101 Mathematical Trivia

1. In 1988, Nicolas Slonimsky (1894-1995) invented a method of beating a different rhythm with each arm–created a new composition by identifying each note in Beethoven’s Fifth Symphony with a number, and then playing the square root of each note.

2. The symbol for infinity (∞) was used by the Romans to represent 1000.


3. All palindromes with even number of digits are divisible by 11.

4. The earliest evidence of a numerical recording device is a section of a fibula of a baboon, with 29 visible notches, dated to about 35000 BC, from a cave in the Lebombo mountains on the borders of Swaziland in Southern Africa.

5. The number 365 is equal to the sum of three consecutive squares and two consecutive squares in which the five squares are also consecutive.

365 = 102 + 112 + 122 = 132 + 142

6. £12 12 shillings 8 pence = 12128 farthings

7. Interesting number relationships:

12 + 42 + 62 + 72 = 22 + 32 + 52 + 82 = 102

1 + 4 + 6 + 7 = 2 + 3 + 5 + 8 = 18

8. Each fraction of the following equation contains all the digits 1 through 9 only once.


9. There are 293 ways to make change for a $1 using pennies, nickels, dimes quarters and half-dollars.


10. 13177388 = 71 + 73 + 71 + 77 + 77 + 73 + 78 + 78

11. 169 is equal to 132 and its reverse 961 is equal to 312.

12. 206156734 = 26824404 + 153656394 + 187967604. This is an integer solution for the equation w4 = x4 + y4 + z4 found by Noam Elkies.

20. 32768=\frac{(3-2+7)^6}{8}

21. A tablet from Susa, dating from the period 1900-1650 BC, uses the Pythagorean theorem to find the circumradius of a triangle whose sides are 50, 50, 60. Pythagoras himself lived in the sixth century BC.

22. 8114118 is a palindrome and the 8114118th prime, 143787341, is also a palindrome.

23. If you concatenate all the palindromes from 1 to 101, the number produced would be prime! In other words, the number 123456789112233445566778899101 is prime.

24. Perfect squares are the only numbers with an odd number of divisors.

perfect squares.png

Perfect Squares

25. From 0 to 1000, only the number “one thousand” has the letter “A”.

26. Saint Hubert is the patron saint of mathematicians.

27. e^\frac{1}{\sqrt 2}\approx 2

28. When the English mathematician Augustus de Morgan was asked for his age, he would reply, “I was x years of age in the year x²” (He was 43 in 1849)

augustus de morgan.jpg

Augustus de Morgan

29. 14641 = (1 + 4 + 6)4 × 1

30. There is only one long division extant in the entire corpus of Greek mathematics.

31. Newton is on record as speaking only once when a member of parliament, to ask that a window be opened.

32. Newton’s annotated copy of Barrow’s Euclid was sold at auction in 1920 for five shillings. Shortly thereafter, it appeared in a dealer’s catalog marked as £500.

isaac newton.jpg

Isaac Newton

33.  The square of 204 is equal to the sum of consecutive cubes 23, 24 and 25.

34. A knight’s tour order-8 magic square has been proven to not exist.

35. 1666666666661 is the smallest prime number which contains 11 6’s and it’s palindromic too!

36. 22273 is the largest prime in the Bible and it’s aptly in Number 3:43.

37. Except for 2 and 3, if you add and subtract 1 to any prime number, one of the results is always divisible by 6.

38. 19683=1\times(9-6)^8\times3

39. The Chinese were the first who used negative numbers around 2200 years ago or maybe even earlier.

40. Cardan (1501-1576) described negative numbers as “fictions” and their square roots as “sophistic”, and a complex root of a quadratic, which he had calculated, as being “as subtle that it is useless”.

41. If A+B+C=180^\circ, then \tan a+\tan b+\tan c=(\tan a)(\tan b)(\tan c).

42. -40 °C is equal to -40 °F.



43. Aside from 144 being the only square Fibonacci number. It is also the 12th Fibonacci number. Note that 12 is the square root of 144.


