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Quiz about Mathematicians and Discoveries
Quiz about Mathematicians and Discoveries

Mathematicians and Discoveries! Quiz


Over time, mathematicians discovered some really interesting properties of some numbers. Now, it's your turn to admire these amazing numbers and find out the stories behind them. Have fun!

A multiple-choice quiz by Matthew_07. Estimated time: 9 mins.
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Author
Matthew_07
Time
9 mins
Type
Multiple Choice
Quiz #
291,046
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
1962
Awards
Top 20% Quiz
Last 3 plays: Guest 14 (10/10), Gispepfu (10/10), Guest 124 (3/10).
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Question 1 of 10
1. Blaise Pascal, a French mathematician was credited for his works on Pascal's triangles and binomial coefficients. Pascal's triangle is a geometric representation of numbers in a triangular shape that displays the values of binomial coefficients when (x+y)^n is expanded, provided that n is a positive integer. Each number in the triangle is the sum of the two numbers that lie above it. The first line consists of a sole number 1. The second line has two 1's. From the third line onwards, the addition operations are required to produce the numbers 1, 2, 1. Meanwhile, the fourth line's numbers are 1, 3, 3, 1. What is the value of the number at the middle of the fifth line? More hint: this number is the first perfect number.

Answer: (1-digit number)
Question 2 of 10
2. This number's irrationality property was first discovered by Pythagoras and it was named after him. What is the value of Pythagoras' constant? The square root of ___. More hints: The only even prime number.

Answer: (1-digit number)
Question 3 of 10
3. In mathematics, Mersenne primes are prime numbers that are in the form of 2^n - 1, where n itself is another prime number. The first Mersenne prime is 2^2 - 1 = 3 and the second being 2^3 - 1 = 7. Pietro Cataldi, an Italian mathematician discovered the sixth and seventh Mersenne primes. The value of n of the sixth Mersenne prime is 17 and the prime number is 2^17 - 1 = 131071. What is the value of n of the seventh Mersenne prime? More clues: this number is smaller than 20.

Answer: (2-digit number)
Question 4 of 10
4. The Greek mathematician, Euclid, or also known as the Father of Geometry discovered the first four perfect numbers, the first three being 6, 28 and 496. What is the fourth perfect number? More clues: the first two digits are the largest two-digit square and the last two digits are the only two-digit perfect number.

Answer: (4-digit number)
Question 5 of 10
5. Perhaps this was not a discovery, but this eight-year old kid was indeed a child prodigy. Carl Friedrich Gauss, better known as the Prince of Mathematics, was asked to calculate the sum of all the integers from 1 to 100 in his mathematics lesson, and he did it within seconds. Can you calculate the sum as well without using a calculator? More clue: try using the method which was used by Gauss, where he broke down the numbers in pairs: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101 and so on.

Answer: (4-digit number)
Question 6 of 10
6. Joseph Lagrange, a Italian mathematician proved Bachet's conjecture in 1770. This conjecture is better known as Lagrange's four-square theorem, which states that every positive integer can be expressed as the sum of four squares. For example, 1 = 1^2 + 0^2 + 0^2 + 0^2, 2 = 1^2 + 1^2 + 0^2 + 0^2 and 3 = 1^2 + 1^2 + 1^2 + 0^2. Now, what is the value of these four squares, 8^2 + 9^2 + 11^2 + 20^2? More clues: this number is the Number of the Beast.

Answer: (3-digit number)
Question 7 of 10
7. This is yet another intriguing and interesting number. This number is the Kaprekar constant, after its discoverer, Dattaraya Kaprekar, an Indian mathematician. So, let's explore this number. Take any four-digit number (not all digits the same like 1111 and 2222) then construct the greatest and smallest numbers that can be formed from the four-digit number. After finding out their difference, repeat the same process for many times and eventually you will reach the Kaprekar constant. Do you know what the value of the Kaprekar constant is? More clues: the first two digits are three less than the square of 8 and the last two digits are seven less than the square of 9.

