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Phi - The Golden Ratio Trivia Quiz

The golden ratio has many interesting properties. How much do you know about this unique number? Give it a try and have fun!

A multiple-choice quiz by Matthew_07. Estimated time: 4 mins.

Author
Matthew_07

Time
4 mins

Type
Multiple Choice

Quiz #
265,360

Updated
Dec 03 21

# Qns
10

Difficulty
Average

Avg Score
6 / 10

Plays
1394

Awards
Top 35% Quiz

One at a Time - Single Page - Timed Game

Question 1 of 10

1. The value of phi, namely the golden number is approximately 1.6180339887... What type of number is it? Hint

A prime number

A rational number

An irrational number

A whole number

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Question 2 of 10

2. The American mathematician, Mark Barr, has chosen Phi as the symbol for the golden ratio. Phi is named after which of the following Greek sculptors? Hint

Philips

Phidias

Phiviles

Phixels

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Question 3 of 10

3. Nowadays, the golden ratio is symbolized by the Greek letter phi. Sometimes, it is also represented by another Greek letter. Which letter is it? Hint

Delta

Tau

Lambda

Sigma

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Question 4 of 10

4. Which famous quadratic equation can be used to derive the golden ratio directly? Hint

x^2+x+1=0

x^2-x+1=0

x^2-x-1=0

x^2+x-1=0

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Question 5 of 10

5. The reciprocal of the golden ratio (phi) shares the same value with which expression? Hint

Phi + 2

Phi + 1

Phi - 1

Phi - 2

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Question 6 of 10

6. The golden ratio is also known by many other names. Which of the following names is NOT one of those? Hint

The golden integer

The golden number

The golden mean

The golden proportion

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Question 7 of 10

7. The earliest written definition of the golden ratio was "the extreme and mean ratio", provided by a famous mathematician. Who is he? Hint

Fibonacci

Euclid

Plato

Fermat

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Question 8 of 10

8. The number pi (3.142...) is celebrated on 14 March. On which day do we celebrate phi day? Hint

16 January

18 June

16 August

18 March

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Question 9 of 10

9. The ancient Egyptians used the golden ratio in their pyramids. At that time, the golden ratio was known to them by another name, which is? Hint

The magic ratio

The sacred ratio

The perfect ratio

The universal ratio

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Question 10 of 10

10. The golden ratio is claimed to appear in many fields, such as cosmology, theology, arts, architecture, botany and others.

True

False

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Quiz Answer Key and Fun Facts

1. The value of phi, namely the golden number is approximately 1.6180339887... What type of number is it?

Answer: An irrational number

The value 1.61803... can also be derived mathematically from the famous Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...), by dividing a successive Fibonacci number by its previous one. The accuracy of the value obtained increases when greater Fibonacci numbers are used. For example, 1597/987 = 1.618034448.

2. The American mathematician, Mark Barr, has chosen Phi as the symbol for the golden ratio. Phi is named after which of the following Greek sculptors?

Answer: Phidias

Phidias was a famous Greek sculptor who designed the Parthenon. It is believed that he applied the golden ratio in the building's architecture.

3. Nowadays, the golden ratio is symbolized by the Greek letter phi. Sometimes, it is also represented by another Greek letter. Which letter is it?

Answer: Tau

The delta symbol is used to represent a small change of a quantity. Meanwhile, the sigma notation represents summation of a set of numbers. On the other hand, the letter lambda represents wavelength.

4. Which famous quadratic equation can be used to derive the golden ratio directly?

Answer: x^2-x-1=0

The 2 solutions to the quadratic equation x^2-x-1=0 are (1+5^0.5)/2 and (1-5^0.5)/2 respectively. The former is the golden ratio itself, namely 1.61803 while the latter gives a value of -0.61803...

5. The reciprocal of the golden ratio (phi) shares the same value with which expression?

Answer: Phi - 1

The reciprocal of the golden ratio is 0.61803, which is exactly 1 less than the golden ratio itself! Moreover, if you square the golden ratio, the value obtained is 2.61803, which is exactly 1 more than the golden ratio itself!

6. The golden ratio is also known by many other names. Which of the following names is NOT one of those?

Answer: The golden integer

Besides those names, it is also called the golden cut, the golden section and the divine proportion.

7. The earliest written definition of the golden ratio was "the extreme and mean ratio", provided by a famous mathematician. Who is he?

Answer: Euclid

Euclid wrote this in his book "Elements".

8. The number pi (3.142...) is celebrated on 14 March. On which day do we celebrate phi day?

Answer: 18 June

The value of phi is 1.618... Besides, its reciprocal is 0.618... And if you square phi, you will get 2.618... The 0.618 portion keeps repeating in all these 3 cases. Therefore, the date 18 June is chosen. Apart from these two constants, the Avogadro constant is also celebrated on 22 June every year.

The value of the widely used Avogadro constant in chemistry is given by 6.22 times 10 to the power of 23. (6.22x10^23)

9. The ancient Egyptians used the golden ratio in their pyramids. At that time, the golden ratio was known to them by another name, which is?

Answer: The sacred ratio

Besides pyramids, the Egyptians also used the golden ratio in many of their other architectures (temples) and arts.

10. The golden ratio is claimed to appear in many fields, such as cosmology, theology, arts, architecture, botany and others.

Answer: True

Yes, it is true. In fact, the golden ratio has captivated many mathematicians and there are some researches going on regarding the application of the golden ratio in stock market and foreign exchange!

Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
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