Approximation in Real Life - a Story on Pi (π) from childhood spent in Tripura
Piyal Sarkar
March 14, 2024, 06:13:41
Pi Day is observed on March 14. This date is 3/14 in the month/day date format. 3, 1, 4 are the first three significant digits of π.
Approximation is a regular phenomenon in various fields of life. While doing mathematical calculations, precision is very important in some cases. Evaluation of the results may have to be done upto 2 or 3 or 4 places after decimal point depending on the problem. Approximation is carried out accordingly. For example, if the calculation gives money in Indian currency, approximation needs to be done upto 2 places after decimal as Paisa values are integers not exceeding 99.
During our school days in Agartala we were introduced to the constant π. We came to know that for calculating the circumference and the area of a circle, the constant π must be used. We learnt that 22/7 is an approximation of π, as an improper fraction, but 3.14159265 is a better approximation. The value of 22/7 is 3.14285714, which is different from 3.14159265 from the 3rd place after decimal point. We understood even in school days that this deviation does not make much of a difference in the problems that we were solving and 22/7 was used just to make things simpler to calculate/ evaluate. Later we came to know that π is also used for problems related to cylinder, sphere, hemisphere etc.
My Father was in the Forest Department of Government of Tripura. He did lots of work in the field of rubber plantations. One day during my childhood he was discussing the necessity to find the diameter of the trunk of a rubber tree. I do not remember the exact reason. He told that measurement around a tree trunk is taken using a measuring tape and then that length is divided by 3 to find the diameter of the tree. Initially, I did not understand what he meant. He made it clear that the ratio of circumference to diameter is π or 22/7, which is very close to 3. The staff members who had to calculate and note down the diameters of the tree trunks were not senior members of the department. In those days, it was not possible to provide them with calculators. The length around the tree trunk is the circumference which divided by 3 would approximately give the diameter of the trunk of the tree. Also, a tree trunk seems to be cylindrical in shape but it is not exactly a cylinder. The circumference will differ depending on the part of the trunk where the length is measured. I understood that π is being approximated as 3 here. While solving numerous problems with 2πr, πr^2, 2πrh, (πr^2)h, (4/3)πr^3, I hardly realised that whether it is 22/7 or 3.14, in real life where the accuracy is not very important, 3 is a reasonable approximation for π.
I never mean to say that we should replace π by 3 in all calculations. In science, technology and other domains there are problems where precision is very important. In these cases it is absolutely necessary to evaluate an expression properly and the result must be as accurate as possible. However it is clear from the example given by my Father that there are real life cases where it is possible to do approximation without thinking too much about the exact value.
When I was introduced to radius, diameter, circumference and area of a circle, I was taught π is the ratio between the circumference and diameter of a circle. However, even after working with numerous problems related to circles, cylinders, spheres, hemispheres etc., when my Father told me about taking one-third of the length around the tree as the diameter of the trunk of the tree, I could not understand it straightaway. I am not blaming the system. It must have been a problem with me that there was a gap between theory and its application in real life.
Please note:
Values of π and 22/7 are as given by the device that I used for this write-up.
(Tripurainfo)