Geometric locus associated with thriedra axonometric projections. Intrinsic curve associated with the ellipse generated

2016 ◽  
pp. 971-978
Author(s):  
Pedro GONZAGA ◽  
Faustino GIMENA ◽  
Lázaro Gimena ◽  
Mikel GOÑI
Keyword(s):  
Geometric Locus

scholarly journals SETI, Evolution and Human History Merged into a Mathematical Model

2013 ◽  
Vol 12 (3) ◽  
pp. 218-245 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Exponential Growth ◽  
Numerical Estimate ◽  
Mean Value ◽  
Darwinian Evolution ◽  
Human History ◽  
The Galaxy ◽  
Positive Time ◽  
A Cell ◽  
Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

Gaspard Monge’s Descriptive Geometry Course

10.12737/2135 ◽  
2013 ◽  
Vol 1 (3) ◽  
pp. 52-56 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
18Th Century ◽  
Descriptive Geometry ◽  
Curved Surfaces ◽  
Fourth Section ◽  
The Third ◽  
Projective Geometries ◽  
Late 18Th Century ◽  
Geometric Locus

The structure of course of lectures, proposed by Gaspard Monge in the late 18th century, is considered in detail. Monge foresees 120 lectures for descriptive geometry. The main course, without shadows and perspective, is divided into 5 sections, each of which is devoted to a certain themes. In the first section the projections deriving is described, and two main goals are given. Here we face with the notion of geometric locus, elements of differential and projective geometries. The second section considers the tangent planes and normals. These elements’ use in painting and building are demonstrated. The third section has been devoted to the theory related to construction of curved surfaces intersections. The solution of tasks has been considered in the fourth section. The fifth section has been devoted to the curved lines. Gaspard Monge proposes the developed course of descriptive geometry not as a set of interesting geometric tasks, but as a solution of specific application tasks inherent to the industry, building, art, and military science.

Research on Interpolation Algorithm of Three-Links Hybrid Machine Tool

2010 ◽  
Vol 97-101 ◽  
pp. 3124-3127
Author(s):  
Li Da Zhu ◽  
Gang Li ◽  
Wan Shan Wang
Keyword(s):  
Machine Tool ◽  
Smooth Function ◽  
Joint Space ◽  
Interpolation Algorithm ◽  
Cnc System ◽  
Hybrid Machine Tool ◽  
Hybrid Machine ◽  
Interpolation Strategy ◽  
And Control ◽  
Geometric Locus

Aiming at the characteristics of structure and control of three-links hybrid machine tool, the interpolation strategy of CNC system is proposed in this paper. Coarse interpolation in workspace and fine interpolation in joint-space are expatiated. The trajectory points are transformed into discrete points by coarse interpolation mapping from workspace to joint-space. At the same time, the plans of trajectory, velocity and acceleration of discrete points in workspace are got, and then joint discrete points are realized by joint fitting smooth function. In order to meet the design demand and enhance effectively interpolation precision, the five polynomial interpolations will be thinning discrete points, and geometric locus will be very smooth.

Developing the Principle of Continuity in the Teaching of Euclidean Geometry

1944 ◽  
Vol 37 (6) ◽  
pp. 258-262
Author(s):  
Daniel B. Lloyd
Keyword(s):  
Seventeenth Century ◽  
Euclidean Geometry ◽  
Algebraic Function ◽  
Algebraic Representation ◽  
Analytical Treatment ◽  
Analytical Geometry ◽  
Entire Field ◽  
Modern Mathematics ◽  
Geometric Locus

The development of modern mathematics has depended considerably upon the concept of functionality. Modern mathematicians have used it as the framework for much of their theory in the advanced fields of analysis and higher algebra. Descartes in the seventeenth century founded Cartesianism, an ingenious system whereby geometric loci can be represented algebraically. In this system, known as analytical geometry, any algebraic function corresponds to a geometric locus, and conversely. This algebraic representation of a curve or surface in space laid the ground work for higher geometry, —the analytical treatment of spacial elements. The paramont importance of functionality is thus evident in the entire field of modem mathematics.

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