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By P. K. Jain, Ahmed Khalid

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Extra resources for A Textbook Of Analytical Geometry Of Two Dimensions

Sample text

But there is a natural frame of reference. Once we are given an object, we know that there i3 a ‘POim' de ned by the Obie“ which. can function as the origin of any frame. From physics we know that for every object with some mass and shape, there is a point Called the centre of mass. 3150. Every figure has a central Point. This centre of mass is a unique pon" once we know the mass distribution in the object. In principle We can calculate it for any Object. It also has Phenomenological implicauom‘ In general the point ofstability of an object is its centre of “1255- “we take a uniform StiCk we can balance it at its centre.

121). Also note that since an event is the change of an object, one can locate the event in the object. But do we really have to inSiSt that a change in a proper part of an object should be identical with a change in the object? He dilutes this condition and suggests that the ‘SUbiCCt Of 3“ cvenr’ is only thcr‘minimally involved object' that undergoes change. Thus the location ofan event is the location of the proper part which undergoes change. Note that this does not refute the above thesis but only Specifies the location of an event.

This change in oriented form actually re ects the change in the triangle mused by rotation. As is easy to see, under a mtarion of120 degrees, the oriented form is speci ed by the triplet [120. 240, 360} and since rotation through 360 degrees is the same as through 0 dcgrm, we can write this as {120, 240, 0}. Now we see why the oriented forrn needs a triplet structure. If it is a triplet, then we know that {0, 120, 240} is the same 85 {120. 240, 0}. Thus we can con dently claim that under rotation of 120 degrees, the _..

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