How is polynomial applicable in real life? Or why am I learning polynomials?

We have been learning about polynomials since middle school. It plays an essential role in the field of Algebra. If you’re not a fan of math or if you find Algebra challenging, you would have wished for the chance to completely opt-out of learning the topic. But, wait! They have a major influence on the world around us. They get a deeper sense of meaning once we relate them to the real world. Polynomials are mathematical expressions that can be used for the representation of real-world entities. Some common applications of polynomials are in the field of geometry, design, business and physics.

A simple example where polynomials are used is geometry. Consider a rectangle of sides x and 2x+3. Since the dimensions of the rectangle depend on x, it is not possible to find its area or perimeter without knowing the value of x. We can simplify this process though. We know that,

Perimeter = 2 [length+breadth]
= 2 [(x)+(2x+3)]
= 6x+6

Area = length*breadth
= (x)*(2x+3)
= 2x2+3x

Hence, we now know what the area and perimeter of the rectangle are using simple expressions. Once the value of ‘x’ is known, we can simply substitute the value and obtain perimeter and area.

You might wonder how this matters in real-life applications. They are integral to the design process. Take a look around you. You are surrounded by buildings. Design engineers apply the same principle extended to 3D for multiple applications. The design of curves also takes the help of polynomials. For example, wind tunnels used for testing the behaviour of vehicles employ higher-order polynomial curves in designing their diffuser and contraction cone. World-renowned monuments such as the Taj Mahal and the Sydney Opera House have applied polynomial curves to perfection, possessing structural integrity on top of their aesthetic architecture.

Let us dive into the world of business and finance. Polynomials are used to model various situations such as in the stock market to see how the price of stocks varies with time. Companies build models to calculate net profit, calculate tax and other economic calculations based on polynomials. They are extensively used in the field of Operations Research which helps optimise cost, time and manpower in various industries. It can be even be applied to banking, wherein simple interest from loans can be modelled for our need.

That’s not all! Polynomials transcend outside mathematics too. They are crucial in the field of physics. They are used to study the variation in deflection of beams with stress. They form the backbone of kinetics and kinematics. Whether it be finding the trajectory of a ball hit for a six in cricket to the motion of vehicles and aeroplanes, polynomial equations help in studying this motion in detail. Even fundamental laws such as Newton’s laws of motion, Newton’s 2nd law and Newton’s law of gravitation to name a few, are mathematically expressed only due to the existence of algebra and polynomials. So the next time you look at the world around you, look beyond what you see and dive deeper into the fascinating world of algebra hiding in plain sight.

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