The Square Root of Two to One Million Digits

A Journey Through Infinite Precision

Since the dawn of mathematics, the square root of 2 has stirred both awe and intrigue. First discovered in the context of a simple geometric puzzle—the diagonal of a unit square—it quickly revealed itself to be anything but simple. Ancient civilizations wrestled with its value, striving to grasp its elusive nature. The Babylonians offered the remarkably precise fraction 305470/216000, accurate to six decimal places. Centuries later, Indian mathematicians refined this with 577/408, correct to five decimal places.

And yet, both fell short of perfection.

Today, we know why: √2 is irrational. Its decimal expansion never ends, never repeats, and holds no hidden pattern—a whisper of the infinite written in numbers. Through clever algorithms and the power of modern computation, mathematicians can now compute this ancient enigma to astonishing lengths.

This book presents one million digits of the square root of 2, meticulously computed and beautifully laid out for exploration and reflection. Whether you're a student of mathematics, a teacher, a number enthusiast, or simply someone who marvels at the wonders of infinity, this book invites you to witness the sublime.

Use it to inspire, to teach, to meditate on the infinite—or simply to hold a tangible slice of the unreachable.