Magic Square

The ancient Chinese Magic Square was followed by the Lo Shu Square, which dates back to 2200 B.C. It symbolizes the natural order of the Universe, promoting logic, strategy and open-mindedness.

The Legend of Lo Shu
During ancient times in China there was a huge flood on the Lo River. The people tried to calm the River god’s anger by offering sacrifices, but each time they prepared an offering a turtle came up from the river and walked around the sacrifice, and the River god wouldn't accept the sacrifice. This happened several times, until one time, a child noticed curious markings forming a pattern on the turtle’s shell. After studying these markings the people realized the correct amount of sacrifices to make, that is 15. Then the river god was placated. The numbers in every row, up and down, across, or diagonally, add up to 15, which happens to be the number of days it takes for the new moon to become a full moon.
The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10 (e.g., opposite corners add up to 10.
This pattern, in a certain way, was used by the people in controlling the river. The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection.
The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos.

Cultural significance of the magic square in India
Magic squares have fascinated humanity throughout the ages, and have been around for over 4,120 years. They are found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.

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Tables made easy

You can multiply most of the problems in your head when you know your multiplication table up to 5 times table. If you know your 2, 3, 4 and 5 times tables up to 10 times each number, then you also know part of your 6, 7, 8, and 9 times table. As you learn your higher tables, mental calculations become much easier. It is easy to learn your 11 times table and the twelve times table is not difficult. Six times 12 is six times 10 plus six times two. It is easy to add answers for 6 times 12 to get 72.
6 X 10 = 60; 6 X 2 = 12; 60 + 12 = 72

We see, how easy it is to learn your tables and how it can be done much more quickly than in olden days.
It is usual to learn tables up to the 12 times table. It is not hard to learn the 13 times table if you know the 12 times table. If you know that 12 times 3 is 36, just add another 3 to get 39. Twelve threes plus one more three makes 13 threes. If you know 12 fours are 48. Just add another four to get 13 times 4 equals 52.

Now that you know your 13 times table, learn the 14 times table. Factor 14 to 7 times 2. Then you multiply the number by 7 and double the answer.
7 X 1 = 7; double = 14; 14 X 1 = 14
7 X 2 = 14; double = 28; 14 X 2 = 28
7 X 3 = 21; double = 42; 14 X 3 = 42
7 X 4 = 28; double = 56; 14 X 4 = 56
7 X 5 = 35; double = 70; 14 X 5 = 70
7 X 6 = 42; double = 84; 14 X 6 = 84
7 X 7 = 49; double = 98; 14 X 7 = 98
7 X 8 = 56; double = 112; 14 X 8 = 112
7 X 9 = 63; double = 126; 14 X 9 = 126
7 X 10 = 70; double = 140; 14 X 10 = 140

Practice these easy steps and you will learn your tables without even trying hard. You will find that you can multiply and divide directly by 13, 14 and 15. This will give you an advantage in your Math Class. comments

Fibonacci sequence in sunflower

The arrangement of seeds on the head of a sunflower is a very good example of the Fibonacci sequence. By closely observing the seed configuration we notice two series of curves, one winding in one direction and one in another. The numbers of spirals are not the same in each direction. If we count the number of spirals given in the figure, we notice the number is 21 and the number of spirals in the opposite direction is 34.

Coincidentally, this number is within the Fibonacci sequence. The numbers of spirals are not the same in each direction. In general they are either, 21 and 34, or 34 and 55, or 55 and 89 or 89 and 144. In principle all the sunflowers show a number of spirals that are within the Fibonacci sequence.
For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that one understands why. It is because of the efficiency during the growth process of plants.
In many cases, the head of a flower is made up of small seeds which are produced at the centre, and then migrate towards the outside to fill eventually all the space. Each new seed appears at a certain angle in relation to the preceding one. In order to optimize the filling, it is necessary to choose the most irrational number there is. This number is exactly the golden mean. The corresponding angle, the golden angle is 137.5 degrees. This angle has to be chosen very precisely. Even the variation of 1/10 of a degree destroys the optimization completely. When the angle is exactly the golden mean, two families of spirals (one in each direction) are then visible. Moreover, generally the petals of flower are formed at the extremity of one of the families of spiral. This explains why the number of petals corresponds on average to a Fibonacci number.
We learn that Nature is fortunately a much better Mathematician than most of us.

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