On a basis of cup half full vs cup half empty, let's consider zero as being infinity and infinity as being zero. This could turn your head inside out.
Math Problem - Not Quite Humor
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Originally Posted By: Shannow
In my "mobius" model of the universe, infinity becomes zero.
Ooooooh, that's even better. Everything is nothing and nothing is everything.
In my "mobius" model of the universe, infinity becomes zero.
Ooooooh, that's even better. Everything is nothing and nothing is everything.
Originally Posted By: TallPaul
Originally Posted By: crinkles
closest i'll ever need in engineering is 3.14159
even that is too accurate given that the error margin on natural materials (soil and dirt) are sometimes order of magnitudes.
Presumably you are a civil engineer. Is it possible that a mechanical engineer may need a couple more digits?
it depends on the accuracy of the measurements and manufacturing tolerances. If those can be guaranteed to X "significant figures" then you can go ahead and use pi equal to "X-1" decimal places.
Originally Posted By: crinkles
closest i'll ever need in engineering is 3.14159
even that is too accurate given that the error margin on natural materials (soil and dirt) are sometimes order of magnitudes.
Presumably you are a civil engineer. Is it possible that a mechanical engineer may need a couple more digits?
it depends on the accuracy of the measurements and manufacturing tolerances. If those can be guaranteed to X "significant figures" then you can go ahead and use pi equal to "X-1" decimal places.
Originally Posted By: Shannow
Saw an absolute revelation the other day.
And am now going to sit down and do it.
have a co-ordinate box, 0,0 to 1,1...area 1 square units.
Throw a huge number of random co-ordinates into the box (I don't think that they need to be random, but that was the premise of it).
Take each and every co-ordinate, and calculate the square root of the (X^2xY^2), i.e the distance from 0,0.
If it's less than, it goes in one bucket. Greater than, the other bucket. The "exactly" 1 gets distributed in the ratio of the buckets.
The first bucket is an approximation to pi/4.
More random numbers (or IMO the tighter the grid), the closer you are.
i'm going to do that now. to test. I have an idea in my mind of why works. i did stochastic processes a long time ago at uni.
Saw an absolute revelation the other day.
And am now going to sit down and do it.
have a co-ordinate box, 0,0 to 1,1...area 1 square units.
Throw a huge number of random co-ordinates into the box (I don't think that they need to be random, but that was the premise of it).
Take each and every co-ordinate, and calculate the square root of the (X^2xY^2), i.e the distance from 0,0.
If it's less than, it goes in one bucket. Greater than, the other bucket. The "exactly" 1 gets distributed in the ratio of the buckets.
The first bucket is an approximation to pi/4.
More random numbers (or IMO the tighter the grid), the closer you are.
i'm going to do that now. to test. I have an idea in my mind of why works. i did stochastic processes a long time ago at uni.
Originally Posted By: Shannow
Saw an absolute revelation the other day.
And am now going to sit down and do it.
have a co-ordinate box, 0,0 to 1,1...area 1 square units.
Throw a huge number of random co-ordinates into the box (I don't think that they need to be random, but that was the premise of it).
Take each and every co-ordinate, and calculate the square root of the (X^2xY^2), i.e the distance from 0,0.
If it's less than, it goes in one bucket. Greater than, the other bucket. The "exactly" 1 gets distributed in the ratio of the buckets.
The first bucket is an approximation to pi/4.
More random numbers (or IMO the tighter the grid), the closer you are.
what do you do in the buckets? do you add them together? average them?
Saw an absolute revelation the other day.
And am now going to sit down and do it.
have a co-ordinate box, 0,0 to 1,1...area 1 square units.
Throw a huge number of random co-ordinates into the box (I don't think that they need to be random, but that was the premise of it).
Take each and every co-ordinate, and calculate the square root of the (X^2xY^2), i.e the distance from 0,0.
If it's less than, it goes in one bucket. Greater than, the other bucket. The "exactly" 1 gets distributed in the ratio of the buckets.
The first bucket is an approximation to pi/4.
More random numbers (or IMO the tighter the grid), the closer you are.
what do you do in the buckets? do you add them together? average them?
crinkles, it was a count.
