# Happy Pi Approximation Day

**Online College Math Teacher**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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π Is defined as the ratio of a circle’s circumference to its diameter. π Is an irrational number (it cannot be expressed as the ratio of two integers), and it has an infinite number of non-repeating digits. Approximations of π date back to ancient civilizations and continue today as people compete to calculate π to billions of decimal places on supercomputers.

The 22/7 approximation only matches π to the second digit after the decimal place, 3.14, and 22/7 is greater than π, a fact known by Archimedes. The error in the approximation is only about 0.04%, which is close enough for most of us.

People also compete in the number of decimal places they can recite by memory such as using mnemonic techniques with words, where the length of each word represents a digit of π . There are many creative π mnemonics , but I am content to remember the 15 word “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”

A quite impressive feat is Apu from the Simpsons who claimed to be able to recite 40,000 digits of π, and proved it by correctly stating that the 40,000th digit is 1. Apu

The R computer language carries 15 or 16 digits. That seems like enough. A NASA engineer says he can’t think of a practical application that would require more than 15 digits of π . NASA

π appears in many areas of math besides geometry and trigonometry. It is hidden away in statistics where the probability density function formula of the normal curve has a √(2π) term in the denominator to get the integral equal to 1, and elsewhere in other branches of math.

Happy Pi Approximation Day.

Here is some R code:

library(dplyr)

library(tidytext)

# compare 15 digits of 22/7 to pi

print(22/7, digits=15)

print(pi, digits=15)

# count word length & number of words in this mnemonic

textfile <- c("How I need a drink",

“alcoholic of course”,

“after the heavy lectures involving quantum mechanics.”)

df<-data.frame(line=1:length(textfile), text=textfile)

df_words <- df %>% unnest_tokens(word, text) %>% mutate(word_length = nchar(word))

df_words

n <- nrow(df_words)

cat(“Number of words: “, n)

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**Online College Math Teacher**.

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