HOW TO DETECT FINANCIAL FRAUD?

6.25 , here 6 is the first digit.
72.5, 7 is the first digit
12.65 1 is the first digit.
We think, all the digits (1 to 9) have equal probabilities to appear as first digit. That is, they has to appear 1 out of 9 times - 11% probability.

But a man, named Benford researched heavily and gave a law. "The 'one' appears as a first digit 30% of the time". The small numbers 1,2,3 appears more as first digit than large numbers like 7,8,9.
Benford law holds good in baseball statistics, area of rivers, population sizes, street address, city populations, super market prices etc.
Let us consider door numbers in a street which has 30 houses.

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19.20,21,22,23,24,25,26,27,28,29,
30.

1 appears 11 times as first digit out of 30. So around 30% times.
Let us say, a price starts at 1 dollar and goes up 10% every time.
1.00.1.10, 1.21,1.33,1.46,1.61,1.77,1.95,2.14,2.36,2.59.....
So naturally 1 appears more times.

SOME PHYSICS CONSTANTS
1. Electronic charge= 1.6021 *10ˆ19 C
2. Magnetic constant= 1.2566...
3. Boltzmann constant =1.3806...
4. Atomic mass constant= 1.6605*10ˆ-27 kg.
5. Atmospheric pressure = 101325 pa
6. Square root of 2 = 1.414
7. Square root of 3 = 1.732
8. Golden ratio =1.618

The human body's vital parameters like, pulse, BP, temperature, oxygen level, waist measurement, sugar level all should be around 100 -one as first digit.

So if you cook up your tax report or balance sheet, a computer software based Benford law will give you away.
According to Benford, the probability of a digit for being a first digit is given below.
1 2 3 4 5 6 7 8 9
30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6%

Small numbers play a major role in our life than large numbers.
We have one sun, one moon and one living planet. Two genders. Three dimensions. Two forms of life- animals and plant. A three letter language called DNA. The most abundant element in the universe is Hydrogen-a one proton -one electron atom. The list goes on.
'One' and 'small numbers' dominate this universe.
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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