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For those who know math, here's a question...

I'm doing a project for school and I need examples of various functions applied in real life.
For example, growth of human population is exponential and relation between height, size of hands and size of feet is linear.
So, I need as many examples as I can get, possibly with some description and elaboration.

Thanks.

Refer to your user name.

quote:

Originally posted by Meat187 Refer to your user name.

Good catch!!
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Decibels are measured on a logarthmic scale.

83dB is actually the electrical double of 80dB. The more SPL you want, the more energy req'd to drive the transducers to move the increased volume of air.

Ahhh...the free flow of electrons. Makes me happy.

quote:

Originally posted by Dr. DAS Decibels are measured on a logarthmic scale. 83dB is actually the electrical double of 80dB. The more SPL you want, the more energy req'd to drive the transducers to move the increased volume of air. Ahhh...the free flow of electrons. Makes me happy.

Nice, didn't know that. I'll look into it some more.

If you mount a piston to a wheel and measure the displacement of the piston as the wheel rotates you get a sine wave.

linear = line
exponential = not line

/thread

My vehicle dynamics teacher showed us a project the kids the year before us did that proves that in order to make a lane change on the highway, your steering input is actually a perfect sine wave (if done perfectly). Also just about everything in your engine that moves is based on a sine function that is based on your crankshaft angle (theta). So your valve timing, piston position, etc. are all done base on equation that contains sin(theta) where theta is the crankshaft angle. I hope explained that clearly enough and didn't totally make myself out to be a nerd.

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Originally posted by Dervish If you mount a piston to a wheel and measure the displacement of the piston as the wheel rotates you get a sine wave.

Yeah... And the obvious one, alternating current.

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Originally posted by tubularbills linear = line exponential = not line /thread

Seriously, you're one of the most useless posters around here. Avoid my threads please... Thanks.
And exponential function is also a line, but not a straight one, dumbass.

quote:

Originally posted by GTS3gEclipse My vehicle dynamics teacher showed us a project the kids the year before us did that proves that in order to make a lane change on the highway, your steering input is actually a perfect sine wave (if done perfectly). Also just about everything in your engine that moves is based on a sine function that is based on your crankshaft angle (theta). So your valve timing, piston position, etc. are all done base on equation that contains sin(theta) where theta is the crankshaft angle. I hope explained that clearly enough and didn't totally make myself out to be a nerd.

Hmm... Wouldn't intercepting a car in front of you make a sine wave?

If you grab a chain by the ends it forms a hyperbolic function (cosh(x)).
Pretty much everything in statistics. I was referring to the Gau�ian Bell Curve in my first reply.
Also, check out fractals.

There's much more, but I'm to lazy to write it all down.

quote:

Originally posted by Gauss Hmm... Wouldn't intercepting a car in front of you make a sine wave?

no, that would make you oversteer and make a sine wave thats not symmetrical. try it. when you change a lane you steer your wheel left maybe an inch, then to straighten back out u steer back to the right a inch. if you go around a car you would steer the wheel left and inch and then back to the righy maybe 2 inches to get all the way back over.

quote:

Originally posted by Gauss Yeah... And the obvious one, alternating current. Seriously, you're one of the most useless posters around here. Avoid my threads please... Thanks. And exponential function is also a line, but not a straight one, dumbass.

a line, by definition, is the shortest distance between two points.

an exponential curve is not the shortest distance between two points. therefore, it is not a line. it is a curve.

you're the one who needs help on math, not me genius

quote:

Originally posted by tubularbills a line, by definition, is the shortest distance between two points.

No, that's a straight line. a line is defined by dictionary.com as: Mathematics: a continuous extent of length, straight or curved, without breadth or thickness; the trace of a moving point.

so exponential is still a line, just not a straight line.

Have u taken Statistics? Its all in there mate.

quote:

Originally posted by GTS3gEclipse No, that's a straight line. a line is defined by dictionary.com as: Mathematics: a continuous extent of length, straight or curved, without breadth or thickness; the trace of a moving point. so exponential is still a line, just not a straight line.

and what does linear mean?

to be following in a straight line

quote:

Originally posted by Meat187 If you grab a chain by the ends it forms a hyperbolic function (cosh(x)). Pretty much everything in statistics. I was referring to the Gau�ian Bell Curve in my first reply. Also, check out fractals. There's much more, but I'm to lazy to write it all down.

