Phi 1.6180339887498948…
Phi is the golden ratio. It splits a line so that the whole is to the longer part as the longer part is to the shorter part.
Where it appears. Fibonacci numbers, the angle between leaves on a stem, pentagons, and proportions in art and design.
Read the full explainer or train the digits below
Learn Phi
About PlayMemorize Pi
PlayMemorize Pi trains you to memorise pi and seven other mathematical constants using the numpad path method · each digit maps to a unique finger position on a 3×3 keypad, so the sequence is stored as visual, spatial, and motor memory at the same time, not just as a string of sounds.
Three modes for one progression. Study reveals the upcoming block so you can rehearse before testing yourself. Learn keeps the six digits on screen, outlines the next key, and draws your path behind you. Play hides everything and runs a pure-recall streak. Switch between modes inside a single session as a block becomes familiar · the same digits, three angles of attack.
Eight digit trainers in total. Pi to 12,000 digits, plus dedicated trainers for e (Euler's number), the golden ratio φ, tau (τ = 2π), √2, ln 2, γ (the Euler-Mascheroni constant), and a prime-number sequence trainer. Each constant keeps its own independent progress slot, so you can drill them in parallel without overwriting your pi record.
Why the numpad path works. A phone-style 3×3 keypad has nine spatial positions plus zero. Every digit you tap traces a path · 314 goes top-right, top-left, middle-left, and 159 goes top-left, centre, bottom-right in one straight diagonal. After a few sessions, common bigrams (94, 26, 53, …) feel like a single gesture rather than two separate digits. Reciting pi to a friend, you'll still tap the rhythm with your finger.
40+ reference articles included. Around the trainers sit short explainers for the constants and the mathematics they come from · the Basel problem, the Gaussian integral, the Wallis product, the Gamma function, Stirling's approximation, the prime number theorem, transcendental and irrational numbers, continued fractions, Euler's identity, de Moivre's formula, the Riemann zeta function, Apéry's constant, the Champernowne and Liouville constants, the Conway, Feigenbaum, Gelfond, Khinchin, Lévy and Meissel-Mertens constants, the silver, plastic, and tribonacci ratios, and more. A dedicated flashcards page holds 48 decks and more than 480 cards on those constants and theorems · it drills the mathematics with spaced repetition, not the digits.
Part of the PlayMemorize family of brain-training games. Runs entirely in your browser, works offline as a Progressive Web App.
FAQ
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How many digits of pi can I memorize?
PlayMemorize ships up to 12,000 digits of pi, plus seven other digit trainers: e (Euler's number), the golden ratio φ, tau (τ = 2π), √2, ln 2, γ (the Euler-Mascheroni constant), and a prime-number sequence trainer. Each constant has its own independent progress slot. Around the trainers sit 40+ reference articles on related mathematical constants and concepts. -
How does my progress save in the Pi Trainer?
Your furthest digit reached is stored locally in your browser for each constant, so coming back tomorrow picks up exactly where you stopped. Sign in to sync the same progress across phone, tablet, and desktop. -
What memorization method does it use?
The numpad path method. You tap digits on a phone-style 3×3 keypad and each tap traces a spatial path your finger learns through repetition · 314 goes top-right, top-left, middle-left, and 159 goes top-left, centre, bottom-right in one straight diagonal. After a few sessions, common bigrams feel like a single gesture, so recall combines visual memory with motor memory rather than relying on verbal rehearsal alone. -
Can I practice specific digit ranges?
Yes. Study mode reveals an upcoming block so you can rehearse it. Learn mode shows one group at a time with the next key outlined, and a grid under the pad jumps you to any group. Play mode hides everything for a pure-recall streak run. The flashcards page is separate · its 48 decks cover the mathematics, not the digits. -
Why does pi matter?
Pi appears wherever a circle, an oscillation, or a wave shows up · the circumference of a wheel, the period of a pendulum, the Gaussian curve in statistics. Memorising digits is a memory-training exercise; pi itself is one of the most useful numbers in mathematics, physics, and engineering. See the included articles on the Basel problem, the Gaussian integral, and the Wallis product for the standard derivations. -
Can I play offline?
Yes. PlayMemorize is a Progressive Web App. Install once and the Pi trainer plays without an internet connection · the digits, articles, and every constant are bundled at install time, so flights, commutes, and tunnels are all fair game. -
Can MemPi help me study and practice this game?
Yes! Click MemPi in the header or on the game board to summon him. He observes the board, thinks out loud, and can demonstrate moves or guide you through tricky steps.