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The Kodaikanal Archive Program (India) is now available to the scientific community in digital form as daily digitized solar white light pictures, from 1923 to 2011. We present here the solar radius data, obtained after a painstaking effort…
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…
Temporal variation of the solar coronal rotation appears to be very complex and its relevances to the eleven-year solar activity cycle are still unclear. Using the modified coronal index for the time interval from 1939 January 1 to 2019 May…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proportional systems, long associated with natural growth and…
Recently Pop ({\it Solar Phys.} {\bf 276}, 351, 2012) identified a Laplace (or double exponential) distribution in the number of days with a given absolute value in the change over a day, in sunspot number, for days on which the sunspot…
Supergranulation on the surface of the Sun is an organized cellular flow pattern with a characteristic scale of 30 Mm. It is superficially similar to the well understood granulation that operates at the 1.5 Mm natural scale of convection,…
In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit…
Based on the nine-palace diagram, we establish the systematical geometric theory of arithmetic, which can realize the arithmetical addition, subtraction, multiplication, division and other operations thoroughly in the mind. In this paper,…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
The statistics of catalogued quadruple stars consisting of two binaries (hierarchy 2+2) is studied in comparison with triple stars, with respective sample sizes of 81 and 724. Seven representative quadruple systems are discussed in greater…
The existence of "dark matter", inferred from the observed rotation curves of galaxies, is a hypothesis which is widely regarded as problematic. This paper proposes an alternative hypothesis based on the space-time geometry near a rotating…
The Hebrew Calendar is based on very deep and complicated mathematics, involving diophantine approximation, but it is very surprising that the gaps between consecutive Christmas-in-Hanukkah years is always a member of the set {2,3,5,8}.…
The spiral galaxies, including our galaxy, are created by the gravito-radiative forces generated by colliding black holes at the center of quasars. The gravito-radiative force is predicted by Einstein's general relativity. A quasar is…
The visible diameter of Sun oscilates with a period of 160 min. The same type of periodicity is also found in a huge number of solar radiation parameters. To elucidate the origin of these longitudinal radial pulsations we have used the…
The parallel globe is an old, very simple and ingenious device that, when systematically employed in astronomy classes, becomes a teaching tool with great potential. Properly oriented according to the local meridian, this instrument allows…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
One of the goals that physicists have been pursuing is to get the same explanation from different angles for the same phenomenon, so as to realize the unity of basic physical laws. Geometry, classical mechanics and classical thermodynamics…
The French Academy units of time and length - the second and the meter - are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each oscillation,…