THE ORIGIN OF CALANDER

The calendar mainly based on the motions of celestial bodies.

We know the time taken by the earth to go round the sun once is taken as one year. We also know the time for the earth to spin is taken as a day. It happens to be 365+ days in a year. That is why, a circle is divided into 360 degrees.

Moon takes roughly 29+ days to go round the earth. Hence 30 days average is taken as the month. The moon revolves around the earth 12 times a year.

Seven days makes a week. Because only seven heavenly objects were known then. Hence the week days were named after them.
Sun - Sunday, moon - Monday, mars - Tuesday, mercury - Wednesday, Jupiter - Thursday, Venus - Friday, Saturn - Saturday.

In the past, sundials (measuring time using shadow) were used to measure daytime. It had 12 equal marks. So we have "12 hours day and 12 hours night" system still.

Each hour is split into 60 minutes and a minute into 60 seconds. Similarly a degree (angle) is split into 60 minutes and 60 seconds.

English calender count the years from the birth of Christ. Other calenders follow their own system.

We can learn some mathematics from calender system.

Modular arithmetic: 10 days have gone by from last Sunday. what is the day now?
'10 modulus 7' is 3. So after 3rd day, 4th day-Wednesday is running now .
Modulus means 'divide by 7 and get the reminder only'.

Base 60 : How much time is between 9:45 a.m. and 12:30 a.m?
12:30-9:45 = 11:90-9:45 = 2:45
The answer is 2 hours and 45 minutes. Here we should bear in mind, the hour and the minute has the base of 60.

The calender becomes meaningless at the north and south poles of earth. The sun never rise or set and it only circles there. Because of the tilting of the earth every six months, "6 month day and 6 month night" prevails there.

If we happen to live in moon, we have to design a new lunar calender because a lunar day is equal to one terrestrial month.

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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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