Special Pi Day Edition, by Carl Sagan

In his novel Contact, Carl Sagan described his character discovering a hidden message in the digits of pi:

"The Argus computer was so persistent and inventive in its attempts to contact Eleanor Arroway that it almost conveyed an urgent personal need to share the discovery.

The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeroes and ones. Compared with what had been received from Vega, this could be at best a simple message, but its statistical significance was high.

The program reassembled the digits into a square raster, an equal number across and down. The final line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros to the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, self-reflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame.

Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.

The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you‘re made of or where you came from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It's inside everything. You don‘t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great mark of art, there is, written small, the artist's signature. Standing over humans, gods, and demons, subsuming Caretaker: and Tunnel! Builders, there is an intelligence that antedates the universe.

The circle had closed.

She found what she had been searching for."