Visual Mathematics

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'Mathematics is for the intellectual giants', is the common belief. This is true as far as the subject mathematics is concerned. But, looking from a different angle, one can find that leading a life without mathematics is impossible, irrespective one's intellectual level. When mathematics is presented as a complicated cluster of theories and formulas which are difficult to crack and digest, common man is never attracted towards it. But if he understands things closely, the picture changes. Perhaps many may start loving it. That is one reason why mathematics is called the servant of all sciences.(It is also known as the Queen of all sciences).

For an ordinary man the knowledge of mathematics is very often limited to numbers and forms. A new born baby gradually gets familiarized with forms from his (or her) contacts. His mother's face may be the form that impress him first. The first geometrical form is printed in him through this acquaintance. Similar faces might attract his attention, but not other faces.

Little later, the child starts understanding about the quantity or numbers. A visual comparison of small and big might be leading him to this understanding. 'One' and 'more than one' could be the starting point. Slowly learns to identify and classify further. It was reported sometimes back that there are certain tribes - Hoten tots- who could not count beyond four (even for 'four', they hadn't got a name!).

The numbers might have followed the man's knowledge about 'one-to-one correspondence'. When human beings started keeping animals like cows, goats, buffaloes, etc., for his day to day living, the missing of them brought new problems. When these animals were sent out for grazing, they noticed that all were not coming back. As a method for finding out whether some were missing, they might have started using one to one correspondence. Against each animal going out, they kept aside a small piece of stone, which would be removed when the animals came back after grazing. If some stones are remained as balance, they understood that some animals were missing. Based on these information they developed management problems to bring back all animals. Later, based on experience, they might have given some marks on a rock corresponding to each animal and rubbed off while the animal returned. These markings gradually would have taken certain shapes and would have given birth to different types of numbers in different parts of the world.

Children are always attracted by the shapes and forms of things. A ball, spherical in size, rolling on the ground attracts every child. Other forms also impress them. A circular form like the full moon is a beautiful sight, not only for children, but for all. A pyramid is always an attractive thing.

Elders are also very much concerned about shapes and forms. In nature itself, the most occurring form is symmetry. Humans adapted this in their constructions and arrangements. This property on an extended manner can be observed in nature, if we try to analyze the frequency distribution of the occurrence of any natural phenomena. For example, the height frequency distribution of the boys belonging to a particular age group (say, five year old) if plotted on a graph, will give a symmetric curve with the peak appearing against the average height, and showing a decreasing trend towards both sides.

The term 'geometry' has been derived from its connection with the measurement of earth. The agricultural land on the banks of the river Nile, used to get eroded due to heavy rain water flow. So it became a necessity to demarcate the river border and land for which measurements of the area were taken. The term geometry was first used in this context, which later gained modified meaning as a subject under mathematics.

Different geometrical forms can be seen in nature. The shapes of leaves and flowers, their distribution, the cells in a honey comb (hexagon), the eggs, the stones in rivers with heavy water flow, the hills, etc., are examples. A sphere is the most stable form in nature. Similarly circular or elliptical movement is stable.

Basic geometrical forms are triangle, rectangle and circle. They are simple, efficient and strong. Because of this, man highly depends on these forms while attempting constructions. The available records indicate that triangle was more popular among Egyptians, while rectangles were preferred by the Greeks. Roman constructions have semi-circular forms as their specialty. Circle was given importance in old Indian constructions.

Studies show that mathematics developed and advanced into different branches based on the experiences gotten from the nature.

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