Tau (τ) is a mathematical constant that is the ratio of a circle’s circumference to its radius. It is approximately equal to 6.28. Tau has a long history that can be traced back thousands of years to ancient mathematicians who studied circles and pi. Here is an overview of the key events and figures in the development of tau throughout history.
Ancient Origins
The origins of tau can be traced back to ancient Egypt, Mesopotamia, and the beginnings of geometry in ancient Greece. The Egyptian Rhind Papyrus from around 1650 BC features a problem involving the area of a circle. The solution uses a value of 256/81 (approximately 3.16) for pi. This shows that the Egyptians had estimated the ratio between a circle’s area and radius squared. However, they did not have a specific symbol or word for this ratio.
In ancient Babylon, clay tablets from around 1900-1600 BC show that mathematicians had calculated the ratio of a circle’s circumference to its diameter as approximately 3 1/8. This is equivalent to a tau of 6 1/4. The Babylonians used their sexagesimal (base 60) number system to make these approximations. Again, there was no specific term like “pi” for this ratio.
When geometry emerged in ancient Greece in the 6th century BC, Greek mathematicians began studying circles more systematically. They proved theorems about the relationships between circles, circumferences, areas, radii, and diameters. The Greek mathematician and philosopher Anaxagoras (c. 510-428 BC) is sometimes credited with first stating the mathematical relationship tau = C/r.
Introducing Pi
It was the ancient Greek mathematician Archimedes (c. 287-212 BC) who is traditionally considered the first person to calculate pi as the ratio of a circle’s circumference to its diameter (C/d). He approximated pi as lying between 3 1/7 and 3 10/71. Interestingly, Archimedes did not actually use the term “pi” in his writings on circles – this was introduced in later centuries.
The first recorded use of the Greek letter π for this constant came in 1706 when William Jones introduced it in his book Synopsis Palmariorum Matheseos. This work covered key mathematical results and helped popularize the use of π. The word “pi” also derives from the Greek word for perimeter “perimetros”.
With pi defined as C/d rather than C/r, this led mathematicians to focus on approximating the constant equal to a circle’s circumference divided by its diameter. Approximating tau = C/r was less common once pi became the standard. However, the constant tau still featured occasionally in mathematical circles.
Rediscovering Tau
In 2001, Bob Palais, a math professor at the University of Utah, wrote an article titled “Pi is Wrong”. Palais argued that tau = C/r is a more natural and intuitive ratio to use than pi = C/d when working with circles. He pointed out advantages such as:
- Tau makes formulas involving circles and angles simpler
- Tau reflects the symmetry between a circle’s radius and diameter better
- Tau aligns better with how people visualize circles
Palais’ article helped ignite interest in tau among some mathematicians and teachers. Supporters of tau say that schools should teach tau alongside pi to provide a more comprehensive understanding.
In 2010, Michael Hartl authored the famous essay titled “The Tau Manifesto”. This influential work made a vigorous case for the use of tau over pi and is considered one of the seminal modern works promoting tau. Hartl later published a book called Tau Day: Why 6.283185… Is Greater Than 3.141592… to further advocate for tau.
Recent Developments
While pi remains the predominant choice in mathematics and science, tau has gained greater visibility and use over the past couple decades. Here are some key developments spreading awareness of tau:
- June 28 (6/28) was designated as Tau Day in 2010 to celebrate tau’s value of approximately 6.28.
- Some textbooks and teachers now introduce tau alongside pi when teaching circles.
- Tau is receiving more coverage in books, articles, videos, and websites explaining its possible advantages.
- Computer language Python adopted tau as a built-in constant in Python 3.6 in 2016.
Organizations such as The Tau Manifesto Foundation have formed to promote the use of tau in education and mathematics. While pi remains deeply entrenched, tau is slowly gaining more acceptance.
Key Figures in Tau’s History
Here is a summary of some of the most important people, events, and milestones in tau’s long history:
| Date | Event/Figure | Significance |
|---|---|---|
| 1650 BC | Egyptian Rhind Papyrus | First evidence of using C/r ratio |
| 1900-1600 BC | Babylonian clay tablets | Approximated tau as 6 1/4 |
| 6th century BC | Anaxagoras | First stated tau = C/r formula |
| 3rd century BC | Archimedes | Approximated pi based on C/d |
| 1706 | William Jones | Introduced pi symbol |
| 2001 | Bob Palais | “Pi is Wrong” article |
| 2010 | Tau Day inaugurated | Celebrates tau on June 28 |
| 2010 | The Tau Manifesto | Influential essay by Michael Hartl |
Conclusion
While pi emerged in ancient Greece and became the standard constant, tau has very old origins tracing back to Egyptian and Babylonian mathematics. After being overshadowed by pi for centuries, tau is gaining renewed interest and advocacy thanks to modern mathematicians. But pi is still the primary circle constant used in math and science. The debate between supporters of pi and tau continues as to which represents circles in the clearest, most natural way.