Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body

Deep Chandra Observations of Abell 2199: the Interplay between Merger-Induced Gas Motions and Nuclear Outbursts in a Cool Core Cluster

We present new Chandra observations of Abell 2199 that show evidence of gas sloshing due to a minor merger, as well as impacts of the radio source, 3C 338, hosted by the central galaxy, NGC 6166, on the intracluster gas. The new data are consistent with previous evidence of a Mach 1.46 shock 100" from the cluster center, although there is still no convincing evidence for the expected temperature jump. Other interpretations of this feature are possible, but none is fully satisfactory. Large scale asymmetries, including enhanced X-ray emission 200" southwest of the cluster center and a plume of low entropy, enriched gas reaching 50" to the north of the center, are signatures of gas sloshing induced by core passage of a merging subcluster about 400 Myr ago. An association between the unusual radio ridge and low entropy gas are consistent with this feature being the remnant of a former radio jet that was swept away from the AGN by gas sloshing. A large discrepancy between the energy required to produce the 100" shock and the enthalpy of the outer radio lobes of 3C 338 suggests that the lobes were formed by a more recent, less powerful radio outburst. Lack of evidence for shocks in the central 10" indicates that the power of the jet now is some two orders of magnitude smaller than when the 100" shock was formed.Comment: 17 pages, 20 figures, accepted for publication in Ap

Population growth, labour absorption and income distribution

The purpose of this paper is to explore the main qualitative relationships between population growth, employment expansion and changes in income distribution. These relationships are extremely complex with an intricate pattern of links and feedbacks not only among these variables, but between them and a host of other economic, sociological, political and institutional variables. The first part of the paper reviews the findings of the quantitative economic-demographic models with respect to the impact of differential rates of population increase on the rate and structure of economic growth. Most of these models ignore the employment and income distribution effects of differential rates of population growth. An attempt is then made to specify the ways in which variations in population growth affect the supply and demand for labour and hence net labour absorption. The usual conclusion that a faster rate of population growth exacerbates the employment problem on the supply side is qualified by considerations of participation rates and quality of labour force under different rates of population increase. On the demand side, the impact of variations in population growth is assessed on capital accumulation, composition of output , pattern of growth and changes in productivity induced by such factors as technical change, nutrition, education and training. The impact on income distribution is evaluated by assessing the effects of differential rates of population growth on the main determinants of income distribution by size. Among the factors considered are: ratio of labour to reproducible capital, distribution of assets, change in the structure of the economy, technical change and the skill composition of labour force. A theme running through the paper is that reduced fertility can create the potential for greater net labour absorption and more favourable income distribution. But this potential can only be realized by the pursuit of an appropriate strategy of development to further these objectives. In its absence, it is not at all clear that reduced fertility will make a decisive difference to income distribution and labour absorption