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What is an example of a real life application that uses irrational numbers?

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- Thread starter jmlink
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What is an example of a real life application that uses irrational numbers?

- #2

Char. Limit

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Let's say you want to make a card in the shape of a circle. Let's say you give this card a width. Now let's say you want to put a border on the card. How long will the border need to be? It's going to involve pi, an irrational number.

The possibilities are endless.

EDIT: Since I just saw the "background" part, I'm a 17-year-old high school student taking AP Calculus in school and independently studying DEs and linear algebra.

The possibilities are endless.

EDIT: Since I just saw the "background" part, I'm a 17-year-old high school student taking AP Calculus in school and independently studying DEs and linear algebra.

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The purpose of this explanation was to show how anyone can understand these things!

- #4

Mentallic

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If you keep compounding in shorter and shorter time intervals, eventually you'll tend towards an irrational sum of money after the first year, nearly $2.72, or $e.

I'm just out of high school, about to begin my major in mathematics and physics at university and I'm 18.

- #5

mathman

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However, the statement that, for example, the square root of two is irrational can be written as a statement of number theory, and some results in number theory do have certain applications in the field of cryptography. So maybe one day people will use their knowledge of numbers being irrational to secure your email account. But don't hold your breath.

I am a freshman in college double majoring in physics and math, and I have taken Calculus, Vector Calculus, Linear Algebra, and Real Analysis, and am currently taking Differential Equations.

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So I don't know what your professor is getting at, but be careful.

Oh, and I am a graduate student in mathematics.

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- #9

Mark44

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If the diameter of the light fixture is 6", a square that is [itex]\sqrt{18}[/itex]" (or about 4.24") on each side will just touch the circle, so anything smaller will be covered by the light fixture.

I taught mathematics in a very small high school in Washington state, US, for two years, and in a Seattle-area community college for 18 years.

- #10

mathman

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You have just illustrated my point. The carpenter cannot measure √18", but he can measure 4.24" to some degree of approximation. Irrational or rational makes no sense in this context.

If the diameter of the light fixture is 6", a square that is [itex]\sqrt{18}[/itex]" (or about 4.24") on each side will just touch the circle, so anything smaller will be covered by the light fixture.

I taught mathematics in a very small high school in Washington state, US, for two years, and in a Seattle-area community college for 18 years.

- #11

Char. Limit

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measurement. However, an irrational number, defined as "cannot be written in a fraction" is, despite being as immeasurable as a rational number, a different concept. Just look at half-lives of first order reactions.

Half-life= ln(2)/k

ln(2) is much different from .693.

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Let's say you want to make a card in the shape of a circle. Let's say you give this card a width. Now let's say you want to put a border on the card. How long will the border need to be? It's going to involve pi, an irrational number.

The possibilities are endless.

EDIT: Since I just saw the "background" part, I'm a 17-year-old high school student taking AP Calculus in school and independently studying DEs and linear algebra.

3.14 will do.

Irrational numbers are useful within mathematics only, but for that exact reason they are useful in the real world. They allow us to develop theories with useful concepts like derivatives, integrals, the various results of analytical geometry, the rules trigonometry etc. These theories are of course very useful in solving real world problems.

- #13

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Then those people will approximate every real number as a fraction with a small denominator, whether that number happens to be a fraction with a very large denominator, or a nonrepeating decimal.

That's crazy! Some people like fractions, like 1/3.

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Well I guess that's my answer,

I am a senior physics major.

- #15

Mark44

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But I think you might be missing mine. An exact measurement of √18" isn't important. My carpenter friend didn't remember how to do the calculation, which requires irrational numbers. Once I did the calculation for him, he knew that all he had to do was measure 4.24" or smaller and his cut wouldn't show under the light fixture.You have just illustrated my point. The carpenter cannot measure √18", but he can measure 4.24" to some degree of approximation. Irrational or rational makes no sense in this context.

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What is now being argued about is what, exactly, is the meaning of this question, "What is a real life application?"

Apparently, I take it, the answer is not expected to be, "None." However, it is a fact of the carpenter that all numbers we use are approximations. So, I assume the question indicates that knowledge of a number's status is understood, and the answer must bear on that. Thus, I answered that one possible answer is the diagonal of a square.

- #17

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I might add that whole numbers often relate to Physics as well. As one author puts it "The revelance of integral quanties in Physics goes back at least 25 centuries and relates to Pythagoras in terms of a stretched sting and the theory of musical harmony.

http://books.google.com/books?id=6X...#v=onepage&q=whole numbers in physics&f=false

Of course, this doesn't tell us about irrational numbers. But we have simple formulas like S=(1/2)gt^2, or t = square root {2S/g}. So we could arrive at a time equal to the square root of 2.

http://books.google.com/books?id=6X...#v=onepage&q=whole numbers in physics&f=false

Of course, this doesn't tell us about irrational numbers. But we have simple formulas like S=(1/2)gt^2, or t = square root {2S/g}. So we could arrive at a time equal to the square root of 2.

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