tau
Represents the mathematical constant equal to 2π (approximately 6.28318), defining the ratio of a circle's circumference to its radius.
Overview
A fundamental mathematical constant gaining popularity as an alternative to pi, particularly valued for its natural relationship to circular and periodic phenomena.
- Increasingly preferred in modern mathematics education for its more intuitive representation of full circle rotation
- Common in physics and engineering for angular frequency and periodic motion
- Appears frequently in trigonometry, signal processing, and quantum mechanics
- Simplifies many mathematical formulas where 2π would traditionally appear
Examples
Express the circumference of a circle in terms of radius using tau.
C = \tau r
Show the relationship between tau and pi.
\tau = 2\pi
Express the period of a simple harmonic oscillator using tau.
T = \tau\sqrt{\frac{m}{k}}