I see... Thanks for your input.
By the way, I'm looking for real life examples, something you see when you walk down the street and such.
Gaussian curve is not really an every day situation, but fractals can be applied to snow drops, so they count.

quote:

Originally posted by tubularbills a line, by definition, is the shortest distance between two points. an exponential curve is not the shortest distance between two points. therefore, it is not a line. it is a curve. you're the one who needs help on math, not me genius

Anyway, we have different terminology in Croatia.
Line is a straight line and curve can be also called a curved line.
Nonetheless, your reply was completely pointless and didn't contribute to the thread a single bit.
Unless you have something helpful to say concerning the subject, avoid this thread.

quote:

Originally posted by GTS3gEclipse no, that would make you oversteer and make a sine wave thats not symmetrical. try it. when you change a lane you steer your wheel left maybe an inch, then to straighten back out u steer back to the right a inch. if you go around a car you would steer the wheel left and inch and then back to the righy maybe 2 inches to get all the way back over.

It's kinda hard to picture it in my head, but I'll take your word for it, you sound quite sure about it.

quote:

Originally posted by GTS3gEclipse No, that's a straight line. a line is defined by dictionary.com as: Mathematics: a continuous extent of length, straight or curved, without breadth or thickness; the trace of a moving point. so exponential is still a line, just not a straight line.

Thanks for proving my point. Cheers mate.

However, let's try to stay on topic, this is important for my math grade.

quote:

Originally posted by Gauss Unless you have something helpful to say concerning the subject, avoid this thread.

and your thread is not contributing anything to the c0r...so why don't you just avoid this whole forum

quote:

Originally posted by Gauss Thanks for proving my point. Cheers mate. However, let's try to stay on topic, this is important for my math grade.

Also anything using an accelerometer converts a voltage and relates it to an acceleration based on the forced applied to the crystal inside. the more force applied to the crystal the higher the voltage and thus the greater the acceleration, just a linear relation using Newton's law of F=ma. and accelerometers are used in tons of shit now adays, like wii controllers. look here for more info: http://en.wikipedia.org/wiki/Accelerometer

And any mass-spring system is a second order differential equation. Like shock absorbers on a car.

So far I have these... Feel free to correct me if there's something wrong.

Relation between height, size of hands and size of feet - linear
Human population growth - exponential
Linear motion - linear
Car acceleration - exponential
Relation between area and radius of a circle - square
Decibel - logarhitmic
Richter scale - logarhitmic
Brightness of stars - logarhitmic
Riemann surface - square root

I know they're not all real life situations, so if you have anything at least related to real life situations, feel free to post.

quote:

Originally posted by GTS3gEclipse And any mass-spring system is a second order differential equation. Like shock absorbers on a car.

Thats a good one...I had a physics 1 exam on that shit, hehe.

quote:

Originally posted by KiNeTiC ENeRgY Thats a good one...I had a physics 1 exam on that shit, hehe.

actually the relationship between the car fame and the road is a forth order differential equation because the tire and rim act as another spring-mass system and then the shock absorber-body is another second order system.

You want real life? How about this:
When processing sound waves, your inner ear does a Fourier Transform, translating a frequency to a linear space axis and generating electrical impulses from there.

quote:

Originally posted by Gauss Car acceleration - exponential

I'm not sure what you mean by that, but it might be wrong. If a car is accelerated by a constant value it's velocity grows linearly, while it's position changes quadratically.

quote:

Originally posted by tubularbills and your thread is not contributing anything to the c0r...so why don't you just avoid this whole forum

By that logic, how are any of your posts contributing to this forum? Why are you posting?
To me, you seem like a sad fuck that has a little too much free time on his hands so he comes here to kill his boredom.
At least do it in some other thread where people are not trying to make serious conversation, there are plenty of such threads around here.
Seriously, what's your point? Just leave this thread alone.

quote:

Originally posted by GTS3gEclipse Also anything using an accelerometer converts a voltage and relates it to an acceleration based on the forced applied to the crystal inside. the more force applied to the crystal the higher the voltage and thus the greater the acceleration, just a linear relation using Newton's law of F=ma. and accelerometers are used in tons of shit now adays, like wii controllers. look here for more info: http://en.wikipedia.org/wiki/Accelerometer

Ahh, I know those. There's an mp3 player produced by Sony that has one built in.
If it detects too high acceleration (when you drop it), it automatically shuts itself down to prevent any serious damage to HDD and other parts. Neat.
You're good at this.

quote:

Originally posted by Meat187 You want real life? How about this: When processing sound waves, your inner ear does a Fourier Transform, translating a frequency to a linear space axis and generating electrical impulses from there.

So which type of function is that?

quote:

Originally posted by Gauss Car acceleration - exponential

Actually is another 2nd order differential equation. acceleration is the second derivative of position. so the equation for position is really

0.5y''(t^2)+y'(t)+y

where y is position.

quote:

Originally posted by Gauss So which type of function is that?

It's not a function in the classical sense, like y = 2x + 3. It's a mathematical transformation, and therefor probably not what you're looking for.

Edit: The function looks like this:



I guess I just wanted to show off a little, but I think that's an awesome example of math in nature.

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