Parallelogram 34 • Level 4 • 25 Apr 2024Mathematical Timeline

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. History of Mathematics

The terrific Mathigon website has loads of great material, including a timeline showing the great mathematicians of past centuries. Visit the timeline (click and it will open up in a new tab) and answer the three questions below. Just enter the name given in the plum box.

So, if the answer is John Napier, just enter Napier, because that is the name that appears in the plum-coloured box on the timeline:

2 marks

1.1 Looking at mathematicians from 1600 to 1700, what is the surname of the mathematician who is best know for his Last Theorem?

Correct Solution: FERMAT

2 marks

1.2 Looking at mathematicians from 1700 to 1800, what is the surname of the mathematician who was from a family of mathematicians and scientists, which meant that he was banned from his father’s house for beating him at an award from the Paris Academy?

Correct Solution: BERNOULLI

2 marks

1.3 Looking at mathematicians from 1800 to 1900, what is the surname of the mathematician who proved that there are different sizes of infinity?

(Clue 1: David Hilbert was so amazed by his work, that he said “No one shall expel us from the paradise that [HE] has created.”)
(Clue 2: initials GC)

Correct Solution: CANTOR

2 marks

1.4 Looking at mathematicians from 1800 to 1900, what is the surname of the mathematician who used statistics to revolutionise medicine and is even credited with promoting ‘infographics’? (Clue: initials FN)

Correct Solution: NIGHTINGALE

2. Intermediate Maths Challenge Problem (UKMT)

2 marks

2.1 An equilateral triangle is placed inside a larger equilateral triangle so that the diagram has three lines of symmetry.

What is the value of x?

100
110
120
130
150
(Not answered)

We label the vertices in the diagram as shown.

Because the figure is symmetrical about the line PS, ∠PSU=∠PST.

Since the triangle STU is equilateral, ∠TSU=60°.

The angles at a point have sum 360°. Therefore:

∠PSU+∠PST+∠TSU=360°

and so

∠PSU+∠PSU+60°=360°.

It follows that

∠PSU=12360°−60°=12300°=150°.

Therefore x=150.

3. Cannonball Numbers

Last week, you watched a video about the mathematical problem of sphere packing.

This week, Matt Parker looks a problem all about stacking spheres. Take a look at the question below.

(If you have problems watching the video, right click to open it in a new window)

4 marks

3.1 If you stack 90,525,801,730 cannonballs in a pyramid, with a base shaped as a 31,265-agon, then how many layers of cannonballs will be in the pyramid?

Correct Solution: 259

4. Intermediate Maths Challenge Problem (UKMT)

4 marks

4.1 How many weeks are there in 8×7×6×5×4×3×2×1 minutes?

1
2
3
4
5
(Not answered)

There are 60=6×5×2 minutes in an hour, 24=8×3 hours in a day and 7 days in a week. It follows that the number of weeks in 8×7×6×5×4×3×2×1 minutes is:

8×7×6×5×4×3×2×16×5×2×8×3×7=4×1=4, after cancelling.

5. The world’s best chalk

I spotted this terrific video on the Great Big Story channel: “Once upon a time, not long ago, the math world fell in love ... with a chalk. But not just any chalk! This was Hagoromo: a Japanese brand so smooth, so perfect that some wondered if it was made from the tears of angels.”

Take a look and answer this question.

(If you have problems watching the video, right click to open it in a new window)

2 marks

5.1 One mathematician likens mathematics to several other activities. Which of the following does he NOT mention?

Craftsmanship
Engineering
Artistry
Science
(Not answered)

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.