44. (9999998+0000001)2 = 99999980000001

45. In chess, there are 4897256 total possible positions after 5 moves by both players.

46. 165033 = 163 + 503 + 333

47. The probability that the thirteenth day of the month being Friday is the highest.

48. Richard Recorde is credited with inventing the equal sign (=) in 1557.

49. 3864 = 3 × (-8 + 64)

50. 26364=26^3\times \frac{6}{4}

51. There is a combination of 26,830 possible Tic-tac-toe games, excluding reflections and rotations.

tic tac to.png

52. 2646798=2^1+6^2+4^3+6^4+7^5+9^6+8^7

53. Every odd number contains the letter “e” in the English language.

54. 6455=(6^4-5)\times 5

55. There are 40320 minutes or 8! minutes in 4 weeks.

56. There are 3628800 seconds or 10! seconds in 6 weeks.

57. 3! × 5! × 7! = 6! × 7! = 10!

58. 15642=1+5^6+4^2

59. 28671=\left (\frac{2}{8} \right )^{-6}\times7-1

60. Given any four consecutive Fibonacci numbers w, x, y and z, yz – wx forms the hypotenuse, and 2xy and wz form the two other sides of the right triangle.

61. 40585 = 4! + 0! + 5! + 8! + 5!. This is the largest number in base 10 that is the sum of the factorials of its digits. the only others are 1, 2 and 145.

62. 48625=4^5+8^2+6^6+2^8+5^4

63. 343=(3+4)^3

64. The polar diameter of the Earth is approximately equal to half a billion inches, accurate to 0.1%.


65. 216 = 65536 might be the only power of 2 in base 10 that does not contain any digit that is a power of two, i.e., 1, 2, 4 or 8.

66. 241=\frac{(2^8 + 4^8 + 1^8)}{(2^4 + 4^4 + 1^4)}

67. Aside from 0 and 1, 82000 (in base 10) is the only number that can be expressed with 0’s and 1’s in bases 2, 3, 4 and 5.

820002 = 10100000001010000
820003 = 11011111001
820004 = 110001100
820005 = 10111000

68. 122 × 213 = 25986. Interestingly, if you reverse 122 and 213, their product would also be the reverse of 25986.

221 × 312 = 68952

69. While we use the base 10 number system (decimal), the Mayans counted by 20’s (vigesimal).

mayan numeral.png

Mayan Numeral

70. The product of two primes can never be a perfect square.

71. 63945 = 63 × (-9 + 45)

72. The sum of any 14 consecutive Fibonacci numbers is divisible by 29.

73. the difference between the time of a sundial and a standard clock is called “the equation of time”.

74. People back then believe that the number of grains of sand is limitless. However, Archimedes argued in The Sand Reckoner that the number of grains of sand is not infinite. He then gave a method for calculating the highest number of grains of sand that can fit into the universe, which was approximately 1063 grains of sand in his calculation.



75. Curiously, the number of nucleons in the observable universe of roughly the Hubble universe is approximately 1080 (this is also known as the Eddington number). Archimedes’ 1063 grains of sand is approximately equivalent to 1080 nucleons.

76. It is impossible to square the circle since the area of the circle is based on π, which is a transcendental number. Therefore, a person who obsessively insists on “squaring the circle” is said to be suffering from morbus cyclometricus.

77. The mathematician G. H. Hardy doesn’t like mirrors. He even covered the mirrors in any hotel rooms that he entered.

G. H. Hardy.jpg

G. H. Hardy

78. 999 is the largest number that can be formed by using three digits without the use of any other symbols. It consists of 369693100 digits!

79. 1285=(1+2^8)\times5

80. 27 × 594 = 16038. This is the only solution for a pandigital multiplication with a pattern of 2, 3 and 5 digits in this form. Also, notice that 27 is a factor of 594.

81. If you multiply all the divisors of 48 together, it would yield 484.

82. 34425 = 34 × 425

83. 1023 – 23 is the largest 23-digit prime. It is equal to 99999999999999999999977.

84. 45632=-4^5+6^{({3\times 2})}

85. 121 and 4 are the only squares that become cubes when increased by 4 (Discovered by Fermat).

