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Buffon's needle problem proof
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Area of the rectangle
Area of the rectangle
13
Expression 14: "S" equals "D" times StartFraction, pi Over 2 , EndFraction
S
=
D
·
π
2
equals
=
1.5 7 0 7 9 6 3 2 6 7 9
1
.
5
7
0
7
9
6
3
2
6
7
9
14
The probability that a toss is a success (crossing)
The probability that a toss is a success (crossing)
15
Expression 16: "P" Subscript, "c" "r" "o" "s" "s" , Baseline equals StartFraction, "A" Over "S" , EndFraction
P
c
r
o
s
s
=
A
S
equals
=
0.6 3 6 6 1 9 7 7 2 3 6 8
0
.
6
3
6
6
1
9
7
7
2
3
6
8
16
Result for pi with analytically obtained Pcross
Result for pi with analytically obtained Pcross
17
Expression 18: pi Subscript, "c" "a" "l" "c" , Baseline equals StartFraction, 2 "L" Over "P" Subscript, "c" "r" "o" "s" "s" , Baseline "D" , EndFraction
π
c
a
l
c
=
2
L
P
c
r
o
s
s
D
equals
=
3.1 4 1 5 9 2 6 5 3 5 9
3
.
1
4
1
5
9
2
6
5
3
5
9
18
Estimated value of pi.
Estimated value of pi.
19
Using Pcross from trowing we can obtain estimation of pi
Using Pcross from trowing we can obtain estimation of pi
20
Let's say we have L = D = 1 and N (number of throws) = 100 with S (crossings) = 62
Let's say we have L = D = 1 and N (number of throws) = 100 with S (crossings) = 62
21
Expression 22: "N" Subscript, "t" "o" "s" "s" , Baseline equals 100
N
t
o
s
s
=
1
0
0
0
0
1000
1
0
0
0
22
Expression 23: "S" Subscript, "t" "o" "s" "s" , Baseline equals 62
S
t
o
s
s
=
6
2
0
0
1000
1
0
0
0
23
Expression 24: "P" Subscript, "e" "s" "t" , Baseline equals StartFraction, "S" Subscript, "t" "o" "s" "s" , Baseline Over "N" Subscript, "t" "o" "s" "s" , Baseline , EndFraction
P
e
s
t
=
S
t
o
s
s
N
t
o
s
s
equals
=
0.6 2
0
.
6
2
24
Expression 25: pi Subscript, "e" "s" "t" , Baseline equals StartFraction, 2 "L" Over "P" Subscript, "e" "s" "t" , Baseline "D" , EndFraction
π
e
s
t
=
2
L
P
e
s
t
D
equals
=
3.2 2 5 8 0 6 4 5 1 6 1
3
.
2
2
5
8
0
6
4
5
1
6
1
25
26
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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