Answer: (4-digit number)
Question 8 of 10
8. Perhaps two of the most beautiful transcendental numbers (not the root of any polynomial functions) in mathematics are pi (3.142...) and e (2.718...). The former is also known as the Archimedes' number while the latter is better known as Euler's number. Leonhard Euler was a Swiss mathematician who introduced the notation of e (exponent) for the base of the natural logarithm (In). Euler was also credited with the introduction of the Greek letter pi in Euclidean geometry. Now, if you solve (e^pi) - pi the answer will approximate to which number? More clues: this number is a multiple of 10.

Answer: (2-digit number)
Question 9 of 10
9. You may have heard of the famous Fibonacci numbers and its sequence (0, 1, 1, 2, 3, 5, 8, 13... where the next number is the sum of its previous two numbers) that was introduced by Leonardo Fibonacci, a Italian mathematician. How about the Lucas number and its sequence? It was named after a French mathematician, Edouard Lucas. While the first two Fibonacci numbers are 0 and 1, the first two Lucas numbers are 2 and 1. So, the Lucas sequence is 2, 1, 3, 4, 7, 11, 18... Only 3 numbers occur in both the Fibonacci sequence and the Lucas sequence. What is the product of these 3 numbers? More clues: this number is a multiple of 3.

Answer: (1-digit number)
Question 10 of 10
10. This number's special property was discovered by Ramanujan, a great Indian mathematician. It is the smallest number that can be written as sum of two cubes in two different ways. More hints: the first two digits is the prime number after 13 and the last two digits is the prime number before 31.

Answer: (4-digit number)

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Quiz Answer Key and Fun Facts
1. Blaise Pascal, a French mathematician was credited for his works on Pascal's triangles and binomial coefficients. Pascal's triangle is a geometric representation of numbers in a triangular shape that displays the values of binomial coefficients when (x+y)^n is expanded, provided that n is a positive integer. Each number in the triangle is the sum of the two numbers that lie above it. The first line consists of a sole number 1. The second line has two 1's. From the third line onwards, the addition operations are required to produce the numbers 1, 2, 1. Meanwhile, the fourth line's numbers are 1, 3, 3, 1. What is the value of the number at the middle of the fifth line? More hint: this number is the first perfect number.

Answer: 6

The answer is 6, as in 3 + 3 = 6.

The patterns are as listed below:

(x + y)^1 = x + y
(x + y)^2 = x^2 + 2xy + y^2
(x + y)^3 = x^2 + 3x^2y + 3xy^2 + y^3

Notice that the corresponding coefficients can be found easily if we compute them from the Pascal's triangle, namely:
_ _ 1 _ _
_ 1 2 1 _
_1 3 3 1_
1 4 6 4 1
2. This number's irrationality property was first discovered by Pythagoras and it was named after him. What is the value of Pythagoras' constant? The square root of ___. More hints: The only even prime number.

Answer: 2

Irrational numbers are those that cannot be expressed in fractions. The square root of 2, or surd 2 is the first known irrational number.

Pythagoras, who was known for his Pythagoraean theorem discovered this number's irrationality geometrically.

Nowadays, surd 2's irrationality can be proved by using the contradiction method. First, we assume that surd 2 is indeed rational (can be expressed in fraction). Then, by doing some algebraic manipulations, we end up in an statement that contradicts to our first assumption. So, we conclude that surd 2 is irrational.

The same method can be used to prove both surd 3 and surd 5 are irrational, too.
3. In mathematics, Mersenne primes are prime numbers that are in the form of 2^n - 1, where n itself is another prime number. The first Mersenne prime is 2^2 - 1 = 3 and the second being 2^3 - 1 = 7. Pietro Cataldi, an Italian mathematician discovered the sixth and seventh Mersenne primes. The value of n of the sixth Mersenne prime is 17 and the prime number is 2^17 - 1 = 131071. What is the value of n of the seventh Mersenne prime? More clues: this number is smaller than 20.

