# Tau versus pi | Graphs of trig functions | Trigonometry | Khan Academy | Summary and Q&A

194.4K views
July 11, 2011
by
Tau versus pi | Graphs of trig functions | Trigonometry | Khan Academy

## TL;DR

Pi is traditionally known as the ratio of the circumference of a circle to its diameter, but some argue that measuring angles in terms of tau (2 times pi) is more intuitive and elegant.

## Install to Summarize YouTube Videos and Get Transcripts

### Q: How is pi traditionally defined?

Pi is traditionally defined as the ratio of the circumference of a circle to its diameter, or the circumference to 2 times the radius.

### Q: How are angles in radians measured?

Angles in radians are measured by the length of the arc subtended by the angle, with the arc length being in terms of the radius.

### Q: What is tau and how is it related to pi?

Tau is defined as 2 times pi, or tau = 2pi. It is proposed as a more intuitive way to measure angles, as one revolution around the unit circle is equal to tau radians.

### Q: What is the significance of measuring angles in terms of tau instead of pi?

Measuring angles in terms of tau simplifies the conversions between radians and revolutions around the unit circle, making it more intuitive to determine angle measures.

## Summary & Key Takeaways

• Pi is defined as the ratio of the circumference of a circle to its diameter, or the circumference to 2 times the radius.

• Angles in radians are measured by the length of an arc subtended by the angle, with the arc length being in terms of the radius or "radiusi."

• Tau, defined as 2 times pi, is proposed as a more intuitive way to measure angles, as one revolution around the unit circle is equal to tau radians.