Pi vs. Tau: Do we have it all wrong?

From Math Goodies Blog:

One of the major contributions Archimedes (287-212 B.C) made to mathematics was his method for approximating the value of pi. For centuries, the number Pi, Greek letter (), has been the symbol for the ratio of the circumference of a circle to its diameter. In 1761 Lambert proved that Pi was an irrational number, which means that the digits never end or repeat in any known way. Throughout history, mathematicians have been fascinated with calculating the digits of Pi. In 1999, millions of digits were calculated at the University of Tokyo using a computer. In 2011 the record was improved to 10 trillion digits.

Each year, Pi Day is celebrated on March 14 by math enthusiasts around the world (3, 1 and 4 are the three most significant digits of p in the decimal form). The earliest known official or large-scale celebration of Pi Day was in 1988. In 2009, the United States House of Representatives supported the designation of Pi Day. Pi Day has become very popular in the mathematics community.

There is now an online movement to celebrate Tau, the number you get when you use a circle's radius instead. Tau is approximately 6.28, instead of the familiar constant Pi, which is 3.14. There is much opinion and controversy surrounding this new movement.

The idea of celebrating Tau is now at least 10 years old, having cropped up in a 2001 essay by Bob Palais called "Pi is wrong!" But it exploded on the Internet on June 28, 2010, when Michael Hartl launched the Tau Manifesto, which explains why pi is confusing and should be replaced with tau.

Click here to read the original Tau Manifesto.

Decoding Da Vinci: Finance, Functions and Art

by Tim Johnson

Dan Brown in his book, The Da Vinci Code, talks about the "divine proportion", an irrational number given the Greek symbol , as having a "fundamental role in nature". Brown’s ideas are not completely without foundation. The proportion crops up in the mathematics used to describe the formation of natural structures like snail’s shells and plants, and even in Alan Turing’s work on animal coats.

But Dan Brown does not talk about mathematics, he talks about a number, . What is so special about this number?

From rabbits to ratios

The divine proportion appears in Fibonacci's 1202 book on financial mathematics, the Liber Abaci. The Liber is a series of increasingly difficult problems (with solutions) that generations of apprentice merchants used to learn their trade in the middle ages. It was the textbook that taught Copernicus, who wrote about money before he wrote about planets, and Simon Stevin(1548 – 1620), who made mathematics useful and helped free the Netherlands from Spain.

One of the simpler problems Fibonacci used was on the business of breeding rabbits. Given that one pair of rabbits produces one other pair of rabbits a month, how many rabbits will there be after a year, assuming that we start with one pair?

To read more, click here for the full article.