Answer: 19

Given that n is smaller than 20 but greater than 17 leaves us with only 2 choices, namely 18 and 19. Since 18 is not a prime number, 19 is the answer we are looking for.

The first seven Mersenne primes are listed below:
2^2 - 1 = 3
2^3 - 1 = 7
2^5 - 1 = 31
2^7 - 1 = 127
2^13 - 1 = 8191
2^17 - 1 = 131071
2^19 - 1 = 524287

As of September 2006, the largest Mersenne prime is 2^32582657 - 1, which has 9808358 digits. This number is found by the Great Internet Mersenne Prime Search (GIMPS). Volunteers can download free software from the site and run the program in their computers. So everyone stands the chance to discover the next Mersenne prime.

The Electronic Frontier Foundation (EFF) even offers 100000 US dollars for the person who discovers the next prime number which contains at least 10,000,000 digits.
4. The Greek mathematician, Euclid, or also known as the Father of Geometry discovered the first four perfect numbers, the first three being 6, 28 and 496. What is the fourth perfect number? More clues: the first two digits are the largest two-digit square and the last two digits are the only two-digit perfect number.

Answer: 8128

The largest two-digit square is 9^2 = 81. The only two-digit perfect number is 28. Combining these two numbers, we obtain our fourth perfect number, which is 8128.

A perfect number is a positive integer which is the sum of its divisor, excluding the number itself. For example, the first perfect number 6 can be expressed as 1 x 6 or 2 x 3. Notice that 6 = 1 + 2 + 3.

The second perfect number is 28, which is the sum of 1, 2, 4, 7 and 14.
5. Perhaps this was not a discovery, but this eight-year old kid was indeed a child prodigy. Carl Friedrich Gauss, better known as the Prince of Mathematics, was asked to calculate the sum of all the integers from 1 to 100 in his mathematics lesson, and he did it within seconds. Can you calculate the sum as well without using a calculator? More clue: try using the method which was used by Gauss, where he broke down the numbers in pairs: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101 and so on.

Answer: 5050

There are all together 50 pairs of 101. So the sum is 50 x 101 = 5050.

Gauss' teacher, Buttner, posted this question during one of his lessons. He expected his students to list down all the numbers and add them one by one. However, Gauss used a different approach and solved it within seconds.

Besides, Gauss was remembered for correcting his father's finance papers.

Gauss was known for his great contributions in the field of statistics, where he introduced the idea of Gaussian distribution (the bell-shaped graph).
6. Joseph Lagrange, a Italian mathematician proved Bachet's conjecture in 1770. This conjecture is better known as Lagrange's four-square theorem, which states that every positive integer can be expressed as the sum of four squares. For example, 1 = 1^2 + 0^2 + 0^2 + 0^2, 2 = 1^2 + 1^2 + 0^2 + 0^2 and 3 = 1^2 + 1^2 + 1^2 + 0^2. Now, what is the value of these four squares, 8^2 + 9^2 + 11^2 + 20^2? More clues: this number is the Number of the Beast.

Answer: 666

The number 666 has many other interesting properties. It is the sum of the squares of the first seven prime numbers, namely 666 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2.

More interesting facts about this number:
666 = 1 + 2 + 3 + ... + 34 + 35 + 36 (this makes 666 the 36th triangular number)
666 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 5^3 + 4^3 + 3^3 + 2^3 + 1^3
666 = 1^6 - 2^6 + 3^6
666 = 18691113009329 - 18691113008663 (these are two consecutive big prime numbers)
666 = 313 + 353 (these are two consecutive palindromic prime numbers)
7. This is yet another intriguing and interesting number. This number is the Kaprekar constant, after its discoverer, Dattaraya Kaprekar, an Indian mathematician. So, let's explore this number. Take any four-digit number (not all digits the same like 1111 and 2222) then construct the greatest and smallest numbers that can be formed from the four-digit number. After finding out their difference, repeat the same process for many times and eventually you will reach the Kaprekar constant. Do you know what the value of the Kaprekar constant is? More clues: the first two digits are three less than the square of 8 and the last two digits are seven less than the square of 9.