The number of "particles" inside the arc from 1,0 to 0,1, versus those outside the arc.
Total should equal 1. Inside the arc, pi/4, outside 1-pi/4.
I'm stuck with those that appear on the line (same at target shooting)...do you split them 50:50, or make the mesh tighter ?
The number of "particles" inside the arc from 1,0 to 0,1, versus those outside the arc.
Total should equal 1. Inside the arc, pi/4, outside 1-pi/4.
I'm stuck with those that appear on the line (same at target shooting)...do you split them 50:50, or make the mesh tighter ?
if each of those points are assigned a very small area, and you create infinitely many points, then in the limiting case where you have infinitely many points of infinitely small area, you have determined the area of the inside of the circle which is pi/4 x r^2. since r = 1 the area is pi/4
if you use true random number generation you are extremely unlikely to fall on the r = 1 line. I have used 1000 points and not one fell on the line in more than 10 random generations of that set of 1000 points
nevermind - it worked. with 1000 particles my count / 1000 is between .775 and .795 with an average of about pi/4
ever use Goldsim? That program would be pure gold for this.
with N = 1000 i get an accuracy of about +- 3% but mostly +- 2%
With N = 10,000 i get an accuaracy of about +- 1% but mostly +- 0.5%
if you use true random number generation you are extremely unlikely to fall on the r = 1 line. I have used 1000 points and not one fell on the line in more than 10 random generations of that set of 1000 points
nevermind - it worked. with 1000 particles my count / 1000 is between .775 and .795 with an average of about pi/4
ever use Goldsim? That program would be pure gold for this.
with N = 1000 i get an accuracy of about +- 3% but mostly +- 2%
With N = 10,000 i get an accuaracy of about +- 1% but mostly +- 0.5%
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no moments, its just a case of plain old areas.
you are not actually working with the radius at all it is just a logic set used to sort the groups.
if a dart is thrown randomly at the square, the likelihood of it hitting the inner circle or outer circle is purely a function of the ratio of each area to the whole area. (this makes intuitive sense)
if you have enough points, you begin to approximate the area - but you need many many points (near to infinity) as in mathematics a point is infinitely small.
you are not actually working with the radius at all it is just a logic set used to sort the groups.
if a dart is thrown randomly at the square, the likelihood of it hitting the inner circle or outer circle is purely a function of the ratio of each area to the whole area. (this makes intuitive sense)
if you have enough points, you begin to approximate the area - but you need many many points (near to infinity) as in mathematics a point is infinitely small.
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Originally Posted By: Shannow
Good work Crinkles.
I can't see a weighted area thing (moment of inertia type thing) working in this...your scattergun seems to have some non randomness to it (which it must)
you are right. I have never trusted a computer to produce a perfectly random set of data, but remember it may well be, just as the winning lotto numbers of 1 2 3 4 5 6 are just as likely as any other number combination.
it's like my iPod - whenever i shuffle it randomly, the songs don't seem random at all - they always repeat the [censored] ones. maybe i jsut notice the [censored] ones more. so we are affected by our perception of the randomness.
Good work Crinkles.
I can't see a weighted area thing (moment of inertia type thing) working in this...your scattergun seems to have some non randomness to it (which it must)
you are right. I have never trusted a computer to produce a perfectly random set of data, but remember it may well be, just as the winning lotto numbers of 1 2 3 4 5 6 are just as likely as any other number combination.
it's like my iPod - whenever i shuffle it randomly, the songs don't seem random at all - they always repeat the [censored] ones. maybe i jsut notice the [censored] ones more. so we are affected by our perception of the randomness.
Human nature will pick up patterns , or what seem like patterns..I loathe the "wallpaper on holywar, because the patterns are too non random.
Just chucked together a 10x10 non random square, and placed units at each point from 0,0 to 1,1. Got 77:31.
You are right...need to get down to calculus levels of "finiteness" to get an approximation.
Just chucked together a 10x10 non random square, and placed units at each point from 0,0 to 1,1. Got 77:31.
You are right...need to get down to calculus levels of "finiteness" to get an approximation.
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