The number π (pi) is called that because the Greek letter π was chosen to represent the ratio of a circle’s perimeter to its diameter. The letter π stands for the first letter of the Greek word “periphery” or “perimeter,” directly linking the symbol to the geometric concept it describes.
π represents a fundamental constant in mathematics. When measuring any circle’s perimeter (circumference) and dividing it by the circle’s diameter, the result is always the same irrational number approximately equal to 3.141592. This ratio does not depend on the circle’s size. This definition underpins the constant’s name and symbolic representation.
Before the use of π, mathematicians referred to this ratio and related concepts using various symbols and notations. Some wrote it as the ratio of two letters, such as π/δ (which likely stood for perimeter/diameter). Others used different letters. For example, John Wallis, around 1655, used a small square symbol in relation to 4/π while working on infinite products.
- In 1689, the mathematician Sturm used the letter **e** to represent the circle ratio.
- Oughtred in 1652 used π/δ to stand for perimeter and diameter ratio.
The modern symbol π for the circle constant was introduced by William Jones in 1706. In his work “Synopsis palmariorum matheseos,” Jones explicitly chose the Greek letter π to denote the ratio now known as pi (approximately 3.14159). He noted that the diameter is to the circumference as 1 is to π. Though he used π previously to mean perimeter, Jones formally applied it as the symbol for this mathematical ratio.
This new notation, however, was not immediately widespread. Leonhard Euler played a crucial role in popularizing the symbol. Initially, between 1732 and 1736, Euler used letters p and g for π and π/2. But from 1736 onward, specifically in works like “Mechanica sive motus scientia analytice exposita,” Euler began consistently using the Greek letter π.
Euler’s vast correspondence spread the notation further. The Bernoulli family, prominent mathematicians, shifted from using other symbols (for example, ‘c’ for circumference) to adoption of π by the 1740s. Over the 18th century, the notation became more common in textbooks and mathematical literature, despite occasional alternative symbols still appearing. By the end of the century, π was well established in schoolbooks and academic texts as the standard notation for the circle constant.
| Timeline | Notation & Notes |
|---|---|
| Before 1650s | No standard symbol; varied notation, including ratios and letters |
| 1655 | John Wallis uses a small square for 4/π |
| 1689 | Sturm uses letter e for the ratio |
| 1706 | William Jones formally introduces π for the ratio |
| 1732–1736 | Euler uses p and g before switching to π |
| 1740s onward | Bernoulli family adopts π in correspondence and papers |
| Late 1700s | π becomes common in textbooks and schools |
The choice of the Greek letter π is intentional and meaningful. The Greek word for perimeter starts with π, making it a natural symbol for the circle’s perimeter divided by diameter. It connects the geometrical intuition to the symbolic representation.
Historical records, including Florian Cajori’s “A History of Mathematical Notations,” confirm this gradual adoption process, emphasizing the important roles played by William Jones and Leonhard Euler in standardizing π.
- π is the Greek letter representing the first letter of “perimeter” in Greek.
- It denotes the ratio of a circle’s circumference to its diameter.
- Early uses of π as a symbol for this ratio appeared in the early 1700s by William Jones.
- Leonhard Euler’s adoption and promotion helped popularize π widely by mid-1700s.
- By the late 18th century, π was the accepted standard in mathematical texts.
- The symbol links the mathematical concept directly to the idea of perimeter.
Why is the Number π (Pi) Called That?
The number π is called that because the Greek letter π stands for “perimeter” or “periphery,” reflecting its geometric meaning as the ratio of a circle’s perimeter (circumference) to its diameter. Simple enough, right? But the story behind this symbol and its adoption is quite a fascinating journey through history, math, and a little bit of “notation politics.” Let’s dive in.
First, let’s talk about what π actually means. Imagine any circle you want. Measure its perimeter, or circumference—say you’re wrapping a string around a cookie. Then measure the diameter, the distance across that cookie straight through the center. If you divide the perimeter by the diameter, that ratio is always the same no matter the size of the circle: approximately 3.141592…
In other words, π = perimeter ÷ diameter. This ratio is constant and fundamental to all circles. Kids learn the formula perimeter = π × diameter, but that often skips the original definition. The “magic” of π appears as the mysterious constant that links a circle’s border to its width.
