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How to Memorize Pi

written by: Bruno Kos • edited by: Donna Cosmato • updated: 8/2/2012

Would you like to know how to memorize thousands of Pi number digits? Well, this is not where you will get an answer. Instead, you will find out how to memorize up to 24 Pi digits, which is quite enough to impress your friends or teacher.

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    Pi (π) is a well-known mathematical constant, which is defined as a ratio of any circle's circumference to its diameter in Euclidean space. It is widely used in mathematics, science, and engineering as part of numerous formulas.

    In the standard decimal notation, Pi equals approximately 3.14159265. The concept of π has become a part of the popular culture, probably due to the simplicity of its definition.

    Furthermore, Pi is an irrational number, and its decimal representation never repeats and ends. Because of this, it is not easy to memorize it, and as a result, techniques on how to memorize Pi were invented.

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    Pi is used in many science areas. It’s used in geometry and trigonometry, complex numbers and calculus, physics and probability, and statistics among others. As mentioned already, it finds its place in numerous formulas, but it is even used in fields with no obvious connection to the circles of Euclidean geometry.

    Numerous techniques for memorizing Pi are available. Some of them are more than enough for a student, as they provide a method to memorize a “reasonable" number of digits, while on the other side, there are some techniques that provide solutions for how to remember hundreds or thousands of digits.

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    Technique #1: Mnemonics

    An easy method for memorizing Pi numbers is by using a sentence (mnemonics) where the number of letters in each word represents a Pi digit.

    Consider the following example. If the letters in words are counted: May (3) I (1) have (4) a (1) large (5) container (9) of (2) coffee (6), the result is 3.1415926.

    In order to memorize a few more digits, use this sentence: How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics! If the same method described above is applied, it results in the first 15 digits of Pi, or 3.14159265358979.

    Here is another sentence, which can be used to memorize 22 digits: Wow! I have a great technique to recall those fun, crazy numerals composing perhaps everyone's all-in-all favorite real number—Pi!

    It is obvious, though, that the efficiency of this method is decreasing as the number of Pi digits is increasing. More specifically, 30 digits is usually the limit, mostly because a zero appears.

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    Technique #2: Phonetic Code

    The phonetic code method is a bit more complicated, but can yield much better results. First, each digit must be assigned a corresponding letter: 1 = t or th or d; 2 = n; 3 = m; 4 = r; 5 = l; 6 = sh, ch, or j ( soft g); 7 = k or hard g (like in a goat); 8 = f or v; 9 = p or b, 0 = s or z. In order to clarify this method, consider the following sentence:

    "My turtle Pancho will, my love, pick up my new mover Ginger.“

    If phonetic code (as defined above) is applied to this sentence, 24 digits can be remembered. One is only required to find a corresponding letter (wherever possible, of course, as not all letters are used) from the phonetic code and “translate" it into a number:

    Consider the first two words: “My turtle". In the phonetic code, M=3, while the letter “y" does not have a corresponding phonetic code. For simplicity's sake, we will use the term “no match" hereafter to refer to these letters. So, on examining the word “turtle" we find: t=1, u=no match, r=4, t=1, l=5, e= no match. In other words, first two words “contain" the Pi digits: 3.1415.

    Let’s consider the phrase “Pancho will". P=9, a=no match, n=2, ch=6 (be careful you don’t omit digraphs!), o=no match, w=no match, i=no match, l=5, second “l" omit. If two or more letters are in a row, use only the first one.

    Finally, consider the “Ginger" word. “G" in this word is soft “g", so g=6, i=no match, n=2, g (soft)=6, e=no match, r=4.

    If this rule is applied to all the words, 24 digits can be extracted: 3.14159265358979323846264. Do not forget that this method requires lots of practice.

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    Technique #3: Memorizing

    If the first two methods do not suit, a student can choose a traditional method such as memorizing three, four, or five digits and repeating them over and over until they are learned. Naturally, some students find this method more convenient, as not all are equally as good with numbers. Memorizing the Pi number can also turn into fun, and there are even competitions concerning memorizing and reciting digits of Pi. For example, Mr. Akira Haraguchi really knows how to memorize Pi, as he is currently a world record holder. On October 3, 2006, he was able to recite an amazing 100,000 digits in 16 hours.

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    Ivars Peterson: Mathematical treks: from surreal numbers to magic circles, MAA, 2002