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Real Life Applications

Polynomials

Polynomial Functions

Algebra

Mathematics

What are the real life applications of polynomials?

25 Answers

Ravi Shankar

Ravi Shankar , b.tech Mining, Indian Institute of Technology , Dhanbad (2021)

according to me answer to this question is:

Engineers use polynomials to graph the curves of roller coastersSince polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.POLYNOMIALS FOR MODELING OR PHYSICSPolynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.POLYNOMIALS IN INDUSTRYFor people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another–without even realizing

The most commonly used polynomial equation is a line. It is used all the time, as Im sure you http://know.So lets go on to quadratic polynomials. These are in the form y=ax2+bx+c[math]y=ax2+bx+c[/math], where a, b, and c are real constants.Youll be surprised by the number of applications that use quadratic equations.Throw a ball in the air. The arc it follows is a parabola. And a parabola can be represented by a quadratic equation.Heres an upside down parabola. Ignore the parts below the x-axis. If you were standing at the far left red dot, and threw the ball up at an angle, the maximum height would be achieved at the blue dot, and it would hit the ground at the far right dot.With a little help from physics, if you know the speed and angle of the ball when it left your hand, you can compute the maximum height, the time it takes to get to that height, and the time it takes to hit the ground, and the speed at any point. You can imagine how much the military uses this in their targeting systems.

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Christian Howard

Christian Howard , Math is fun! 🙂

In my life, polynomials are used everywhere. Here’s some examples:

  • Want to approximately represent curved surface geometry? Use a polynomial basis across a triangulation of the surface to approximate the surface curvature simplex by simplex.
  • Want to approximate the solution to a system of hyperbolic partial differential equations using a spacetime formulation? Use a polynomial basis local to spacetime cells and approach the solution using a Spacetime Discontinuous Galerkin method.
  • Want to capture some nonlinearities in a large dataset using non-parametric methods? One approach is when you wish to evaluate your non-parametric model at some state, grab data near to this state and perform a weighted least square regression using a low-order polynomial basis.
  • Want to perform a change of variables to go from global coordinates to barycentric coordinates of a simplex? Use Lagrange polynomials to help with this and obtaining the desired Jacobian.

And the list could go on. Polynomials are used everywhere. They are convenient to use and show up all over the place.

Deepank Tyagi

Deepank Tyagi , studied at Dron Public School

Originally Answered: What are the real-life applications of polynomials?

Polynomials helps us to find out the solution of our problems with the help of an initial condition given in it. Some of the applications which are coming in my mind are,

*Finding the dimensions of a rectangle (gate,room,etc.)for a given area and sum of the dimensions.

*Finding the speed of any vehicle for a given time with the help of any initial condition of it.

*In business related calculations(sale,purchase ,tax,etc.)

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Makarand Apte

Makarand Apte , Works on Computational Geometry

You may not realise it, but the use of polynomials is pervasive in our day to day life. Almost all manmade objects you see nowadays, from mobile phones and shampoo bottles to cars and aircrafts, are designed on a computer. How do you think a computer represents the 3D curves and surfaces of the objects? They mostly use polynomials.

Why polynomials? Because of the ease of their use. Compared to other functions such as trigonometric or logarithmic functions, polynomials are the fastest to evaluate, easiest to differentiate and integrate.

So the next time you find yourself amazed looking at a sleek bike or a funky building, close your eyes and take a moment to thank polynomials.

Senia Sheydvasser

Senia Sheydvasser , PhD in Mathematics

Originally Answered: How is polynomial used in daily life?

I decided to think a little bit about what is likely to be the single application of polynomials that is probably used the most. My guess is that in the modern age of high frequency trading algorithms and online banking, most anything to do with how to securely transmit financial information is a likely winner. Are polynomials used in this? You better bet they are.

Allow me to introduce you to secret sharing . We’ll start with a toy example, and then we’ll see how this might actually be practical: suppose that you are the manager of a bank. You have a cache of money coming that needs to be locked away in the safe, but you won’t be there when the delivery is made. You will have to ask your tellers to unlock the safe for you. Unfortunately, you don’t trust any single one of them enough to just give them a key, out of fear that they might steal something. However, you feel quite confident that if three of them are watching each other, then none of them will attempt anything. So, what you would like to do is to set up a system where each of them has part of a key that doesn’t allow them to open the safe by itself, but if any three of them get together, then they can open the safe.

This is the basic idea behind secret sharing—you want to distribute a share of a secret between a number of recipients, such that no one of them can determine the secret by themself, but if some specified number of them get together, then they can. This has very practical application in computer security, because you might have a number of different servers that you would like to collectively have access to secure information, such as someone’s banking information, or perhaps a database of passwords. However, you might be wary that any of these servers might get compromised, so you set things up so that only multiple servers working together can actually do the desired task.

How do you actually make secret sharing work? Well, this is where polynomials come into play. There are a couple of different schemes, but the original one, and the one that is probably still the most widely used, is Shamirs Secret Sharing . Here’s a simplified version of it (in practice, you need some modifications to both make everything efficiently computable and secure): suppose that you want any [math]k[/math] shares to be able to recover the password, which is some integer [math]N[/math]. You make the complete key a [math]k – 1[/math] degree polynomial, where [math]N[/math] is the constant term—so, for instance, in the example above where we want three tellers to be able to open the safe, maybe the password is [math]1043[/math], so we might make the secret polynomial be [math]3X^2 – 531X + 1043[/math]. Each of the shares will be a point on this polynomial—so, if there are six tellers, you might give each of them one of the following points:

[math]\displaystyle (-3, 2663), (-2, 2117), (-1, 1577), (1, 515), (2, -7), (3, -523). \tag*{}[/math]

Here’s the kicker: no one teller can figure out from their one point what the original quadratic polynomial was. No two tellers can figure out what the original quadratic polynomial was. But if any three of them come together, they can work out that there is a unique quadratic polynomial passing through all three points, and from that they can work out the password is [math]1043[/math].

Harlock Ulric

Harlock Ulric

WHAT IS A POLYNOMIAL?

Polynomials are algebraic expressions that add constants and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents.

HOW TO SOLVE A POLYNOMIAL

These equations are solved by finding for the variable. Polynomials come in varying degrees, some of which are solved by particular equations. Factoring, rational equations and root extractions can solve those in the lowest four orders. For example, second-order equations (of the form f(x) = ax^2 + bx + c) can be solved by the quadratic equation (ax^2 + bx +c = 0). Third-order equations are solved by the cubic equation and fourth-order equations are solved by the quartic equation.

HOW DO PEOPLE USE POLYNOMIALS?

Engineers use polynomials to graph the curves of roller coasters

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

POLYNOMIALS FOR MODELING OR PHYSICS

Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.

POLYNOMIALS IN INDUSTRY

For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another–without even realizing it.