121 + 4 = 53; 4 + 4 = 23

86. The first seven digits of the golden ratio (1618033) concatenated is prime!


87. \left (\frac{5}{8} \right )^2+\frac{3}{8}=\left (\frac{3}{8} \right )^2+\frac{5}{8}

88. 7 x 11 x 13 x 17 x 19 = 323323. The product of five consecutive primes yielding a palindrome.

89. Moreover, using the same five consecutive prime numbers, the sum of their squares is also a palindromic number!

 72 + 112 + 132 + 172 + 192 = 989

90. Some mathematical celebrations: March 14 – Pi Day; June 28 – Tau Day; October 10 – Metric Day.

91. If you stack one dollar bills equivalent to the approximate debt of the U.S. government, then the dollar bills would reach the moon five times over!



92. The symbol for division (÷) is called obelus.

93. On the other hand, the division slash (/) is called virgule.

94. When you multiply 21978 by 4, the product is the reversal of the number.

21978 × 4 = 87912

95. Negative numbers don’t have logarithms.

96. 987 × (9 + 8 + 7) + 1 and 987 × (9 + 8 + 7) – 1 are both primes. This is the only 3-digit number with consecutive descending digits that has this property.

97. 18 is the only number that is twice the sum of its digits. (18: 1 + 8 = 9: 9 × 2 = 18)

98. 11 is the only palindromic prime with an even number of digits.

99. The Babylonian mile is approximately equal to 11.3 km (about 7 miles).

100. 736=7+3^6

101. 9893941210243728=98939412^2+10243728^2

Posted by

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

137 thoughts on “101 Mathematical Trivia

  1. Who knew?! Pi has a golden ratio and Pi defines Quadrature!

    Golden Rectangle of Quadrature (diagonal = circle’s diameter,
    ratio of long side to short side):

    Qphi = Phi of Pi = sqrt(Pi)/sqrt(4-Pi) = sqrt(Pi/4-Pi)
    = 1.9130583802711007947403078280203..

    Pythagorean Quadrature (hypotenuse = diameter,
    ratio of hypotenuse to long side = Qcue):

    Qcue = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(sqrt(1/Pi))
    = 1.1283791670955125738961589031215..


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  3. Reblogged this on e-Quips and commented:
    These 100 bits of math trivia range from I got that to What???!!!. For math nerds and other who appreciate unusual trivia or want to learn something.


  4. Wow, this is very interesting. I used to teach primary students mathematics and I am sure the smarts ones would love these trivia.
    By the way, thank you very much for visiting my site.


  5. Great post! Slonimsky also created a “Thesaurus of Scales and Melodic Patterns” that influenced many modern composers and jazz musicians. He was a frequent guest on Johnny Carson’s “Tonight Show”. Music and mathematics – perfect partners!

    Liked by 1 person

  6. Wow … this was fun! Definitely one I need to keep coming back to to really absorb. It really needs more of a middle of the day read when my brain is fully engaged, rather than the early morning fog that my brain is in presently! I think I’ll re-blog this too …

    Liked by 1 person

  7. Really enjoyed this post! I was recently thinking about palindrome numbers at work today and wondered if there was any connection to events of synchronicity in life. I’m also enjoying a wonderful mathematical book called, “Gödel, Escher, Bach: An Eternal Golden Braid”. Thank you for stopping by my blog! 🙂

    Liked by 2 people

  8. Lovely collection of facts as usual. Can’t take all this in at once so will keep coming back! I hope you don’t give us a pop quiz like we had at school! Thanks for posting and keeping my brain alert.

    Liked by 2 people

  9. You have a fascinating web site. I wrote a post several months ago about mathematics being the cosmic language. When the “little green men” come for a visit, we will communicate using math and not verbal language. Thank you so much for taking a look at GQ. Take care.

    Liked by 1 person

  10. I love math but got stuck on the palindrome with even numbers always being able to be divided by 11. If you take 2, 4, 6 & 8 and 8, 6, 4, 2….both add up to 20 and neither can be divided by 11. Where oh where did I go wrong?

