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Polynomials...
- Thread starter Durakken
- Start date
borrofburi
New Member
I use them for all sorts of things... The reason the common person should learn them is for interest calculations (though those aren't usually strictly polynomial, you need to understand polynomial to understand them), and the basic ability to understand financial mathematics.
Marcus said:
I have just never seen them used... or at least i don't think i have. They're one of those types of things that my mind just forgets as soon as i get out of a math class.
I figure they must be useful for something but I haven't ever run across them for some odd reason.
aeroeng314
New Member
Polynomials are to functions as integers are to real numbers...sort of...not really. You could sort of consider them to be a functional basis from which you can construct almost any other function. As mentioned, one use is in interpolation since polynomials are very easy to compute. I mean, you really are almost asking what use integers are if all we use are real numbers. Polynomials are a pretty fundamental foundation of a lot of things in mathematics. So many things that I can't really think of anything specific.
I don't believe this. Something as simple as linear interpolation is an application of a polynomial. In fact, what strikes me as so unbelievable about this statement is that rational functions (the quotient of two polynomials) are the only actual functions that a computer could potentially compute exactly in a finite number of operations. Any other function you see is only an approximation (polynomials are too because of floating point errors, but if you could theoretically avoid that you'd still have approximations for anything other than rational functions). Those approximations are almost always arrived at using polynomials or rational functions (and, to some degree, root finding algorithms).
For an every day use, just look at the nearest paved road. Chances are the ground isn't perfectly flat along the length of the road and it has to go up and down. This profile is sometimes designed as a piecewise second order polynomial (quadratic interpolant) which is a polynomial (my dad's a civil engineer and designs all roads this way; the alternative is to use circular arcs but those can be expressed as the locus of roots of a multivariate polynomial).
Ever need to convert Celsius to Farenheit? Polynomial.
I don't believe this. Something as simple as linear interpolation is an application of a polynomial. In fact, what strikes me as so unbelievable about this statement is that rational functions (the quotient of two polynomials) are the only actual functions that a computer could potentially compute exactly in a finite number of operations. Any other function you see is only an approximation (polynomials are too because of floating point errors, but if you could theoretically avoid that you'd still have approximations for anything other than rational functions). Those approximations are almost always arrived at using polynomials or rational functions (and, to some degree, root finding algorithms).
For an every day use, just look at the nearest paved road. Chances are the ground isn't perfectly flat along the length of the road and it has to go up and down. This profile is sometimes designed as a piecewise second order polynomial (quadratic interpolant) which is a polynomial (my dad's a civil engineer and designs all roads this way; the alternative is to use circular arcs but those can be expressed as the locus of roots of a multivariate polynomial).
Ever need to convert Celsius to Farenheit? Polynomial.
ImprobableJoe
New Member
You can't do anything besides flip burgers or dig ditches without polynomials... and even then, I'll bet your boss or his boss uses them. Hell, you can't even work the cash register without polynomials.
Wow, that's an incredibly dumb question... see, teachers, there IS such a thing as a dumb question!! :lol: That's like asking why we bother to learn punctuation, since we only use it in writing and reading.
Wow, that's an incredibly dumb question... see, teachers, there IS such a thing as a dumb question!! :lol: That's like asking why we bother to learn punctuation, since we only use it in writing and reading.
Hrmmm...
Perhaps what I'm talking about that is referred to by polynomials around here is different than what it is you guys are talking about...
c = a + b <- if that's a polynomial then i use them a lot
but what I am referring to something that looks something like this...
(x3) (3+5) (rx)
and then you shuffle those things around somehow...
I don't see them often...like in nearly 3+ years so I don't recall exactly how they look.
Perhaps what I'm talking about that is referred to by polynomials around here is different than what it is you guys are talking about...
c = a + b <- if that's a polynomial then i use them a lot
but what I am referring to something that looks something like this...
(x3) (3+5) (rx)
and then you shuffle those things around somehow...
I don't see them often...like in nearly 3+ years so I don't recall exactly how they look.
