The document introduces the mid-square random number generation method, invented by John von Neumann, which involves squaring a seed number and extracting digits to produce pseudorandom numbers, though it is not reliable due to its short period. It outlines the method, provides an example of generating random numbers, discusses its limitations, and highlights various applications of random numbers in fields like simulation, sampling, numerical analysis, and decision-making. The document concludes by noting the historical and recreational significance of randomness, linking it to the Monte Carlo method.

1. Welcome

2. Topic Name : Mid-Square Random Number Generation
Presented By
Md: Arman Hossain

3. OUTLINE
 Introduction
 Mid-square Method
 Example of Mid-square
 Departures of Mid-square Method
 Applications of Random Numbers
 References

4. INTRODUCTION
Mid-square method was invented by John von Neumann, and was described at a conference in 1949.
In mathematics, the mid-square method is a method of generating pseudorandom numbers. In practice it is
not a good method since its period is usually very short.

5. Mid-square Method
1. Starting with n digit number
2. Squaring it
3. For 8 digit : Remove two lower and higher order digit
4. For 7 digit : Remove one lower and two higher order digit
5. Taking n digits in the middle as the next number
6. Repeat from number no. 2.

6. Example of Mid-square
For an example, we are using 4 digit which is called seed number, we are showing generate 5 random number
here,
5673
1. (5673)2 = 32 1829 29 = 1829
2. (1829)2 = 3 3452 41 = 3452
3. (3452)2 = 11916304 = 9163
4. (9163)2 = 83960569 = 9605
5. (9605)2 = 92256025 = 2560
Remove two
higher order digit
Remove two
lower order digit
Next seed
number
Square seed
number
Remove one
higher order digit
Remove two
lower order digit

7. Departures of Mid-square Method
Converge on a constant :
 2500
(2500)2 = 6 2500 00 = 2500 This will repeated.
 2504
(2504)2 = 6 2700 16 = 2700
(2700)2 = 7 2900 00 = 2900
(2900)2 = 8 4100 00 = 4100
.
.
(2100)2 = 4 4100 00 = 4100 This will repeated also.
There more constant number like this.
seed
seed

8. Applications of Random Numbers
 Simulation : when a computer is being used to simulate natural phenomena, random numbers are
required to make things realistic. Simulation covers many fields, from the study of nuclear physics to
operations research.
 Sampling : It is often impractical to examine all possible cases, but a random sample will provide
insight into what constitutes “typical behavior”.
 Numerical analysis : Ingenious techniques for solving complicated numerical problems have been
devised using random numbers.
 Computer programming: Random values make a good source of data for testing the effectiveness of
computer algorithm.
 Decision making : There are reports that many executives make their decisions by flipping a coin or
by throwing darts, etc. It is also rumored that some college professors prepare their grades on such a
basis. Sometimes it is important to make a completely "unbiased decision; this ability is occasionally
useful in computer algorithms, for example in situations where a fixed decision made each time would
cause the algorithm to run more slowly. Randomness is also an essential part of optimal strategies in
the theory of games.
 Recreation : Rolling dice, shuffling decks of cards, spinning roulette wheels, etc., are fascinating
pastimes for just about everybody. These traditional uses of random numbers have suggested the name
"Monte Carlo method," a general term used to describe any algorithm that employs random numbers.

9. THANK YOU