Answer: 6174

Kaprekar was only a school teacher in a small town in India, Devlali, yet he discovered many interesting properties in the field of number theory.

Now, back to the famous Kaprekar constant, the number 6174. Let say we start with 1234. So, 4321 - 1234 = 3087. Then, 8730 - 0378 = 8352. 8532 - 2358 = 6174. Once we reach 6174, further calculations will only result in the same number, namely 7641 - 1467 = 6174.

Let us try with another number, let say 2008.

8200 - 0028 = 8172
8721 - 1278 = 7443
7443 - 3447 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174

We arrive at 6174 again. In fact, it has been proven that it takes at most 7 steps to reach 6174 with any four-digit number, provided that the individual digits are not all the same such as 1111 and 2222.
8. Perhaps two of the most beautiful transcendental numbers (not the root of any polynomial functions) in mathematics are pi (3.142...) and e (2.718...). The former is also known as the Archimedes' number while the latter is better known as Euler's number. Leonhard Euler was a Swiss mathematician who introduced the notation of e (exponent) for the base of the natural logarithm (In). Euler was also credited with the introduction of the Greek letter pi in Euclidean geometry. Now, if you solve (e^pi) - pi the answer will approximate to which number? More clues: this number is a multiple of 10.

Answer: 20

Both pi and e are irrational and they are transcendental numbers, too.

The value of e is 2.718... which approximates 3. Meanwhile, pi approximates 3. So, 3^3 - 3 = 27 - 3 = 24. So 20 is the best answer.

By using a calculator, the exact solution of (e^pi) - pi is 19.99909998, which is very close to 20, with only a relative error of 0.0045 percent.
9. You may have heard of the famous Fibonacci numbers and its sequence (0, 1, 1, 2, 3, 5, 8, 13... where the next number is the sum of its previous two numbers) that was introduced by Leonardo Fibonacci, a Italian mathematician. How about the Lucas number and its sequence? It was named after a French mathematician, Edouard Lucas. While the first two Fibonacci numbers are 0 and 1, the first two Lucas numbers are 2 and 1. So, the Lucas sequence is 2, 1, 3, 4, 7, 11, 18... Only 3 numbers occur in both the Fibonacci sequence and the Lucas sequence. What is the product of these 3 numbers? More clues: this number is a multiple of 3.

Answer: 6

Lucas was also credited for finding the formula to find the nth Fibonacci number.

Only 1, 2, and 3 occur in both Lucas sequence and Fibonacci sequence, and their product is 1 x 2 x 3 = 6. 6 is the first perfect number.

The first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13...
The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18...

The Lucas numbers are related to the Fibonacci numbers in many ways. One of them is that the nth Lucas number is the sum of (n-1)th and (n+1)th Fibonacci numbers. For example, the fifth Lucas number, 7 is the sum of the fourth and sixth Fibonacci numbers, as in 2 + 5 = 7.
10. This number's special property was discovered by Ramanujan, a great Indian mathematician. It is the smallest number that can be written as sum of two cubes in two different ways. More hints: the first two digits is the prime number after 13 and the last two digits is the prime number before 31.

Answer: 1729

1729 is also known as the Hardy-Ramanujan number. Godfrey Hardy, an English mathematician was visiting Srinivasa Ramanujan in a hospital when Ramanujan told him about this number.

Here are Hardy's words:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Notice that 1729 = 1^3 + 12^3 = 9^3 + 10^3.

=====

I hope you enjoy playing this quiz and learn something as well. I end this quiz with a quote from G. H. Hardy, Cambridge number theorist.

"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean."

Thanks for playing and have a nice day!
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.
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