The Image and Imagination of the Fourth Dimension in Twentieth-Century Art and Culture

One of the most important stimuli for the imaginations of modern artists in the twentieth century was the concept of a higher, unseen fourth dimension of space. An outgrowth of the n-dimensional geometries developed in the nineteenth century, the concept predated the definition of time as the fourth dimension by Minkowski and Einstein in relativity theory. Only the popularization of relativity theory after 1919 brought an end to the widespread public fascination with the supra-sensible fourth dimension between the 1880s and 1920s. initially popularized by figures such as E. A. Abbott, Charles Howard Hinton, Claude Bragdon, and R D. Ouspensky (as well as science-fiction writers), the fourth dimension was a multivalent term with associations ranging from science, including X-rays and the ether of space, to idealist philosophy and mystical "cosmic consciousness." This essay focuses on the differing approaches to higher spatial dimensions in the cubism of Pablo Picasso and Juan Gris, the suprematism of Kazimir Malevich, and The Large Glass project of Marcel Duchamp in the early twentieth century. It concludes by examining contemporary artist Tony Bobbin's thirty-year engagement with the mathematics of four-dimensional geometry and computer graphics, as well as his current work with knot theorist Scott Carter.Art Histor

An application of Groebner bases to planarity of intersection of surfaces

In this paper we use Groebner bases theory in order to determine planarity of intersections of two algebraic surfaces in ${\bf R}^3$. We specially considered plane sections of certain type of conoid which has a cubic egg curve as one of the directrices. The paper investigates a possibility of conic plane sections of this type of conoid

From Models to Simulations

This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s. Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows how and why computers, data treatment devices and programming languages have occasioned a gradual but irresistible and massive shift from mathematical models to computer simulations

Integral of radical trigonometric functions revisited

This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form $\sqrt{1 \pm \sin x}$ or $\sqrt{1 \pm \cos x}$. The integral has applications in Calculus where it appears as the length of cardioid represented in polar coordinates.Comment: 12 pages, 4 figure

Microalgae production in fresh market wastewater and its utilization as a protein substitute in formulated fish feed for oreochromis spp.

Rapid growing of human population has led to increasing demand of aquaculture production. Oreochromis niloticus or known as tilapia is one of the most globally cultured freshwater fish due to its great adaptation towards extreme environment. Besides, farming of tilapia not only involves small scales farming for local consumption but also larger scales for international market which contributes to a foreign currency earning. Extensive use of fishmeal as feed for fish and for other animals indirectly caused an increasing depletion of the natural resource and may consequently cause economic and environmental unstable. Microalgae biomass seems to be a promising feedstock in aquaculture industry. It can be used for many purposes such as live food for fish larvae and dried microalgae to substitute protein material in fish feed. The microalgae replacement in fish feed formulation as protein alternative seem potentially beneficial for long term aqua-business sustainability. The present chapter discussed the potential of microalgae as an alternative nutrition in fish feed formulations, specifically Tilapia