The Origin of the Symbol π
The choice of the Greek letter π wasn’t random. It comes from the Greek word “περίμετρος” (perimeter) or “περίφραξις” (periphery). Both start with the letter π in Greek. Using the first letter of a word related to the shape or quantity was a practical thing. People love shortcuts.
But here’s a twist: the symbol π had been floating around since antiquity just as a letter ‘P’ to the Greeks. Its mathematical use wasn’t cemented for centuries. Back then, π was just a simple letter standing for many things.
Early Uses Before π Became a Thing
Long before π became Queen of the circle, mathematicians used all kinds of symbols, sometimes even inventing new ones. John Wallis, in 1655, was working on infinite products involving the number 4/π but didn’t use π yet—instead, he used a small square symbol. Odd, but true!
Another guy, Sturm, in 1689, used the letter “e” to represent the ratio of circumference to diameter. Confusing? Sure. At times, this ratio was written as a fraction of letters like π/δ, where π stood for perimeter, and δ meant diameter. It was more a puzzle than notation.
William Jones Steps Into the Spotlight (1706)
The story takes a turn when William Jones decided in his 1706 book Synopsis Palmariorum Matheseos to use the Greek letter π specifically to symbolize the constant 3.1415… This was the first intentional use of π as we know it today.
Jones explained π as the ratio of diameter to circumference, writing, “the diameter is to the circumference as 1 is to π.” That notation, however, didn’t catch on immediately. Mathematicians were still quite attached to their own favorite letters.
Enter Euler: The Popularizer of π
Leonhard Euler, one of math’s greatest rockstars, started using π in his works from 1736 onward. Before that, he sometimes used letters like ‘p’ and ‘g’ to represent π and π/2, but as his work gained popularity, so did his notation.
Euler was a prolific letter writer and correspondent. His letters to fellow mathematicians—like the Bernoulli family—helped spread π’s fame. By the mid-1700s, even the Bernoullis switched from using ‘c’ (for circumference) to the Greek letter π.
Slowly, but surely, π replaced the older, clunkier notations. By the late 18th century, π was standard enough to appear in schoolbooks, sticking as the symbol for that magical circle ratio ever after.
Why Does This History Matter?
Understanding why π is called π reveals a lot about how mathematical notation evolves. The symbol we see today wasn’t always obvious or inevitable. It reflects choices made for clarity, practical reasons, and the power of popular mathematicians.
If you’ve ever scratched your head over why math uses certain symbols, remember: behind every letter, there’s a story. π’s story connects ancient Greek geometry, 17th-century mathematical juggling, and 18th-century popularization—a neat slice of math history that shows notation is as human as numbers.
Practical Tips for Remembering π’s Story
- Think of π as the Greek letter “P” for “perimeter.” Easy to remember once you know its origin.
- Recall that π equals the circumference divided by diameter, the key relationship for circles.
- Remember William Jones named π, but Euler’s endorsement sealed the deal.
- Next time you use π, imagine the centuries-old quest to find the perfect symbol for this constant.
Quick Historical Timeline
| Year | Event |
|---|---|
| Ancient Greece | π used as the Greek letter “P,” meaning perimeter/periphery |
| 1655 | John Wallis works with 4/π but uses a small square instead of π |
| 1689 | Sturm represents circumference/diameter ratio with letter e |
| 1706 | William Jones introduces π as the symbol for 3.1415… |
| 1736 onward | Euler popularizes π in his works and correspondence |
| Late 18th century | π becomes standard in textbooks and academic works |
In Closing
Who knew a tiny Greek letter could hold so much history and mathematical power? The choice of π is an elegant nod to geometry’s roots and centuries of human curiosity.
Next time you see π, think of perimeter, diameter, ancient Greeks, and Euler’s letters—just a few examples of how math is a story told across time. And maybe, just maybe, π feels a little less mysterious and a lot more like a well-earned name.
For an in-depth read on the history of mathematical notations, Florian Cajori’s 1929 book A History of Mathematical Notations is the gold standard reference.
