Contrary to popular belief, pi is not equal to 22/7

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

15 October 2006

Reader Paul Ngotho sent in a couple of questions: He says, “We are told that a month is made of 4 weeks. A week is made up of 7 days. If we multiply this by 4 we get 28 days. This is the number of days that we could be getting in a month. How then do we have some moths having 30 days and others 31 days? Secondly, we are told that a year (not a leap year) has 365 and 1/4 days. Can you please explain to me how we get a 1/4 day?”

Well Paul, the problem is that you got the definitions wrong. A month is NOT equal to four weeks. In fact a month is not even defined in terms of the number of days but in relation to a year! It is one of the twelve divisions of a year. That does not imply in any way that months are equal in duration. Thus some have 28 days, others 30 and 31.

Since a calendar year has 365 days, it turns out that, on average, a month is 30.42 days long. This is about 4.35 weeks (4 weeks and 2 days) or approximately 4 weeks. Now you took this approximation as the definition of a month. Consequently, when you work backwards, your numbers don’t add up correctly.

But don’t lose heart; you are not alone: There is another common misconception that arises from a definition turned inside out. In mathematics, there is a constant known as pi. It is used in the calculation of the circumference of a circle. Its value is approximately 22 divided by seven (22/7) or 3.14. It is defined as the ratio of the circumference to the diameter of a circle.

Unfortunately, many teachers tell their pupils that pi is exactly 22/7 and approximately 4.14. This is NOT true. If you divide 22 by seven, you get 3.142857142857142… (rounded off to 15 decimal places).  Notice that the decimals repeat after every six digits (142857). But the value of pie (to the same accuracy) is 3.141592653589793…

The truth is that 22/7 is an approximation that gives the value of pi accurate to only two decimal places! A better fraction would be 355/113 – it works out to 3.1415929… (six decimals accuracy)

Regarding the question of the quarter day in a year, again the issue of definitions comes up. A year is defined as the duration taken by the earth in making one complete revolution around the sun. That is about 31,558,150 seconds, or 525969.167 minutes, or 8766.15 hours, or 365.256 days. Now the decimal value 0.256 is approximately equal to a quarter of a day.

Talking about definitions turned inside-out, were you taught that “Rotation is the spinning of the Earth on its axis” and that “Revolution is the motion of the earth around the Sun”? Well, what the teacher meant is that the Earth ROTATES on its axis and REVOLVES around the Sun. Is there any difference between my statement and the teacher’s version?