Isn't Calculus just about the greatest thing ever?

[blingdomepiece]

[blingdomepiece]

[bclare]

http://en.wikipedia.org/wiki/Mega_Millions#Playing_the_game

[bclare]

http://en.wikipedia.org/wiki/Mega_Millions#Playing_the_game

[THABEAST721]

Okay well I've never played the lottery, but I guess if those are the numbers then that would change things. But if it is 56 choose 5, that means the order doesn't matter. So choosing the numbers 1 2 3 4 5 would still be a winner if the drawing came up as 5 4 3 2 1. I didn't know it worked that way, but the calculation makes sense if that is the case.

If there are only 175 million possibilities, then it might be plausible to suspect that every combination of numbers has been chosen with so many people playing and a lot of those people playing 10+ tickets.
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[THABEAST721]

Okay well I've never played the lottery, but I guess if those are the numbers then that would change things. But if it is 56 choose 5, that means the order doesn't matter. So choosing the numbers 1 2 3 4 5 would still be a winner if the drawing came up as 5 4 3 2 1. I didn't know it worked that way, but the calculation makes sense if that is the case.

If there are only 175 million possibilities, then it might be plausible to suspect that every combination of numbers has been chosen with so many people playing and a lot of those people playing 10+ tickets.
_________________

This does not leave my sig!!!

[bclare]

(I actually this written up before I just looked up the rules of Mega Millions)

Most lotteries I've seen just put the numbers in ascending order, whatever order they were picked in. Makes it easier to tell if your ticket won or not. You could get the same number of ticket combinations with fewer numbers per choice if you did it with order matters.

59 choose 6 (order not important) = 45 million tickets

30 pick 6 (order important) = 42 million tickets
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I'm back I suppose

[bclare]

(I actually this written up before I just looked up the rules of Mega Millions)

Most lotteries I've seen just put the numbers in ascending order, whatever order they were picked in. Makes it easier to tell if your ticket won or not. You could get the same number of ticket combinations with fewer numbers per choice if you did it with order matters.

59 choose 6 (order not important) = 45 million tickets

30 pick 6 (order important) = 42 million tickets
_________________

I'm back I suppose

[Vampyromaniac]

I guess this goes into topology a bit but a thought experiment I was doing the other day left me with a pretty cool and surprisingly simple equation. The idea is this: you have two spaceships with a (preferably extremely long) cable of length d connecting them, each one with a perfectly accurate gyroscopic compass (compass as in, it measures angles). You synchronize your compasses so that they're both pointing in the same direction. One spaceship then flies straight forward until the cable is perfectly taut, stops, and engages a rocket on any side of it perpendicular to the cable (left, right, up, or down), flying in an arcing path while keeping the cable taut until it is on the exact opposite side of the stationary spaceship. Then the moving one returns from there straight to the original ship.
Now, the idea is that if our 3-dimensional universe is curved through 4-dimensional space, the (perfectly accurate) gyroscopes will no longer coincide. In fact, it seems reasonable that if the universe was perfectly spherical in that way (and thus, travelling in a straight line long enough would return you to your original position) that you could determine its circumference with simply:
C=4πd/ΔΘ
Where C is the circumference, d is the length of your cable, π is scorehero not being able to display pi, and delta theta (ΔΘ) is the change in angle (in radians, because it's the fucking future). Interestingly, it shouldn't matter if the spaceships are "moving" or not, as long as their motion is perfectly uniform. Also note that this only works if your cable is less than or equal to 1/4 the circumference of the universe (the assumption being that it's actually some ridiculously small percentage of C only calculable because of an impossibly precise gyroscopic compass.)
And ya know, in degrees you could just replace 4pi with 720...
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[/u]

[Vampyromaniac]

I guess this goes into topology a bit but a thought experiment I was doing the other day left me with a pretty cool and surprisingly simple equation. The idea is this: you have two spaceships with a (preferably extremely long) cable of length d connecting them, each one with a perfectly accurate gyroscopic compass (compass as in, it measures angles). You synchronize your compasses so that they're both pointing in the same direction. One spaceship then flies straight forward until the cable is perfectly taut, stops, and engages a rocket on any side of it perpendicular to the cable (left, right, up, or down), flying in an arcing path while keeping the cable taut until it is on the exact opposite side of the stationary spaceship. Then the moving one returns from there straight to the original ship.
Now, the idea is that if our 3-dimensional universe is curved through 4-dimensional space, the (perfectly accurate) gyroscopes will no longer coincide. In fact, it seems reasonable that if the universe was perfectly spherical in that way (and thus, travelling in a straight line long enough would return you to your original position) that you could determine its circumference with simply:
C=4πd/ΔΘ
Where C is the circumference, d is the length of your cable, π is scorehero not being able to display pi, and delta theta (ΔΘ) is the change in angle (in radians, because it's the fucking future). Interestingly, it shouldn't matter if the spaceships are "moving" or not, as long as their motion is perfectly uniform. Also note that this only works if your cable is less than or equal to 1/4 the circumference of the universe (the assumption being that it's actually some ridiculously small percentage of C only calculable because of an impossibly precise gyroscopic compass.)
And ya know, in degrees you could just replace 4pi with 720...
_________________

[/u]

[THABEAST721]

I really hate differential equations (the class) so much. I hope I never have to do anything with them again. My calc 4 class is obviously geared toward engineers and physicists, but for some odd reason they make math majors take the class too. We have not proved a single thing in that class, and my teacher just posts the equations and how to do it... hardly a class fit for a math major.
_________________

This does not leave my sig!!!

