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Pi (π) - Monomath Math Dictionary
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Pi (π)

Geometry
rdππ = C/d ≈ 3.14159C = 2πr

📖 Definition

Pi (π) is the mathematical constant representing the ratio of a circle's circumference to its diameter, approximately 3.14159.

📝 Detailed Explanation

π = 3.14159265358979323846... is an irrational number, meaning its decimal representation never repeats or terminates. It is also transcendental (not the root of any polynomial with integer coefficients). π appears in countless formulas across geometry, trigonometry, calculus, physics, and probability.

📐 Formula

π = C/d  |  Area = πr²  |  e^(iπ) + 1 = 0

📜 History & Origins

Ancient Babylonians estimated π ≈ 3.125, Egyptians π ≈ 3.1605. Archimedes (250 BCE) bounded π between 3.1408 and 3.1429. William Jones first used the symbol π in 1706, and Euler popularized it. In 2022, π was computed to 100 trillion digits.

🔗 Related Terms

CircleRadiusDiameterAreaSineCosine
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Monomath Math Dictionary — Pi (π)

Constant

π (Pi)

Value: π ≈ 3.14159265358979323846...

Definition: The ratio of a circle's circumference to its diameter. π is an irrational and transcendental number.

History: π has been known for nearly 4000 years. The ancient Babylonians approximated it as 3.125, while the Egyptians used 3.1605. Archimedes (250 BCE) first used a rigorous method to bound π between 3.1408 and 3.1429. The symbol π was first used by Welsh mathematician William Jones in 1706 and popularized by Leonhard Euler.

Interesting facts: π's decimal expansion never repeats or terminates. March 14 (3/14) is celebrated as Pi Day. The current record for π digits is 100 trillion, computed in 2022. π appears in formulas across geometry, trigonometry, probability (Buffon's needle), and physics (Heisenberg's uncertainty principle).

Common formulas:
Circumference = 2πr
Area of circle = πr²
Volume of sphere = 4πr³/3
Euler's identity: e^(iπ) + 1 = 0