Ashutosh Kumar

Ways of Calculating PI

1) Calculate PI by by "shooting a cannon" at a round pond of radius 1 unit inscribed within a 2X2 square of land.Corners of land are: (0,0),(1,0),(1,1),(0,1)

A "Splash" is defined as the event when the cannon lands in water.
A "Thud" is defined as the event when the cannon lands on ground (in square).
Shots=Number of shots fired.
Ratio=Splashes/Shots.
Now ratio=1/(4*PI)

ALGORITHM:
1)Generate X & Y coordinates of shots randomly, shots++
2)dx=1-X,dy-i-Y,i.e ditance from origin.
3)dist=sqrt((dx*dx)+(dy*dy))
4)if disy<=1.0 splashes++ else thuds++
5)ratio=splashes/shots
6)PI=ratio * 4;
7)Go to 1 if accuracr not achived.

2) There is wooden plan with planks of equal width.Drop a pin on floor.If any part of pin touches the crakcs b/w boards, it is a HIT.
ratio=HITS/Total drops of pin, and
PI=ratio/10

ALGORITHM:
1)Generate horizontal position of one end of pin as dx.Generate angle of pin from horizontal as theta.
2)If theta<=90)
If (dx+Cos(theta)>=1)hits++
else If (dx-cos(180-theta))<=0) hits++
3)ratio=hits/drops

3)(PI/6)^2=1= (1/2)^2 + (1/3)^2 + (1/4)^2 +.........

There are only 10 kinds of people, those who understand binary, and those who dont. (source unkown, {its my email signature also.})

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"Suppose that we think of the integers lined up like dominoes. The inductive step tells us that they are close enough for each domino to knock over the next one, the base case tells us that the first domino falls over, the conclusion is that they all fall over. The fault in this analogy is that it takes time for each domino to fall and so a domino which is a long way along the line won't fall over for a long time. Mathematical implication is outside time."
Peter J. Eccles (An Introduction to Mathematical Reasoning, p. 41)

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"When I entered graduate school I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann's and Feynman's doors and asked them what they were currently doing. Murray wrote down the partition function for the three-dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman's answer was 'nothing'."
Ken G. Wilson (quoted in J.M. Yeomans, Statistical Mechanics of phase transitions, p. 35)

A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e , where e need not be the base of the natural logarithms." A Mathematician's Miscellany, Methuen Co. Ltd., 1953.

"1/r^2 has a nasty singularity at r=0, but it did not bother Newton--the Moon is far enough."
Edward Witten (AMS Gibbs Lecture, Baltimore, Jan. 7, 1998)

Maths

"Who has not be amazed to learn that the function y = e^x , like a phoenix rising again from its own ashes, is its own derivative? "

le Lionnais, Francois Great Currents of Mathematical Thought, vol. 1, New York: Dover Publications.

Ways of Calculating PI

A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e , where e need not be the base of the natural logarithms." A Mathematician's Miscellany, Methuen Co. Ltd., 1953.

"1/r^2 has a nasty singularity at r=0, but it did not bother Newton--the Moon is far enough."
Edward Witten (AMS Gibbs Lecture, Baltimore, Jan. 7, 1998)

"All means (even continuous) sanctify the discrete end."
Doron Zeilberger (Wed, 14 Aug 2002 16:29:35 -0400 (EDT))

Maths

"Who has not be amazed to learn that the function y = e^x , like a phoenix rising again from its own ashes, is its own derivative? "

le Lionnais, Francois Great Currents of Mathematical Thought, vol. 1, New York: Dover Publications.

Ways of Calculating PI

A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e , where e need not be the base of the natural logarithms." A Mathematician's Miscellany, Methuen Co. Ltd., 1953.

"1/r^2 has a nasty singularity at r=0, but it did not bother Newton--the Moon is far enough." Edward Witten (AMS Gibbs Lecture, Baltimore, Jan. 7, 1998)

"All means (even continuous) sanctify the discrete end." Doron Zeilberger (Wed, 14 Aug 2002 16:29:35 -0400 (EDT))

"1/r^2 has a nasty singularity at r=0, but it did not bother Newton--the Moon is far enough."
Edward Witten (AMS Gibbs Lecture, Baltimore, Jan. 7, 1998)

"All means (even continuous) sanctify the discrete end."
Doron Zeilberger (Wed, 14 Aug 2002 16:29:35 -0400 (EDT))