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Fun Facts About the Number 55

The number 55, like other repeated digit numbers such as 666 and 1111, is often thought to have mystical properties. Fifty-five is an age at which many people start to feel old. In mathematics, 55 is a semi-prime number, a number that can be expressed as the product of two prime numbers. The 55th sonnet of Shakespeare is one his best-loved poems. Here are more fun facts and useless bits of trivia about the number 55.

Shakespeare's Sonnet 55
Shakespeare's Sonnet 55

11 Math Facts about 55

  • The sum of the digits of 55 is 10.
  • 55 is the 10th triangular number, aka the sum of the first 10 positive integers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.
  • 55 is also the 10th Fibonacci number: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The only numbers that are both Fibonacci numbers and triangular numbers are 1, 3, 21, and 55.
  • 55 is the fifth square pyramidal number, aka the sum of the first five squares: 1 + 4 + 9 + 16 + 25 = 55.
  • The heptagonal number sequence is 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, .... Thus, 55 is also the fifth heptagonal number.
  • The square of 55 is 3025, and 30 + 25 = 55.
  • 55^55 is a number with 96 digits.
  • 55! (factorial) is a number with 74 digits.
  • 36 is a number with many interesting properties and the sum of the proper factors of 36 is 55: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55.
  • There are many ways to arrive at the number 55 using five 5s and various arithmetic operations. For instance, 5 x [5 + 5 + (5/5)] = 55, and (5 x 5) + (5 x 5) + 5 = 55.
  • The quadratic residues of 55 are 0, 1, 4, 5, 9, 11, 14, 15, 16, 20, 25, 26, 31, 34, 36, 44, 45, and 49. Their sum is 385, which is a multiple of 55.

The Number 55 in Science, History, and Pop Culture

  • 55 miles per hour is a common speed limit and has often been proposed as a maximum speed limit on highways.
  • The atomic number of the element cesium is 55. Cesium (abbreviated Cs and also spelled caesium) is the softest element with a hardness of 0.2 mohs.
  • The state of California in the United States has 55 electoral votes in the electoral college, more than any other state.
  • The unicameral legislature of São Tomé and Príncipe, called the National Assembly, has 55 seats.
  • Fifty-five in Roman numerals is LV.
  • Fifty-five in binary is 110111.
  • "55 Days at Peking" from 1963 is the most notable film with the number 55 in its title.
  • The 55th episode of "The Simpsons" was "Colonel Homer," in which Homer manages a waitress's country music career.
  • The 55th episode of "Mad Men" was "Tea Leaves," in which Betty learns she has cancer.
  • The 55th episode of "South Park" was "Chef Goes Nanners," in which Kenny explodes by eating antacid tablets.
  • 55 Cancri is a binary star in the constellation of Cancer. It consists of a yellow dwarf and red dwarf.
  • Reclusive Massachusettes poet Emily Dickinson died at age 55.
  • Oklahoma-born humorist Will Rogers also died at age 55. One of his most popular quotes is "Good judgment comes from experience, and a lot of that comes from bad judgment."
  • The address of the National City Bank Building, a New York City landmark in the financial district, is 55 Wall Street.

55 Wall St., NYC
55 Wall St., NYC

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Comments 2 comments

LD 7 weeks ago

I noticed this pattern:

5 is 5th fibonacci number and 5th integer.

55 is 10th fibonacci number and 10th triangular number.

144 is 12th fibonacci numer and 12th square number.

It's "X is the nth fibonacci number and the nth ___ number. Are there any more fibonacci numbers like this besides 5, 55 and 144?


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calculus-geometry 7 weeks ago from Germany Author

Hi LD, thanks for the great questions. The answer is yes, but the way to get them might be disappointingly trivial. If F(n) is the nth Fibonacci number, then it is possible to create another non-Fibonacci sequence that has F(n) as its nth term. Often, the easiest way is to concoct simple linear sequences.

For example,

34 is the 9th Fibonacci number and the 9th positive integer of the form 4k - 2.

233 is the 13th Fibonacci number and the 13th positive integer of the form 18k - 1.

46368 is the 24th Fibonacci number and the 24th positive integer of the form 1932k.

It turns out that F(5^m) is always divisible by 5^m, so there are infinitely many Fibonacci numbers that have the same index in the Fibonacci sequence as in a linear sequence.

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    TR Smith (calculus-geometry)214 Followers
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    TR Smith is a mathematician, programmer and product designer who has taught math for 30 years, and uses it every day.



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