Coordinate geometry is an interesting branch of mathematics. In plane coordinate geometry, there are two axes, namely, ‘X’ and ‘Y’, crossing each other at right angles. The point of intersection is known as the origin. The origin is given the coordinates, zero-zero. All other points lying on the plane of these two axes are given coordinates with respect to the origin. Thus, each point has two coordinates known as ‘X’ and ‘Y’ coordinates. Depending upon the position of the point, these are either positive or negative or a combination. Since the plane is divided into four quadrants, one quadrant has both the coordinates positive, one both negative and the remaining two quadrants have one coordinate positive and one negative. In graphic form, these may be shown as below:
Based on the relationship of these coordinates, various figures are studied in this branch of mathematics. Starting with a straight line, there are complex figures of various shapes.
Overall, the study is very interesting. From two-dimensional geometry we proceed to three-dimensional, which is a little complicated but the basic principles remain the same. Here, the study is made in respect of three-dimensional figures instead of two-dimensional figures. Viewed philosophically, the basic principles of this branch give some very interesting lessons for life. I intend to share my reflections, confining them to the lessons which can be learnt from two-dimensional coordinate geometry.
Firstly, the four quadrants can be compared with the different states of mind. The quadrant with both positive coordinates indicates the happy state of mind when one feels everything positive in life. The quadrant with both negative coordinates indicates the gloomy state of mind when everything appears to be negative. The remaining two quadrants indicate a mixed state where some aspects appear to be positive and some negative. The lives of most of us pass through these three phases and we accept them as such. In all these phases we dissipate our energy either by enjoying or suffering and eventually depart from the earth. The cycle goes on till we understand the truth and realise it. In fact, the truth lies in rising above both positive and negative. Such a position is possible only at the origin which is the supreme reality, or in other words, God. Till we realise this position, we keep on dissipating our energy, irrespective of our coordinates.
An interesting comparison can also be made with three tendencies, namely Sattwik, Rajasik and Tamasik. The first quadrant represents the Sattwik tendencies, the second and fourth represent the Rajasik and the third represents the Tamasik. Most of us have Rajasik tendencies and that is why they occupy two quadrants. Such tendencies motivate us to act for the fulfilment of a desire. If the desire is fulfilled we feel happy and if not, we feel unhappy. On the other hand, the Sattwik tendencies always keep us happy while the Tamasik keep us unhappy. Again the fact is that we stay away from the truth and keep dissipating our energy in all the three situations. The only difference is that in the Sattwik situation, energy is used for good purposes, in Rajasik, for mixed purposes while in Tamasik, for bad purposes. Therefore, the answer lies in rising above all the three tendencies and to become Gunatita. This state is possible only when we take our position at the origin which is nothing but the supreme reality or God. This is what is concluded by Lord Krishna also, in the 18th chapter of the Gita.
There can be two ways of achieving such a position. One is not to move from the origin, which means that we remain engrossed in God and do not come out in the world at all. This is not possible for most of us who have to lead an active life in the world. The alternative, therefore, is to see God in each happening and object of the world. It means that whatever interaction we have in the world should be seen as emanating from the supreme reality and we should accept it in a detached manner. In that case, everything will appear to be from the origin and the question of positive or negative will not arise at all. In terms of coordinate geometry, it amounts to shifting the axes in such a manner that whatever point we see should appear to be the origin. After all, God is said to be omnipresent and it should not be difficult to see Him everywhere. In coordinate geometry, an exercise for shifting the axes is given occasionally and in life it should be a constant exercise.
Rakesh Mittal IAS
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