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The Fibonacci Numbers: A Link with Geometry, Art and Music
2021In this paper we will show some properties of the Fibonacci numbers from the mathematical and the historical points of view. We will focus on their applications concerning art, music and geometry, especially in connection with the golden section. In fact, these important numbers, known in the West since the Middle Ages as a solution of the famous ...
Conti G., Paoletti R.
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On the geometry of homotopy invariants of links
Mathematical Proceedings of the Cambridge Philosophical Society, 1992One of the central problems in higher-dimensional knot theory is the classification of links up to concordance. In 14, Le Dimet constructed a universal model for (disk) link complements, which allowed him to formulate this problem in the framework of surgery theory by applying the Cappell-Shaneson program for studying codimension two embeddings of ...
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Linking Structure and Parametric Geometry
Architectural Design, 2013AbstractThe Karamba plug‐in developed by Clemens Preisinger in collaboration with Bollinger + Grohmann Engineers has been developed to predict the behaviour of structures under external loads. Intended to be used by architects rather than being solely confined to an engineering setting, it enables a seamless flow of data between structural and ...
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Multiple Coordination Geometries Supported by Methylene-Linked Guanidines [PDF]
Inorganic Chemistry, 2004 The methylene-linked bicyclic guanidine based on the 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine (hppH) framework provides a versatile platform able to support trigonal-planar, tetrahedral, and square-planar metal centers.
Martyn P. Coles +2 more
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Teacher spatial skills are linked to differences in geometry instruction [PDF]
British Journal of Educational Psychology, 2017 BackgroundSpatial skills have been linked to better performance in mathematics.AimThe purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction.SampleFifty‐six middle ...
Beryl Otumfuor, Martha Carr
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Linking complex analytic to nonstandard algebraic geometry
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2020In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit
Siegmund Kosarew, Adel Khalfallah
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Some links between turtle geometry and analytic geometry
International Journal of Mathematical Education in Science and Technology, 1985The computer language LOGO facilitates the teaching of analytic geometry and calculus from the notion of curvature, through its ‘turtle geometry’ facility [2]. We provide some theoretical basis for finding turtle geometry equivalents of familiar curves in analytic geometry, and vice versa, by some simple methods which apparently have not been noticed ...
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1997
An alternating diagram for a link is, as explained in Chapter 1, one in which the over or under nature of the crossings alternates along every link-component in the diagram; the crossings always go “… over, under, over, under,…” when considered from any starting point. A link is said to be alternating if it possesses such a diagram.
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An alternating diagram for a link is, as explained in Chapter 1, one in which the over or under nature of the crossings alternates along every link-component in the diagram; the crossings always go “… over, under, over, under,…” when considered from any starting point. A link is said to be alternating if it possesses such a diagram.
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A Survey on the Differential and Symplectic Geometry of Linking Numbers
Milan Journal of Mathematics, 2006The aim of the present survey mainly consists in illustrating some recently emerged differential and symplectic geometric aspects of the ordinary and higher order linking numbers of knot theory, within the modern geometrical and topological framework, constantly referring to their multifaceted physical origins and interpretations.
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Stable Geometry of a Plane Five-Link Mechanism
Russian Engineering Research, 2018A five-link mechanism of parallel structure with rotary kinematic pairs is considered. Possible configurations of the mechanism, its working regions, and singular positions are discussed. Possible optimization of its working zone without singular positions of the second kind is analyzed.
K. G. Erastova +2 more
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