MANY DIMENSIONS OF THE ART

The man loves art. He fills space and time with art. He can create art in any dimension.

Lines and curves are one-dimensional art. Also frieze and calligraphy.

Painting, photographs are two-dimensional art.

Sculpture, architecture are 3-dimensional art forms.
If we add 'time' (fourth dimension) to these spatial dimensions, what it will yield?
If we add 'time' to one dimension, we get 'music'.
If we add time to photo (2-dimensional), we get a movie.

Adding time to frozen actors yields drama and theatre.

If you move the time to and fro in a movie or drama, you get historical or science fiction. If time takes many paths, you get a variety of stories with many endings (black mirror in Netflix).

Fractional dimensions also exist
A straight line occupies one dimension. A photo fills two dimensions. Suppose, you create an intricate pattern on a sheet of paper with a pencil, its dimension is between 1 and 2. A fractional dimension.

A solid stone pillar occupies three dimensions. Suppose you carve out some figurines in the pillar, its dimension goes below two.
Adding time (motion) to cartoons (fractional dimension) gives animation.
A white moon on a black sheet looks great. A sprinkle of rose flowers in a green field looks beautiful. A white chalk writing on a blackboard yields information. Hence fractional dimensional art has great scope and beauty.

BEYOND DIMENSIONS
1. Mathematical fractals are itself an art -form.

CREATED BY MATH.

2. Fourier theory says that any curve, any repeated pattern can be represented as " a combination of sine waveforms".
3. Suppose you scan a painting. The picture is divided into numbers of lines. Each line further divided into no.of points. Colour info. and intensity info. of each point is converted into numbers.
A thing of beauty and math is a joy forever.
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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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