HOW TO SELECT A PRODUCT ONLINE?

On a online store X, a product costs 200 dollars and it has 15 positive reviews. Another online store Y features the same product for a price of 250 dollars with 32 positive reviews. Which one to buy?
Little Math:
Find the product of prices and reviews . Then take the square root of the answer. Do it for the both the stores.

For store X:
Square root of (200*15) = 54.77
For store Y:
Square root of (250* 32) = 89.44

89.44 is greater than 54.77. Hence go for the store Y. These numbers called geometric mean. This 'measure' is used to compare widely different values like 200 and 15. Average stand best for closely related numbers like 120, 125, 101.

SOME MORE USES OF GEOMETRIC MEAN
1. Making square out of rectangle:

Say, 18 cm and 2 cm are the sides of a rectangle. Find the geometric mean of them.
Square root of( 8*2) =6.
Now draw a square with 6 cm side. The rectangle and the square will have the same area.
In other words
18 * 2 =6*6

2. Making cube from cuboid:
Say, a cuboid has sides 10 *51.2 *8.
Take geometric mean. Here we have to take cube root. Since we have three numbers.
Cube root of(10 * 51.2 * 8) = 16.
If you build a cube with side 16 CM, then the cuboid and the cube will have the same volume.
In other words
10 *5 * 2 * 8 = 16*16*16.

We can extend the principle of geometric mean to any number of numbers. For example
G.M of 1,3,9,27,81
1*3*9*27*81 = 59049
5th root of 59049 =9
Since there are five numbers, we take 5th root. Now,
1*3*9*27*81 = 9*9*9*9*9

GM Definition: For n numbers; multiply them all together and then take the nth root.

UNITED NATIONS HUMAN DEVELOPMENT INDEX -HDI
It is "..... a summary measure of average achievement in key dimensions of human development; 1. a long and healthy life 2. being knowledgeable 3. have a decent standard of living. The HDI is the "geometric mean" of normalized indices for each of the three categories."

A simple "GM" has many many applications. Math is fun and useful.
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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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