Not an expert on this subject, but polynomials are required when for example doing Fourier transformations, so when you transform e.g. a radio wave to a digital signal you have use for polynomials. Also, I use FTIR (Fourier transformed infra-red) spectroscopy in my research to look at what chemicals are formed over my catalyst, the instrument uses polynomials to convert the adsorption of the laser light into concentrations of different compounds in the gas.
If you think about it polynomials are used very often in everyday application, such as your cellphone (turning the radio signals into sound/images). The thing is that if you don't work with constructing these kind of machines, you don't really think about it and it could be hard to realize where it's used.
If you think about it polynomials are used very often in everyday application, such as your cellphone (turning the radio signals into sound/images). The thing is that if you don't work with constructing these kind of machines, you don't really think about it and it could be hard to realize where it's used.
Marcus
New Member
A polynomial is any function made up of a sum of multiples of powers of the variables. For one variable, x, this means things like 5x^3 - 2x^2 + 5.
Need to work out the breaking strain of a rod of a given material with a given radius? Polynomial. Need to know the braking distance of a car moving at a given speed? Polynomial. Need to know the speed a rollercoaster will reach at the bottom of its long drop? Polynomial. Need to know the thickness of joist you'll need to support a weight over a given span? Polynomial.
Seriously. Absolutely anything of any complexity above a pile of bricks* that you want to engineer or build will involve the use of polynomials at the design stage if it's going to be done safely and economically. Asking those of us who do any sort of calculations in our everyday lives when polynomials are used is like asking a painter when a paintbrush is used.
*Actually, you'd need a polynomial to work out the maximum tonnage of bricks that you could pile up in a given plot of land before they started tumbling down the sides of the pile.
Need to work out the breaking strain of a rod of a given material with a given radius? Polynomial. Need to know the braking distance of a car moving at a given speed? Polynomial. Need to know the speed a rollercoaster will reach at the bottom of its long drop? Polynomial. Need to know the thickness of joist you'll need to support a weight over a given span? Polynomial.
Seriously. Absolutely anything of any complexity above a pile of bricks* that you want to engineer or build will involve the use of polynomials at the design stage if it's going to be done safely and economically. Asking those of us who do any sort of calculations in our everyday lives when polynomials are used is like asking a painter when a paintbrush is used.
*Actually, you'd need a polynomial to work out the maximum tonnage of bricks that you could pile up in a given plot of land before they started tumbling down the sides of the pile.
Master_Ghost_Knight
New Member
Are you serious? Polinomials are one of the best behaved functions out there, if everything could be modeled simply using a polinomial you could bet your ass I wouldn't use anything else. Unfortuantly they indeed popup to unfreaquently as far as applications go, but still there is an amazing ammount of aplications out there for them.
Gunboat Diplomat
New Member
Asking "what good are polynomials?" is like asking "what good are words?" You obviously use words and, if you do any mathematics at all, you obviously use polynomials. Obviously you don't use all possible polynomials but, then again, you obviously don't use all words either. Yet, for some reason, you don't wonder what good words are...Durakken said:
If x is a variable then all of the following are polynomials:
- x
- x + 2
- x^2 - 4
- x^3 - 2x + 8
- 5x^2 + 6x + 7
You claim to have not used them in three years. Please describe to us some of the things you have done in the past three years that require any math at all. Even if you exclude first order polynomials, I'll be shocked and awed if there aren't any higher order polynomials involved in that work...
Master_Ghost_Knight
New Member
That is wrong. Polinomial are sums of monomials (special case a polinomial made of one monomial). A monomial is a natural power of x multiplied by a coeficient (i.e. constant; special cases of constants are 1 and 0).Gunboat Diplomat said:
ln(x)+x^2, not a polinomial.
sin(x) not exactly a polinomial (depending of the way you want to see it)
Gunboat Diplomat
New Member
Emphasis added for clarity.Master_Ghost_Knight said:
I'll have you know that neither ln nor sin functions are arithmetic. Instead, they are transcendental.
We all know what polynomials are except the original poster, apparently. That's why I deliberately kept my post very basic. Why you don't think that I understand these things is beyond me. Haven't you seen my other posts in this forum?
Master_Ghost_Knight
New Member
No? I don't remember you, seriously.Gunboat Diplomat said:
Counterpoint
New Member
Have you ever taken a calculus class? Polynomials are extremely important.