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# Airplanes & Mobile Phones – Real World Examples Of Quadratic Equation

There are various equations we learn and understand in the elementary of high school. Some of those equations are easy, some are complex, and some are plain boring. Whether math is easy for you or difficult, one thing is true – there is no other equation to rival the majestic quadratic equation. I am not just talking about the equation itself but also about the practical implications of the quadratic equation. Let’s be truthful, how many times you have thought that why are you learning this stuff and where it will be useful in the practical world? The answer is almost everywhere. From mobile phone to airplanes, engineers and mathematician are still using the quadratic equation to solve the complex problem.

The story of quadratic equation was started long time ago when the Babylonians introduced the tax system to the farmer. Understandably, the farmers were not happy about the tax so they had to calculate the land needed to be cultivated to make up for the loss in taxes. They came up with the quadratic equation to make up for their loss and estimated the land on which they had to grow crop in order to make the ends meet. As ‘necessity is the mother of invention’, the solution to a simple farming problem is still being used to solve greater problems.

There are hundreds of used of quadratic equation which we observe in the daily life. What we lack is the understanding that this equation can help us estimate the results or simply understand the phenomena. Today, I have compiled a list of practical uses of quadratic equation so the next time you are solving it – you know where it can be used.

### Quadratic Chaos – When Math Meets Biology

The concept of quadratic chaos is defined by the quadratic equation with the focus on biology. Thhe population of a specific species can be estimated accurately with the help of quadratic equation. There is no patter to the growth of species hence it is considered as chaos. In this case x is the population while ‘n’ is the years so xn+1 is considered to be the sub function of xn. If axn was bred successfully while bxn2 dies due to overcrowding – the equation will be,

$$xn + 1 = rxn(1 – xn)$$

The focus of the equation is not just estimating the growth – it is more about understanding and evaluating if the prediction is accurate or hopeless.

### Mobile Phone and Complex Quadratic Equation

The imaginary number were first discovered trying to find an answer to the cubic equation actually. When the imaginary numbers were used to solve the cubic equation, mathematicians were actually able to find the actual results. It was important to justify this mathematical fix otherwise we would have been keep on introducing new letter ultimately running out of letters. Thus the complex umbers were introduced which are the combination of number and alphabets. The incorporation of cubic equation with complex number ultimately led to solve quadratic equation that helped in predicting electron motion. It also assisted in designing the integrated circuit that can perform complex tasks. These circuits are still being used in almost every technological invention including DVDs, computer, cars, and mobile phones. Phone signals convert the speech into high frequency radio waves and this behavior was understood by the quadratic equation. You can say that without the simple quadratic equation ‘x2 = -1’, we would not have invented the mobile phones!

Whether we think about simple machines or the more advanced one – one thing is very clear, it wouldn’t have been possible without calculation. We owe almost all of our invention to mathematics. From growing food as per the need of the population to trying to predict the natural phenomena from observing the movement of galaxies to stepping foot on moon, from calling our loved ones thousand mile away to predict the spread of infection – everything became possible for us when we dived into the realm of mathematics and its branches. One thing is very clear here – if we want to progress further, we need to reintroduce this subject to our student. Making the student understand the concept and logic behind the mathematical equation is the only way forward and we need to focus on it immediately. May be we will get lucky and find next Einstein or Newton!

# Mathematical Equations That Remarkably Impacted The World

Calculation, equation, and, math is continuously revolutionizing our world. From the time mankind wanted to calculate the field area for growing crops – there was a thirst to know and understanding the secrets of the world. Why apple always fall down rather than flying, is there a pattern to the movement of star, what can assist in navigation, and why birds fly while we cannot – these questions of the curious minds lead to the thirst of known and the answer provided the mean to modernize the world one invention at a time!

1- Calculus

Due to the applicability of calculus, it is not only used in mathematics but in engineering biology, physics, chemistry, and many more branches of science. Calculus can help you in the determination of weather pattern movement of sound, movement of light, and motion of astronomical objects.
Euler’s Polyhedra Formula
Fourier Transform

2- Law of Gravity

Gravity is an undeniable force responsible for the existent of our planet. The law of gravity helps in the evaluation of weight and speed leading to significant modernizations including race car amd airplanes.

3- Logarithms

There are many example of the use of logarithms in the real world starting from interest rate to Google page rankings. Logarithms are also used to detect changes in multiplication and help count them.

4- Maxwell’s Equations

It is the set of 4 differential equations that describe the relation between electricity and magnetism. These equations are the basis for understanding the behavior of electromagnetism. From MRI scanners in the hospital to computer – the credit goes to the basic understanding of Maxwell’s equations.

5- Navier-Stokes Equations

These differential equation helped us understand the behaviors of flowing liquids such as smoke rising from cigarette, water moving through pipes, and air flow over plane wings. Navier-Stokes Equations are also used to model the weather and observe ocean currents.

6- Normal Distribution

Normal probability also known as normal distribution forms a bell curve and it is signifint in statistics. It is used in social sciences, physics, and biology to define the behavior of large groups of independent processes. Normal distribution is followed in the measurement of errors, heinght, IQ score, and blood pressure.

There are various functions that are modeled by quadratic equation including shooting a cannon, hitting golf ball, and diving. You can calculate the expected profit you are going to get if you are using the quadratic equation. It can prevent unwanted surprises and provide you with the accurate numbers and what to expect in the future. Even in the business where you are simply selling bottled water, it can help you estimate how many bottles you have to sell to generate the profit you want.

8- Relativity

Relativity opened the door to understanding – be it our understanding of the outer space or the speed of light. It provided us with the idea that light speed is universal but the time factor is different for the speed of people or objects. Relativity helped us understand the fate, structure, and the origin of the universe.

9- Schrodinger’s Equation

The behavior of atomic and subatomic particle is defined by Schrodinger’s Equation. It enhance the understanding of quantum physics hence played a huge role in the development of computing devices. Computational chemistry is the direct application of Schrödinger equation and it is currently being used in medication and engineered food.

10- Second Law of Thermodynamics

According to the second law of thermodynamics, heat flow from hot to cold environment due to the change in temperature. This is the concept used in the working of internal combustion engines used in airplane, ship, car, and motorcycles. The law is applicable to all engine cycles and led to the progress of modern vehicles.

11- The Pythagorean Theorem

Whenever you need to find out if a triangle in acute, right-angled, or obtuse – you can use Pythagoras theorem for that. It made the life of mathematicians easier as it help them to find the missing length of any side of a triangle.

12- The square root of -1

The square root of -1 = I, this process gave rise to complex numbers that are supremely elegant. In case an equation have complex number solution, it will represented by ‘I’. With the help of this equation, mathematicians were able to find symmetries and the properties of the number which are implemented in signal processing and electronics.

13- Wave Equation

Wave equation as the name indicates describe the behavior of waves along with ripples, guitar strings, and incandescent bulb light. It is one of the first differential equations that helped us understand other differential equations as well.

The world of mathematics is abundant with equations that helped us revolutionize the world as we know it today. We were not only able to understand the concept behind natural phenomenon ut also manipulate them for the modern advancement. These were just the few examples, stay tuned to know more!