Parallelogram 26 • Level 1 • 1 Mar 2024The golden egg
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. How do you like your eggs?
Egg shapes might seem a little wobbly and weird, and not at all what geometry is about!
Watch this video where Johnny Ball transforms a pentagon into a perfect egg shape, using nothing but a straightedge and compass.
(If you have problems watching the video, right click to open it in a new window)1.1 Which famous mathematician had a cult which explored the geometry of the pentagram?
- Uomo Delle Uova
- Pentagoras
- Pythagoras
- Johnny Ball
- (Not answered)
1.2 The ratio between the edge and the diagonal of a pentagon is very interesting mathematically, and crops up in many places - it is called the Golden Ratio.
Calculate the Golden Ratio to 3 decimal places.
- 1.618
- 1.62
- 1.22
- 1.73
- (Not answered)
1.3 The diagram shows a regular pentagon with two of its diagonals.
If all the diagonals are drawn in, into how many areas will the pentagon be divided?
Correct Solution: 11
2. Puzzles
2.1 Wendy The Wizard was making a magic potion by mixing 350ml of spit with 150ml of venom.
How much more venom would need to be added to achieve a ratio of spit to venom of 7:4?
- 25ml
- 50ml
- 100ml
- 150ml
- 200ml
- (Not answered)
Starting with the ratio 7:4 we can multiply both sides by 50.
Scaling up the ratio would give us 350:200.
Meaning for 350ml of spit we would need 200ml of venom to achieve the correct ratio.
Since we already have 150ml, we only need to add 50ml more!
2.2 The diagram shows a regular hexagon with an equilateral triangle inside it.
What is the size of the angle marked?
- 12°
- 15°
- 20°
- 30°
- 60°
- (Not answered)
Two useful facts:
- The angles at each vertex in an equilateral triangle are 60°
- The angles at each vertex in a regular hexagon are 120°
The vertex of the hexagon is 120°.
If we subtract the 60° taken up by the triangle vertex we are left with 60°.
This accounts for two of the marked angle, so by halfing we can conclude the marked angle is 30°.
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 and Ayliean.