Parallelogram 27 • Level 2 • 7 Mar 2024The Secret of Happiness
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.
- 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 Zen of Venn
You will come across a lot of Venn diagrams while studying mathematics, but perhaps this is the most important one. It is a guide for life. Ikigai, which is the bit in the centre, is your “reason for being”. It describes the thing that you love, which the world needs, which you are good at and which you can be paid for. Find that thing and you will be happy for your whole life.
2. Junior Maths Challenge Problem (UKMT)
2.1 What is 2010 + (+2010) + (-2010) - (+2010) - (-2010)?
- 0
- 2010
- 4020
- 6030
- 8040
- (Not answered)
The expression = 2010 + 2010 - 2010 - 2010 + 2010 = (2010 - 2010) + (2010 - 2010) + 2010 = 2010.
3. Junior Maths Challenge Problem (UKMT)
3.1 Heidi is 2.1 m tall, while Lola is only 1.4 m tall. What is their average height?
- 1.525 m
- 1.6 m
- 1.7 m
- 1.725 m
- 1.75 m
- (Not answered)
The average height, in metres, is
4. QI – what is the correct way to cut a cake?
Here is something for you to think about from BBC2’s QI, which often features mathematical puzzles. You will hear the question in the video clip, but here it is so there is no confusion. If you cut a standard slice of cake (basically a triangle, with one curved side), then the sides next to the removed slice are exposed to the air and will dry out.
So, how do you cut the cake in a radically difference way (3 cuts, 2 pieces please), so that you minimise the amount of cut cake exposed to the drying effects of the air?
Perhaps pause the video and think about possible solutions before they give you the answer.
(If you have problems watching the video, right click to open it in a new window)5. Junior Maths Challenge Problem (UKMT)
What is the value of
- 25
- 35
- 40
- 65
- 155
- (Not answered)
Let the other angles be as marked in the diagram. Then
Because the angles in a triangle sum to
Now,
Therefore
6. What is 0!
We have covered factorials in recent Parallelograms. Remember 3! just means 3 × 2 x 1 = 6.
Or 5! means 5 × 4 × 3 × 2 × 1 = 120.
But what is 0! (zero factorial)?
James Grime explores this question in this video, but have a think about the answer before you hear James’s take on this mystery.
6.1. 0! is equal to what number?
Correct Solution: 1
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
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QI explores physics by seeing what happens when you take two large books and weave the pages – they are impossible to pull apart. Try it for yourself.
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Mythbusters took the phenomenon to the next level, and then the next level again.
_ -
This article from Chalkdust magazine explains why interleaved books are so sticky. It is written for university students, so it is fairly technical, but it is worth a quick look and don’t worry if you are confused by some bits.