Figure 1: Pi’s geometrical illustration

Pi, or in symbol known as π serves as a fundamental mathematical constant, representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. As an irrational number, π cannot be precisely expressed as a ratio of two integers, although approximation such as  is commonly used. Archimedes, one of the most famous mathematician and inventor in ancient Greece, took a major step forward by devising a method to obtain pi to any desired accuracy. By inscribing and circumscribing regular polygons about a circle to obtain upper and lower bounds, he obtained 223/71 < π < 22/7, or an average value of about 3.1418. Consequently, its decimal representation extends infinitely without termination or the establishment of a permanent repeating pattern.

 

The formula for calculating the circumference of a circle using Pi is as below:

 

Bringing  to the left hand side of Equation (1) will be:

 

where

• 𝐶 is the circumference of the circle,
• is a mathematical constant approximately equal to 3.14159,
• 𝑟 is the radius of the circle,
• is the diameter of the circle.

Figure 2: Pi’s application to the Great Pyramid design

The roots of Pi extend deep into the dawn of civilization, where ancient cultures such as the Egyptians and Babylonians grappled with its concept while delving into the intricacies of circles and spheres. In their quest to understand these fundamental geometric shapes, these

Figure 3: Pi in real-life application

early societies developed initial approximations of Pi, laying the foundation for its eventual mathematical exploration. These early approximations were not merely academic exercises but found practical application in the construction of monumental structures like the pyramids, where precise geometric calculations were essential for architectural integrity and symbolism. Thus, Pi emerged not only as a mathematical curiosity but also as a crucial tool in shaping the physical world around us.

Pi is also a constant presence in our everyday experiences, seamlessly integrated into familiar objects like clocks, watches, and measuring instruments. For instance, consider the analog clock with its circular face; each sweep of the second hand represents a precise measurement of time, and this accuracy is made possible by the relationship between the circumference of the clock face and the value of Pi. Similarly, when we use rulers or tape measures to gauge the dimensions of circular objects, Pi plays a crucial role in ensuring the accuracy of our measurements.

On a journey through time, the significance of Pi transcends its practical applications. It has been the subject of extensive study and refinement throughout history and captivating the minds of brilliant mathematicians across civilizations. This enduring fascination with Pi reflects not only its mathematical importance but also its cultural and intellectual significance. Indeed, Pi stands as a profoundly significant symbol of the enigmatic constant that lies at the core of mathematics.

 

Prepared by:

Nurul Amira binti Aslan

Mathematics Division

 

Tarikh Input: 07/05/2024 | Kemaskini: 07/05/2024 | hasniah