Parallelogram 26 Level 1 1 Mar 2024The golden egg

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. 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 mark

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 mark

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)
2 marks

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 marks

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!

3 marks

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)
Show Hint (–1 mark)
–1 mark

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.