own mnemonic for π.

6. A New Year reminder

As it is the start of the year, I thought it would be good just to remind you that Parallelograms are really tough, they cover topics that you might not have seen before and they are designed to confuse you. If too many people get 100%, then I will just have to make the Parallelograms tougher, weirder and more confusing. In short, if you only get 50%, don’t worry. If you get less than 50%, don’t worry. Just make sure you go through the solution sheet and try to find out why you got a question wrong. I really do mean it when I say that I am overjoyed if a student gets 25%, as long as they did their best, looked at the solution sheet, and then learned something. That is far better than getting 100% and learning nothing... although well done if you do get 100%.

Does that make sense? I just wanted to remind students, teachers and parents that Parallelograms are a major challenge, and to a large extent the scores don’t matter.

By the way, it does say at the start of every Parallelogram: “Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.”

3 marks

6.1 Are you cool about Parallelograms being hard and therefore not necessarily getting a high score every week?

  • Yes, I am very cool about it. Positively chilled. Or maybe negatively chilled.
3 marks

6.2 Are you going to promise to go through the solution sheet every week and learn from your mistakes?

  • Yes, I promise to go through the solution sheet every week. Really. Seriously. I mean it. If not, then may the ghosts of dead mathematicians haunt me during maths lessons.

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

From now on, Parallelograms will often contain this Additional Stuff section, which carries no mark, but which you might find interesting. Why not take a look? However, it is optional, so you can also just skip to the SUBMIT button and click.

This video shows a young lad called Benjamin Most reciting from memory 2,422 digits of π. I should stress that memorising numbers has nothing to do with being good at mathematics, but you have to admire his determination to memorise so many digits.

And Benjamin has a long way to go to beat the world record for memorising π, which stands at 70,030 digits.

Here is one of my favourite cartoons about π – see if you can understand the joke. If not, ask your teacher to explain it.