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#26 2012-09-07 12:50:10
- Agnishom
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Re: Python!
I also use Python 
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#28 2013-02-25 01:17:19
- Agnishom
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Re: Python!
I do not understand the program at podt #1
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#29 2013-02-25 04:22:15
- bobbym
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Re: Python!
Hi;
He is making use of a geometric probability to evaluate pi.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#30 2013-02-25 06:26:10
- Shivamcoder3013
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Re: Python!
I do not tend to use Python at all anymore.
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes
My maturity level depends on the people I am around.
#31 2013-02-25 12:49:16
- Agnishom
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Re: Python!
Hi bobbym,
I don't understand at all.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#32 2013-02-25 19:42:10
- bobbym
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Re: Python!
Hi Agnishom;
You are picking random numbers in the range 0 - 1 for x and y, yes?
Do you follow so far, I can not upload a drawing so I will talk you through.
Last edited by bobbym (2013-02-25 20:30:01)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#33 2013-02-25 23:23:37
- Agnishom
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Re: Python!
Yes, two random numbers b/w 0 & 1
Then they are checking how many of them satisfy x^2 + y^2 < 1
So?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#34 2013-02-25 23:27:41
- bobbym
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Re: Python!
You can pair the x's and y's to make points. They would all be inside of a 1 x 1 rectangle in the first quadrant. Do you agree?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#35 2013-02-25 23:33:14
- Agnishom
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Re: Python!
Ya.. All the points within a radius of 1 in the 1st quadrant
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#36 2013-02-25 23:36:46
- bobbym
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Re: Python!
Not yet. You are jumping ahead. If we generate x's from 0 to 1 and y's from 0 to 1 and form ordered pairs and then plot them we would get something like this:
Last edited by bobbym (2013-02-25 23:37:05)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#37 2013-02-25 23:39:11
- Agnishom
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Re: Python!
And then we check how many of them are within a radius of 1 ?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#38 2013-02-25 23:43:11
- bobbym
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Re: Python!
Yes, and form the ratio
if you throw a lot of points it will approximate π/4.
This is called "Monte Carlo Simulation" and is a very powerful technique.
Last edited by bobbym (2013-02-25 23:57:14)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#39 2013-02-26 01:01:23
- Agnishom
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Re: Python!
Wonderful!
However that would hugely depend on the capability to generate random numbers
I think it would be a better idea to try this
Code:
...
for x in xrange(0.1, 1.0, 0.01):
for y in xrange(0.1, 1.0, 0.01):
.....So that the points are not taken at random
Last edited by Agnishom (2013-02-26 01:05:29)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#40 2013-02-26 03:26:22
- bobbym
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Re: Python!
Hi;
The randomness is very important. It is the whole key to the algorithm.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#41 2013-02-26 06:12:26
- Agnishom
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Re: Python!
Why??? What If we try all the possible points?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#42 2013-02-26 06:15:59
- bobbym
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Re: Python!
It would take too many to try them all there are an infinite number. The random generator samples the points that your scheme might miss.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#43 2013-03-02 21:53:45
- Agnishom
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Re: Python!
I will see which is better .... I shall do the experiment
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#44 2013-03-03 06:12:29
- bobbym
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Re: Python!
It is easy to design areas that a uniform spread of points such as yours might miss.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#45 2013-03-03 15:04:30
- Agnishom
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Re: Python!
I did it.
You seem to be correct........
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#46 2013-03-03 15:17:31
- bobbym
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Re: Python!
Hi;
That was an interesting idea though.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#47 2013-03-03 22:02:16
- anonimnystefy
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Re: Python!
Hi bobbym
Is it just me or do the points in the plot in post #36 look a little denser near the line x=1/2?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#48 2013-03-03 22:05:39
- bobbym
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Re: Python!
Yes, that was when we could not upload any pictures and I had to use one from the internet. Unfortunately I chose one from a math forum. The guy who wrote the routine did a bad job and the points are not randomly placed.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#49 2013-03-03 22:07:48
- anonimnystefy
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Re: Python!
Maybe they are randomly placed but with a different distribution.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#50 2013-03-03 22:09:04
- bobbym
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Re: Python!
Nah, his method of generating random numbers was not good.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.