Pi Explorer
A Journey Through the Infinite
3.14159265358979323846264338327950288419716939937510…
Begin the Journey
A Journey Through the Infinite
Take any circle in the universe — from a grain of sand to a distant galaxy. Measure its circumference (the distance all the way around). Measure its diameter (straight through the centre). Divide one by the other.
You will always get the same number: 3.14159265358979…
This number never ends. It never repeats. Somewhere inside it, every sequence of digits that has ever existed — or ever will — is hidden, waiting to be found.
We call it Pi (π), and it is one of the deepest mysteries in all of mathematics.
Pi's decimal expansion never ends. Mathematicians have now calculated over 100 trillion digits — and it keeps going forever.
Pi cannot be written as a simple fraction. There are no whole numbers p and q where p ÷ q = π exactly.
Pi cannot be the solution to any algebraic equation with whole-number coefficients. It transcends algebra itself.
Pi appears in physics, probability, quantum mechanics, waves, and DNA — far beyond circles alone. It is woven into the fabric of the universe.
From the banks of the Nile to the courts of ancient China, every great civilisation on Earth independently discovered Pi — each finding their own piece of the infinite.
The Harpedonaptai use knotted ropes to map out circular temples and sacred spaces with remarkable accuracy.
π ≈ practical geometryThe proportions of Khufu's pyramid encode Pi in stone — perimeter ÷ twice the height ≈ π.
π ≈ 3.1435Clay cuneiform tablets record 25 ÷ 8 as the ratio of a circle's circumference to its diameter.
π ≈ 3.125Scribe Ahmes uses 256/81 to solve circular field area problems — only 0.6% off from the true value.
π ≈ 3.16049The Bible describes a great circular basin: "ten cubits across and thirty cubits around" — implying π ≈ 3.
π ≈ 3Ancient Vedic texts on constructing sacred fire altars contain precise π approximations for circular layouts.
π ≈ 3.088 – 3.141The first rigorous mathematical proof of π, using polygons with up to 96 sides inscribed in and around a circle.
3.1408 < π < 3.1429Using a polygon with 3,072 sides, Liu Hui calculates π to five accurate decimal places.
π ≈ 3.14159Calculates π to 7 decimal places and finds 355/113 — a record that would stand unbeaten for nearly 1,000 years.
π ≈ 3.1415929 ✦ World record × 1,000 yearsComputes 62832 ÷ 20000 and explicitly notes it is an approximation — a remarkably modern scientific attitude.
π ≈ 3.1416Jamshīd al-Kāshī of Samarkand computes π to 16 decimal places using a polygon with billions of sides.
π ≈ 3.1415926535897932 ✦ World recordWelsh mathematician William Jones is the first to use the Greek letter π in print to represent the circle ratio. The symbol spreads worldwide after Euler adopts it in 1737.
The symbol π is bornComputers have now calculated over 100 trillion digits of π. The journey that began with a knotted rope in ancient Egypt has no end in sight.
π = 3.14159265358979… ∞Egyptian scribe Ahmes copied a remarkable document now known as the Rhind Mathematical Papyrus. Problem 50 asks: "A circular field has diameter 9 khet. What is its area?"
Ahmes solved it by squaring 8/9 of the diameter:
This implies π ≈ 256/81 ≈ 3.16049… — only 0.6% off from the true value. Astonishing for 3,600 years ago.
The Great Pyramid of Khufu contains a stunning hidden ratio. Take its base perimeter and divide by twice the height:
Many scholars believe the architects intentionally encoded π into the pyramid's proportions — a monumental tribute to the circle, 4,500 years before the concept was formally named.
Ancient Egyptian surveyors — called Harpedonaptai (rope stretchers) — used knotted ropes to lay out fields, temples, and cities with extraordinary precision.
Marking curved temple walls and circular ritual spaces required understanding how far a circular path would travel. Their practical mastery of circles was passed down through generations, forming the living roots of formal geometry.
Without these rope stretchers, the great monuments of Egypt could never have been built.
Clay cuneiform tablets unearthed in Mesopotamia show that Babylonian mathematicians used 25/8 as their approximation for π:
Remarkably, some tablets suggest they also knew 3 + 1/8 = 3.125 was only an approximation — showing genuine mathematical self-awareness thousands of years ago.
The Bible (1 Kings 7:23) describes a great circular basin built for King Solomon's Temple:
This gives π ≈ 3 — a rough but functional approximation. Some scholars argue the text implies a more precise inner measurement that brings the ratio closer to the true value.
Archimedes of Syracuse was the first to rigorously calculate π using mathematics alone. He inscribed and circumscribed polygons with up to 96 sides around a circle, proving:
The symbol π itself comes from the Greek word periphery. It was the Welsh mathematician William Jones who first used the symbol in 1706.
The Sulbasutras (~800–200 BC) are ancient Vedic texts on constructing sacred fire altars. They contain precise π approximations used for laying out circular altars with exact areas.
Then in 499 AD, the great mathematician Aryabhata calculated:
He also noted it was an approximation — a remarkably modern scientific attitude.
Mathematician Liu Hui (263 AD) used a 3,072-sided polygon to calculate π to five decimal places. Then Zu Chongzhi (480 AD) went further, calculating:
This was the most accurate value in the world for nearly 1,000 years, and 355/113 remains one of the best simple fractional approximations of π ever found.
Islamic scholars translated and expanded upon Greek and Indian mathematics, preserving ancient knowledge during Europe's Dark Ages. Al-Khwarizmi (whose name gave us the word algorithm) used π = 3.1416.
By 1400 AD, Jamshīd al-Kāshī of Samarkand calculated π to an extraordinary 16 decimal places — the world record at the time — using a polygon with 3 × 2²⁸ sides.
March 14 (3/14) is celebrated as Pi Day worldwide. It is also the birthday of Albert Einstein! On March 14, 2015 at 9:26:53 AM the date and time spelled out 3.14159265358 — a once-in-a-century Pi moment.
At position 762 in Pi's digits, six 9s appear in a row: …999999… Physicist Richard Feynman joked he'd memorize Pi to that digit, then say "nine nine nine nine nine nine and so on" — making it sound like Pi was a repeating decimal!
NASA's Jet Propulsion Laboratory uses only 15 digits of Pi to calculate spacecraft trajectories to other planets. With just 40 digits you could measure the circumference of the observable universe with an error smaller than a single hydrogen atom.
Pi appears in what many call the most beautiful equation ever written: eiπ + 1 = 0. In one elegant line it connects five of mathematics' most fundamental constants: e, i, π, 1, and 0.
Pi governs the period of a pendulum, the way rivers meander across flat plains, the width of DNA strands, the shape of rainbows, and the fundamental equations of quantum mechanics. It is truly woven into the universe.
Drop a needle of length L onto parallel lines spaced L apart. The probability of it crossing a line is exactly 2/π ≈ 63.66%. This surprising connection lets you calculate Pi using pure physical chance — a technique called the Monte Carlo method!
The world record for memorising Pi is held by Rajveer Meena of India, who recited 70,000 digits in 2015. It took 9 hours and 27 minutes — and he wore a blindfold the entire time to prove there was no cheating.
In 1897 the Indiana state legislature nearly passed a bill that would have legally defined Pi as 3.2. A mathematics professor from Purdue happened to be visiting the capitol that day and convinced the senators to drop it permanently.
How many digits of π can you recite from memory? Type each digit after the decimal point. One mistake ends your run — but you can always try again!
📱 On mobile: tap the digit display, then use your number keyboard
Digits light up gold as you type them correctly.