DOUBLING IS THE BEST WAY

ADVT: HOME PROJECTOR IN AMAZON

1. CODE

Double the number as follows

1, 2, 4, 8

= 2^0, 2^1, 2^2, 2^3

Now reverse them as 8 4 2 1

Now code as follows

8 4 2 1

0 0 0 0 represents 0

0 0 0 1 represents 1

0 0 1 0 represents 2

0 0 1 1 represents 3

0 1 0 0 represents 4

0 1 0 1 represents 5

..... .... ... .... ......

.... ..... .... .. ......

1 1 1 1 represents 15

8 4 2 1 code can represent up to 15. But 0 to 9 is enough to represent all numbers.

8 4 2 1 8 4 2 1 8 4 2 1

345 = 0 0 1 1(3) 0 1 0 0(4) 0 1 0 1(5)

this code is used in digital gadgets.

2. Weights:

In those days, weighing stones were used by traders. To measure up to 255 kg, the following weights are enough.

1,2,4,8,16,32,64,128

(doubling way)

To weigh 153 kg, use

128+16+8+1 =153

You can try any other weight.

3. Doubling money:

Normally, coins and notes in the following denominations are in circulation.

1,2,5,10, 20,50,100,200,500,1000, 2000

Here, instead 4, five is used. So, it will be practical and round one. Now the transaction and trading will be easy with those banknotes and coins.

4. Egyptian Multiplication:

We want to multiply 13 and 7. Let 13 be the multiplicand and 7 be the multiplier. Now, write doubling numbers in one column up to multiplicand and not exceeding the multiplicand.

Not 16, it exceeds 13.

In the next column, start with multiplier and double it every step.

Multiplicand multiplier

1 7

2 14

4 28

8 56

In the first column, if you add 1+4+8 = 13, we get the multiplicand. In the second column, add the corresponding numbers, you get the answer 91 (7+28+56).

Principle: We want 13 times7. Adding 1 times 7, 4 times 7, and 8 times 7, we get 91 which is 13 times 7.

Egyptians practiced this kind of multiplication in 2000 BC. How smart they were!

Comments

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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