π
The ratio of a circle's circumference to its diameter.
3.1415926535...
This abstract explores Pi (π), one of mathematics' most revered and mysterious constants. This application transforms a comprehensive technical report into a dynamic journey. Scroll down to trace its history, uncover its properties, see its applications, and explore its infinite digits.
The Quest for Pi
For nearly 4,000 years, humanity has been on a quest to calculate Pi. This interactive timeline highlights key milestones, from the practical approximations of ancient civilizations to the rigorous calculations that defined entire eras of mathematics. Click on any point to learn more about that discovery.
The Nature of Pi
Pi is more than just a number; it possesses fundamental properties that place it in a special class of mathematical objects. This section explores three key characteristics that define the deep and enigmatic nature of Pi. Understanding these properties reveals why Pi is so central to mathematics.
Irrational
Pi is an irrational number, meaning it cannot be expressed as a simple fraction of two integers (like a/b). First proven by Johann Heinrich Lambert in the 1760s, this means its decimal representation is infinite and never settles into a permanently repeating pattern.
Transcendental
Proven by Ferdinand von Lindemann in 1882, Pi is also a transcendental number. This stronger property means Pi is not the root of any non-zero polynomial with rational coefficients, which famously proved "squaring the circle" impossible with only a compass and straightedge.
Normal? (A Mystery)
It is widely conjectured, but not yet proven, that Pi is a "normal" number. This means any sequence of digits appears as often as any other sequence of the same length. While statistically supported, a formal proof remains a great unsolved problem in mathematics.
Pi in Our Universe
Pi's influence extends far beyond pure geometry, appearing in formulas that describe the universe at every scale. From the mathematics that underpins our digital world to the physics governing stars and atoms, Pi is a fundamental constant of reality. Select a domain below to explore its diverse applications.
Calculating Pi's Digits
The quest to compute Pi is a story of human ingenuity. The chart below visualizes the explosive growth in calculated digits since the advent of computers. The explorer below lets you search the first 100,000 digits to find patterns and their exact locations.
Growth of Computed Digits of Pi
Pi Digits Explorer
Search for a number sequence (e.g., a birthday MMDDYY) in the first 100,000 digits of Pi. The famous Feynman Point (999999) can be found at postion 762.