“[...] a description is an objective depiction and a depiction is a subjective description. Interesting idea, hard to illustrate.” A quote from the blog of Paul Pope (pulphope.blogspot.com). We looked at this sentence with great care. In it we found something similar to our recent inquiry of research. At first we thought these examples were constellations mapped out, having read Mr. Pope’s thoughtful paraphrased sentence, we looked at the examples again and found more to it than that. We now believe these examples to be that of dots and points.
1. A spatial point is a concept used to define an exact location in space. It has no volume, area or length. Points are used in the basic language of geometry, physics, vector graphics (both 2d and 3d), and many other fields. In mathematics generally, particularly in topology, any form of space is considered as made up of points as basic elements.
2. A point in Euclidean geometry has no size, orientation, or any other feature except position. Euclid's axioms or postulates assert in some cases that points exist: for example, they assert that if two lines on a plane are not parallel, there is exactly one point that lies on both of them. Euclid sometimes implicitly assumed facts that did not follow from the axioms (for example about the ordering of points on lines, and occasionally about the existence of points distinct from a finite list of points).
3. Therefore the traditional axiomatization of point was not entirely complete and definitive.
4.When used as a diacritic mark, the term dot is usually reserved for the Interpunct ( · ), or to the glyphs 'combining dot above' and 'combining dot below' which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese.
5. In mathematics and physics the dot denotes the time derivative.
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