Week 8The Man Who Knew Infinity

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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.
  • 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. The tale of Ramanujan

S. Ramanujan was one of the greatest mathematicians who ever lived. His story has even been turned into a movie, because he led such a remarkable life. He was born near the city of Madras in India in 1887, and his family were relatively poor, so he never went to university. However, he seemed to have a gift for mathematics and began creating new mathematical ideas that were far beyond the comprehension of his friends and family. Fortunately, a Cambridge professor called G.H. Hardy heard about this incredible young mathematician and invited Ramanujan to Cambridge University, where his genius flourished. Nevertheless, settling into his new life, far from his family, was a daily struggle.

Here is a clip from “The Man Who Knew Infinity”, all about the life of Ramanujan.

1 mark

1.1. In the clip, one of the mathematicians asks about Ramanujan’s first name. What does the S. stand for? The answer is not in the clip, so you might need to search online for the answer.

  • Shivesh
  • Srinivasa
  • Sushim
  • Sutosh
  • Swanand
2 marks

1.2. At one point in the clip, Ramanujan touches the feet of a statue of Isaac Newton, and you glimpse Newton’s memorial inscription. It is in Latin. Your challenge is to find the inscription, note down the Latin phrase, find out what it means and fill in the missing word: “Whose genius _____ the human race.”

  • delighted
  • inspired
  • elevated
  • surpassed
  • mystified

2. Partitions

Ramanujan was interested in something called partitions.

Partitions explores how many ways it is possible break up a positive number into positive whole numbers.

For example, 1 can only be (1).
So, there is only 1 way to partition 1.

However, 2 can be (2) or (1 + 1).
So, there are 2 ways to partition 2.

3 can be (3) or (1 + 2) or (1 + 1 + 1).
So, there are 3 ways to partition 3.

2 marks

2.1 How many ways can you partition 4?

Correct Solution: 5

(4) or (3 + 1) or (2 + 2) or (2 + 1 + 1) or (1 + 1 + 1 + 1)

2 marks

2.2 How many ways can you partition 5?

Correct Solution: 7

(5) or (4 + 1) or (3 + 2) or (3 + 1 + 1) or (2 + 2 + 1) + (2 + 1 + 1 + 1) or (1 + 1 + 1 + 1)

2 marks

2.3 How many ways can you partition 6?

Correct Solution: 11

(6) or (5 + 1) or (4 + 2) or (4 + 1 + 1) or (3 + 3) or (3 + 2 + 1) or (3 + 1 + 1 + 1) or (2 + 2 + 2) or (2 + 2 + 1 + 1) or (2 + 1 + 1 + 1 + 1) or (1 + 1 + 1 + 1 + 1 + 1)

3. Junior Maths Challenge Problem

2 marks

3.1 What is (999 − 99 + 9) ÷ 9?

  • 91
  • 99
  • 100
  • 101
  • 109

We can calculate the value in more than one way.

One method is to first work out the value of the expression in the brackets and then divide the result by 9. This gives:

(999 − 99 + 9) ÷ 9 = 909 ÷ 9 = 101.

Alternatively, we can first divide each number in the bracket by 9 and then evaluate the resulting expression. This gives:

(999 − 99 + 9) ÷ 9 = (111 − 11 + 1) = 101.

Of course, both methods give the same answer.

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 Parallelogams.

Cheerio, Simon.