Gnomon

Stapleton, H.E. The Gnomon as a possible link between (a) one type of Mesopotamian Ziggurat and (b) the magic square numbers upon which Jabirian alchemy was based. Ambix 6, no. 1 (Aug 1957) 1-9. 

In the Hebrew, this versicle consists of exactly twenty-five letters, the number of the letters of the square. It will be at once noticed that both this form and that given by Abraham the Jew [a legendary Alchemist] are perfect examples of double acrostics, that is, that they read in every direction, whether horizontal or perpendicular, whether backwards or forwards.. .. It is also to be observed, that while many of the Symbolic Squares of Letters of the Third Book present the nature of the double Acrostic, there are also many which do not, and in the case of a great number the letters do not fill up the square entirely, but are arranged somewhat in the form of a gnomon. Others again leave the center part of the square blank. ... 

Centuries ago, time was measured by the gnomon, the clepshydra, weights and gears (eventually controlled by an escapement), incense sticks, hourglasses, and then finally mechanical clocks, pendula, and self-winding watches (mechanically wound, self-winding, or by now controlled by a quartz crystal oscillator tank circuit). 

In a triangle, the lines from the vertices to the points of contact of the opposite sides with the inscribed circle meet in a point called the Gergonne point, gnomon magic square... 

A projective plane may be generated by adding to the Euclidean plane a line at infinity. The Euclidean plane itself is equivalent to the gnomonic projection of a sphere on a plane, a shown in figure 12. Each point P in the... 

Figure 7.12 Gnomonic projection of point Pi on P in the Euclidean plane a. The line m maps the stippled great circle.

McGregor JL (1997) Semi-Lagrangian advection on a cubic gnomonic projection of the sphere. In Lin C, Laprise R, Ritchie H (eds) Numerical methods in atmospheric and oceanic modelling the Andre J. Robert Memorial (Companion volume to atmosphere-ocean). Canadian Meteorological and Oceanographic Society, Ottawa, Canada, pp 153-169... 

Chau, P.-L. and Dean, P.M. (1987). Molecular Recognition 3D Surface Structure Comparison by Gnomonic Projection. J.MoLGraphics, 5, 97-100. 

A useful transformation of the flat film Laue pattern is the gnomonic projection. This converts the pattern of spots lying on curved arcs to points lying on straight lines. This is advantageous in determining the soft limits Amin, Amax and dmin (Cruickshank, Carr and Harding, to be... 

It follows from the mapping of the points on a sphere to a tangential plane using central or gnomonic projection through the centre O of the sphere as... 

Fig. 1 - Natural numbers. The gnomon (generator) of the -th number, in its familiar rows-of-balls manifestation, is a single ball. The conotation of the term gnomon is that originally given by Hero of Alexandria A gnomon is that form which, when added to some other form, results in a new form similar to the original [5, 6].

Fig. 5 - Odd numbers have the form of the gnomon of a square. The most familiar form of a gnomon is the L-shaped object of that name that serves as a sundial pointer.

Fig. 6 - Square numbers composed from L-shaped gnomons.

Note that the second differences are constant (i.e., 15). If and when we reach a row that contains a constant value, we can write an explicit expression for fin). In Pythagorean terms one would say that if the method of finite differences is applicable, each difference can be considered as a gnomon for a previous series. We can consider numbers in Table 4 as Pascal s triangle modification C . 

It then appears that clusters at the beginning and in the continuation of the series correspond to different gnomons. 

In this paper we have attempted to couple modem atomic theories with an ancient guiding principle. In particular, a parallel between atomic, nuclear and cluster shells is carried out using a fundamental concept of the Pythagorean school known as the gnomon. 

Midhat J. Gazale, Gnomon From Pharaohs to Fractals, Princeton University Press, 1999, 259 pages. 

J. Schombert, Gnomones http //zebu.uoregon.edu/-is/glossarv/gnomones.html... 

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