# meta data, consisting of a set of parameters

Geometric objects require meta parameters. For polygons, one such parameter is the Boolean (‘yes’ / ‘no’) variable as to whether any side length information is given. An answer of ‘no’ is colloquially referenced by saying that the triangle is ‘scalene’. (In the absence of conscious use of meta parameters, a ‘scalene’ triangle is crudely taken to be a triangle having 3 sides of unequal length.) Another meta parameter, for trapezoids, is which parallel sides (in case there are more than one pair of such) are to be considered the bases of the trapezoid, the other two sides being considered the ‘legs’ of the trapezoid, referred to colloquially as ‘the non-parallel sides of the trapezoid’ even if they are in fact parallel (in the case of a parallelogram). (Thus, the use of meta parameters eliminates the confusion as to whether a parallelogram should be considered a trapezoid. Without meta parameters, the phraseology forces a negative answer, but at the cost of making the Trapezoidal Rule (in Calculus) awkward to apply.)
Another meta parameter is the Boolean variable as to whether the geometric object is to be considered as a point-set, or as distinguished object. For example, a square, considered as a point set is not convex, but considered as a distinguished object, is (convexity for a distinguished Jordan curve being defined in terms of the convexity of the region that it bounds). Also, a square, considered as a point set, has area 0, but considered as a distinguished object, has positive area (area for a distinguished Jordan curve being defined in terms of the area of the region that it bounds). In short, lack of an acceptance of a framework of meta data causes exclusivity-based definitions. This is why such definitions are the rule in elementary school – because the concept of meta data is somewhat sophisticated and automatically presumed to be beyond the capabilities of young students – if the concept of meta data is even consciously entertained by their teachers at all. (Chesterton would likely weigh in here with something about gentle contempt.)
keywords: language, Geometry, Mathematics