[THABEAST721]

I really hate differential equations (the class) so much. I hope I never have to do anything with them again. My calc 4 class is obviously geared toward engineers and physicists, but for some odd reason they make math majors take the class too. We have not proved a single thing in that class, and my teacher just posts the equations and how to do it... hardly a class fit for a math major.
_________________

This does not leave my sig!!!

[louster200]

So, the AB calculus AP test is tomorrow.

brb freaking out.
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GH Acc./RB Acc./Twitter/Last.fm/My Red SG Microwaved/My DLC/It''s pronounced ''loo-ster-two-hun-dred''

[louster200]

So, the AB calculus AP test is tomorrow.

brb freaking out.
_________________

GH Acc./RB Acc./Twitter/Last.fm/My Red SG Microwaved/My DLC/It''s pronounced ''loo-ster-two-hun-dred''

[yksi-kaksi-kolme]

I am SO FUCKING PUMPED for calc BC tomorrow. I think I've achieved the best level of comfort I need with series for the exam; I know all my convergence tests, Maclaurin series expansions for the functions that the exam focuses on (e^x, cosx, sinx, 1/(1-x)), how to do Taylor series/polynomial approximations of functions (a lot easier than I first thought), finding power series representations of functions, and Taylor remainders. Meanwhile I am very happy with my grasp on the fundamental concepts of calculus, like derivatives and integrals make a ton of sense to me now just looking at a graph and imagining what the function's derivative or integral looks like.

I am ready to get a 5. This is the one AP I truly care about and I am ready to make it happen.
_________________

My Accomplishments - GH | RB || My Youtube Channel || My Customs

[yksi-kaksi-kolme]

I am SO FUCKING PUMPED for calc BC tomorrow. I think I've achieved the best level of comfort I need with series for the exam; I know all my convergence tests, Maclaurin series expansions for the functions that the exam focuses on (e^x, cosx, sinx, 1/(1-x)), how to do Taylor series/polynomial approximations of functions (a lot easier than I first thought), finding power series representations of functions, and Taylor remainders. Meanwhile I am very happy with my grasp on the fundamental concepts of calculus, like derivatives and integrals make a ton of sense to me now just looking at a graph and imagining what the function's derivative or integral looks like.

I am ready to get a 5. This is the one AP I truly care about and I am ready to make it happen.
_________________

My Accomplishments - GH | RB || My Youtube Channel || My Customs

[Vampyromaniac]

[Vampyromaniac]

[Sarg338]

Fellow math nerds, I require your help! If I'm asked to find the "Smallest positive root of a funtion f(x)", that just means to find the smallest positive number such that f(number) = 0, correct?

Second part of my question is, I'm suppose to implement this into my program using a "Subinterval Search" method. Not sure if that's a math or Programming term, but does anyone have an idea of what that is? Any specific algorithms I could use?
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[Sarg338]

Fellow math nerds, I require your help! If I'm asked to find the "Smallest positive root of a funtion f(x)", that just means to find the smallest positive number such that f(number) = 0, correct?

Second part of my question is, I'm suppose to implement this into my program using a "Subinterval Search" method. Not sure if that's a math or Programming term, but does anyone have an idea of what that is? Any specific algorithms I could use?
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[Vampyromaniac]

[Vampyromaniac]

[Sarg338]

[Sarg338]

[bclare]

Newton-Raphson method could work, depending on what the function is, see http://en.wikipedia.org/wiki/Newton-Raphson#Failure_of_the_method_to_converge_to_the_root

The short answer is that N-R is probably fine though, as long as you've got the derivative easily calculated. You could go even brute-force-r and just fucking plug in values but that's a little inelegant
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I'm back I suppose

[bclare]

Newton-Raphson method could work, depending on what the function is, see http://en.wikipedia.org/wiki/Newton-Raphson#Failure_of_the_method_to_converge_to_the_root

The short answer is that N-R is probably fine though, as long as you've got the derivative easily calculated. You could go even brute-force-r and just fucking plug in values but that's a little inelegant
_________________

I'm back I suppose

[Sarg338]

Well, my teacher sent me the PDF giving me an example problem and a more in-depth instruction on what I'm suppose to do.

[Sarg338]

Well, my teacher sent me the PDF giving me an example problem and a more in-depth instruction on what I'm suppose to do.

[bclare]

So, split up [0,1] into 10 subintervals, width 0.1. Check which interval(s) have roots in them, then take the lowest one of those and divide it into 10 subintervals, etc. Terminate after 11 steps.
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I'm back I suppose

[bclare]

So, split up [0,1] into 10 subintervals, width 0.1. Check which interval(s) have roots in them, then take the lowest one of those and divide it into 10 subintervals, etc. Terminate after 11 steps.
_________________

I'm back I suppose