Polygon convex

The actual program used at NPL was written by N.P. Barry on the basis of the methods described previously. It is written in FORTRAN and has been implemented on IBM 370 and UNIVAC 1100 computers operated by computer bureaux. Vector algebra is employed. The reason why the graphs have double boundaries is that the calculation can be performed for boundaries of any convex polygon of up to 30 sides. This permits calculations to be restricted to the stability range of particular components, for example, that of water or chloride. 

As stated, the Platonic solids constitute a family of five convex uniform polyhedra made up of the same regular polygons and possess either 32, 432, or 532 symmetry. As a result, the three coordinate directions within each solid are equivalent, which makes these polyhedra models for spheroid design. 

These are cells of transition between the basal and superficial cells. They constitute the thickest and biggest layer. They are polygonal cells, with a convex front side and a concave back side. They are arranged on two or three layers at the center and five to six layers on the edge. Their nucleus is active and stretched out along the big axis of the cell. Their cytoplasm contains a very developed Golgi s apparatus as well as tonofilaments (microtubules and keratin filaments) connected to the desmosomes. Their cytoplasmic membranes are only united desmosomes and gap junctions that enable both the unity of intermediate cells and the union of intermediate and basal cells (Figs. 4.3. 5). 

Remark 1 A convex set may have no vertices (e.g., a line, an open ball), a finite number of vertices (e.g., a polygon), or an infinite number of vertices (e.g., all points on a closed ball). 

The comparison to a reference shape, which is generally the convex bounding polygon provides another set of descriptors, at a mesoscopic level of details. The index of concavity in length or in surface measures globally how the object departs from a convex shape ... 

Fig. 16. Concavity index measurement a Schematic somatic embryo b Convex bounding polygon, c Residual set...

CHALLENGING MATHEMATICAL PROBLEMS WITH ELEMENTARY SOLUTIONS, A.M. Yaglom and I.M. Yaglom. Over 170 challenging problems on probability theory, combinatorial analysis, points and lines, topology, convex polygons, many other topics. Solutions. Total of 445pp. 5S 8b. Two-vol. set. 

In addition to the Platonic solids, there exists a family of 13 convex uniform polyhedra known as the Archimedean solids. Each member of this family is made up of at least two different regular polygons and may be derived from at least one Platonic solid through either truncation or twisting of faces (Figure 3, Table 2). In the case of the latter, two chiral members, the snub cube and the snub dodecahedron, are realized. The remaining Archimedean solids are achiral. 

A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length, equilateral polygon... 

The five fundamental solids, the tetrahedron, the octahedron, the icosahedron and the dodecahedron were known to the Ancient Greeks. Constructions based on isosceles triangles are described for the first four by Plato in his Dialogue Timaeus, where he associated them with fire, earth, air, water and noted the existence of the fifth, the dodecahedron, standing for the Universe as a whole. These five objects are now known as the Platonic solids — defined as the convex polyhedra because they exhibit equivalent convex regular polygonal faces. 

To avoid undercutting, compensating structures must be used, generally simple polygonal extensions of the mask at the convex corners. A large variety of such convex corner-compensating structures have been proposed [22, 23]. 

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