Prompt Cast
The Case for Using Tau Instead of Pi in Mathematics
TLDR The use of pi in mathematics to represent the ratio of the circumference to the diameter of a circle has caused unnecessary confusion. Some mathematicians argue for the adoption of tau, which would simplify calculations and make mathematics easier to understand.
Timestamped Summary
00:00
The world of mathematics has been teaching in a way that's unnecessarily confusing and complicated, causing generations of students unnecessary headaches.
01:46
The problem is that when defining the most important ratio found inside every circle, we use the diameter rather than the radius, even though it's the radius that defines the circle.
03:25
The calculation of the circle ratio using pi and the diameter rather than the radius goes back to antiquity, but the modern usage of pi to represent the ratio of the circumference to the diameter is attributed to the Swiss mathematician, Leonhard Euler, in the 18th century.
05:04
In his book, Euler defined pi as half the circumference of a circle of radius one, which is why one circle is equal to two pi and half a circle is equal to pi.
06:55
The mathematician Robert Palais argued for using a single constant, tau, to represent two pi, suggesting that a circle should be considered one turn instead of two pi.
08:41
Since 2010, there has been a movement for the adoption of tau amongst mathematicians, with some programming languages and educational platforms already accepting tau instead of pi.
10:20
Mathematics would be simpler and easier to understand if tau had originally been adopted as the circle constant rather than pi.
