Parallelogram 13 • Level 5 • 28 Nov 2024Gravitational Waves
Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/
- a portmanteau 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.
- When you finish, remember to hit the SUBMIT button.
- Finish by Sunday night 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 examine the solution sheet to learn from your mistakes.
1. Writing one hundred
Can you write the number one hundred on a piece of paper, but without taking your pen off the paper?
Have a think about the problem, and perhaps take a lateral approach. That means, instead of taking a headlong run at the problem, think about it from different angles, examine what the question might mean, or what it might not mean. Be creative.
The answer is in the short video below, but have a hard think before you click play. You really need to come up with some sort of answer, even if it is not brilliant, or even correct.
(If you have problems watching the video, right click to open it in a new window)1.1 How well did you do?
- I got the correct answer as shown in the video, or I got a different answer, but one that was interesting and perhaps equally good.
- I had no idea.
2. Gravitational Waves
One of the greatest scientific discoveries this century was the detection of gravitational waves, which were predicted by Albert Einstein at the start of the previous century.
Take a look at the video below, presented by Professor Kelly Holley-Bockelmann. It is longer than the usual videos we have in Parallel, but it is a brilliant lecture, so it is well worth watching all 18 minutes.
(If you have problems watching the video, right click to open it in a new window)2.1 When you hug someone, is that hug written on spacetime?
- Yes
- No
2.2 When you smile, will those spacetime ripples travel to distant stars?
- Yes
- No
2.3 Do your actions matter on a cosmic level?
- Yes
- No
3. Intermediate Maths Challenge Problem (UKMT)
3.1 Which of the following is not the sum of two primes?
- 5
- 7
- 9
- 11
- 13
4. Prime sums
4.1 Is 63 the sum of two primes?
- Yes
- No
4.2 Is 95 the sum of two primes?
- Yes
- No
5. Intermediate Maths Challenge Problem (UKMT)
5.1 The diagram shows a regular octagon.
What is the ratio of the area of the shaded trapezium to the area of the whole octagon?
- 1 : 4
- 5 : 16
- 1 : 3
2 - 3 : 8
6. Intermediate Maths Challenge Problem (UKMT)
6.1 In a particular group of people, some always tell the truth, the rest always lie. There are 2016 in the group. One day, the group is sitting in a circle. Each person in the group says, "Both the person on my left and the person on my right are liars."
What is the difference between the largest and smallest number of people who could be telling the truth?
- 0
- 72
- 126
- 288
- 336
There will be more 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.
When you see your % score, this will also be your reward score. As you collect more and more points, you will collect more and more badges. Find out more by visiting the Rewards Page after you hit the SUBMIT button.
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.