    Loved your post. Oh by the way, Abbott and Costello’s girl never reaches the same age as her fella, right?

    Liked by 2 people

  11. A Matemática é maravilhosa…..desde a mais tenra idade eu dizia isso para meu filho….fazia brincadeiras usando a matemática…..dados….pregava a tabuada pela casa….perto da tv….no quarto….no banheiro…..eu não queria que ele não gostasse da matemática como a maioria das pessoas, e eu sempre gostei muito…..acho que minha intenção valeu…..hoje em dia ele faz MATEMÁTICA na melhor universidade daqui….minha maior alegria……(parabéns pelo seu blog)
    The Mathematics is wonderful ….. from the very young age I said this to my son …. made jokes using math ….. data …. preached the table by the house …. near the tv …. in the bedroom …. in the bathroom ….. I did not want him to dislike math like most people, and I always liked it ….. I think my intention was worth it .. … nowadays he does MATH in the best university here … my greatest joy ……(Congratulations on your blog)

    Liked by 1 person

  12. A mathematical problem from the minds of Abbott & Costello.
    A girl of 10 was seeing a man of 40. Her parents said he was 4 times older than her, so didn’t want her to see him.
    So the girl waited 5 years. She was 15, he was 45. Now he is only 3 times older than her, but her parents still weren’t happy.
    So she waited another 15 years. She was 30 and the man was 60, only 2 times older than her.
    The question is, how long did they have to wait until they were the same age?

    Liked by 2 people

  13. From the brilliant minds of Abbott & Costello (not mathematicians).
    A girl, 10 years of age, was seeing a man of 40. Her parents pointed out that he was 4 times older than her.
    So the girl waited for 5 years. She was now 15 and the man 45, now he was only 3 times older than her, but her parents still disapproved.
    So she waited for another 15 years, she was now 30 and the man was now 60, only twice as old as her.
    How much longer did they have to wait until they were the same age

    Liked by 1 person

  14. As to your number 70–the product of two prime numbers can never be a perfect square…isn’t the number 1 a perfect square AND the product of two primes (1 x 1 = 1)? Let me know if I am wrong (thinking maybe the number 1 is NOT a prime number?)

    Liked by 3 people

  15. Thank you so much for visiting and ‘liking’ my Photo Blog! I have to say that your post has frightened the life out of me …. I think I must be a mathematical dislexit – my brain just isn’t wired up properly for it and the fuse just blows!! I run for refuge to making pictures, but even then, it’s hard for me to get my head around the maths of my camera, but I persevere cos the end result is worth it (I hope!)

    Liked by 1 person

    1. Like you, this is like a foreign language to me. I am almost 60, and still can not do division without a calculator. But it didn’t stop me from being given a job calculating doctors financial claims. It did however stop me from keeping it. The boss was happy with my work, if a bit slow, but it was too much for me and I was getting too stressed just doing fairly simple calculations. I admire anyone that can do this.

      Liked by 2 people

  16. 25. From 0 to 1000, only the number “one thousand” has the letter “A”.
    Sorry, that is wrong. There are one hundred and one, one hundred and two etc.
    Why not replace it with this:
    “TWELVE PLUS ONE” is an anagram of “ELEVEN PLUS TWO.”

    Liked by 1 person

    1. This is just the difference between British and American English usage. For example, AE uses “one hundred one” and “one hundred sixty·five” while BE uses “one hundred and one” and “one hundred and sixty-five”.

      Both usage is correct and in Hong Kong, both are accepted, albeit the AE usage is more common especially for writing checks as it looks neater. For example, $125.40 is written as “one hundred twenty-five and fourty cents”.

      Liked by 1 person

    2. Remember that in America they don’t use the ‘and’. The numbers are just one hundred, one; One hundred, two; etc.
      But then again, Americans do terrible things, for a simple example; British call dealing with numbers MATHS, but in America it is singular…MATH.
      But that is countered by their champions, who might be Worlds champion, although they only competed in one world. (and often they only compete in America, like their football teams. They win the American NFL competition, but become worlds champion).


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