Pi There to Stay

Some of you who read the Daily News of 6^th July, 2011 may have read the article entitled Mathematicians want to say goodbye to Pi, it was a thrilling article although no specific author claimed it. Maybe it originated from the internet where the issue of Pi has attracted a lot of debate. However the article mentions some names including quotations to which references can be made. I wish, in this article, to react to some of the arguments presented.

Let me start with Bob Palais essay title Pi is wrong!. If you read the article carefully you will discover that there is nothing wrong about Pi. These were just catch words to attract attention. The article said, “Palais argued that, for thousand years, humans have been focusing their attention and adulation on the wrong mathematical constant” Palais admits that both 3.14 and 6.28 are ratios of the circumference to diameter and circumference to radius respectively. Both are good approximations of the relevant ratio and they are mathematical constants.  The 3.14 is an approximation for Pi whereas the 6.28 is an approximation for tau. Both constants have a right to exist. So there is nothing wrong with Pi. The constants have been given different names.

The article claims that diameter is a largely irrelevant property in geometry! This is a bit difficult to accept. We all know how the diameter in important in geometry especially in circles. We may recall the important theorem about the angle subtended at the circumference by the diameter. The angle subtended at the circumference by the diameter is a right angle! Those who have studied Geometry know how useful this theorem is especially when used as an application to the Pythagoras theorem. In many circumstances, diameters are easier to measure. The centres for most cylindrical objects such as wires and pipes cannot be located. Such objects are easily measured by vernier calipers and micrometer screw gauge.

We know historically, the concept of the ratio of circumference to diameter has been there thousands of years ago. We are told that even the legendary Archimedes who is well know for the Archimedes principle used it in his geometrical activities. He is also said to have estimated the ratio to 3¹/₇  or²²/₇  as some people know it today. The ration continued to be used in circle calculations (probably without a name) until William Jones proposed Pi in 1706. The 16^th Greek letter Pi represented the symbol π was accepted and used to ease the work of computations where the ratio of circumference to diameter were involved. The symbol has now been used comfortably over 300 years.

The new claim of introducing tau is just a mathematical extension of William Jones work. The relation is that 2Pi = tau (or 2 π = τ). That is why some people are thinking of the new constant tau. Those who celebrate tau day instead of Pi day have a right to do so but they will have got the idea from the teacher in Francisco who proposed Pi day. Celebration days have been given to constants such as Avogadro Day in October 23^rd and Euler in February, 7^th , We also know that there is little Pi Day on March 15^th and Pi Approximation Day on July 22^nd. In Tanzania we celebrate Pi Day on 14^th March.

Kelvin Houston’s explanation cannot be wholly accepted in spite of his you tube video. He talks of circular measures called radians in measuring angles. The radian measure is defined as one radian =180^o or π radians = 180^o.

π

 Houston writes it in a different way by multiplying both sides by 2        to obtain 2π = 360^o. The arguments given are quite valid for the whole circle. The diameter is clearly seen as a straight line and hence we have a straight angle measuring 180 degrees. The semicircle can be divided into two equal parts. Each half of the semicircle has 90^owhich is half Pi radians and a quarter of the semi-circle bearing 45 degrees will be quarter Pi radians. In trigonometry both π= 180 degrees and 2π=360^o  have equal footing since, for example,sin π = -1 and sin 2π = 0 and sin τ= -1 and sin τ = 0.  In calculus, the treatment is thesame. It is not clear from the article how “silly” errors are made by mathematics, physics and engineering students. Tend to believe that such errors.

The issue of simplifying computations by introducing a factor of 2 should not worry a mathematician. It is just a way of making life easier. In fact, a person using a calculator fitted with Pi will not face any problem if he/she uses it competently. I agree with Palais when he says that the opportunity to impress students with a beautiful and natural simplification has tuoned into an absurd memorization and dogma. The way some teachers present Pi is questionable. Some give formula without deriving them or giving the meaning of the attributers. Students end up memorizing. However, this would happen to tau if it follows the same trend.

I appreciate the news that tau advocates claim that they have noticed a significant improvement in the ability to learn math especially geometry and trigonometry where factors of 2Pi show upmost, when the students learn with tau rather than Pi this is usual in solving problems. In formulating equations from word problems some students prefer y to x or vice versa in their choice of variables. I tend to believe that the improvement was coupled with some other motivation factor not just tau. Houston of the university of leads in the UK who in pro-tau admits, “I am pro-tau, Hence, anyone could use Pi when they had a calculation involving half a tau”

In Tanzania primary school Pi is taught in Kiswahili. In secondary schools it is taught in English. The mathematics syllabuses for both levels demand that the students should know the meaning of Pi and how to use it in calculations involving circles. At primary school there is a word for diameter called  “kipenyo”. Radius is “nusukipenyo” therefore using radius in the definition will make it more cumbersome. So primary schools will continue with Pi despite the proposed new definition. Secondary schools and higher levels should not worry about the suggestion because they use both radius and diameter inclusively.

An interesting thing the article did not mention is the square of Pi which is approximately equal to ten. Tau squared is approximately equal to forty. Ten is easier to work with than forty. This favours Pi. It reminds us of a book called Power and Root get married in which power two requested Pi to accept to be changed into ten when he sits on her top right side so that they could be married. The last paragraph of the article clearly admits the difficulty expected in the proposed change. “Pi is too ingrained in our culture to succumb to tau overnight” in fact they can co-exist and probably Michael Hart and Peter Harremoes may later be honored for suggesting tau the 19^th letter of the Greekalphabet to represent 2Pi. Therefore Pi is there to stay.

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