Teaching the Notion Conic Section with Computer

2021 ◽  
Vol LXIV (4) ◽  
pp. 395-409
Author(s):  
Marin Marinov ◽  
◽  
Petya Asenova ◽  
Keyword(s):  
Conical Surface ◽  
Conic Section ◽  
3D Graphics ◽  
Mathematical Concepts ◽  
Symbolic Calculation ◽  
Wolfram Mathematica ◽  
Symbolic Calculations ◽  
Conical Section ◽  
Calculation System

The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.

Design of a Manual Calculation System of Drawing Quantity with "Read Schemata”

2014 ◽  
Vol 496-500 ◽  
pp. 1774-1778
Author(s):  
Xing Ji Wang
Keyword(s):  
Main Function ◽  
3D Graphics ◽  
Direct Visualization ◽  
Counting System ◽  
Work Habits ◽  
Manual Counting ◽  
Low Threshold ◽  
Calculation System ◽  
Manual Calculation ◽  
Clear Presentation

To solve the problem of "reliablity", calculation scope and the high thresholds in the operation of the 3D graphics automatic calculation quantity system in the practical use, "read schemata" graphics manual calculation quantity technology is analyzed. This technology has the features of direct visualization, clear presentation, no requirement for memory in work, revisability, meeting cost engineers work habits, low threshold in operation, wide application scope, easy proofreading and so on. The main function of graphics manual counting system is described with "reading schema". The functions of the drawing display and the manual calculation area are given. The experimental results show that the method is effective, feasible and superior to other 3D graphics quantity calculation system and can be applied in the quantity calculation of various professional engineering.

Geometrical characteristics of the stability domain in the restricted problem of eight bodies

2019 ◽  
Vol 28 (1) ◽  
pp. 49-52
Author(s):  
ELENA CEBOTARU ◽  
Keyword(s):  
Restricted Problem ◽  
Stability Domain ◽  
Stationary Solutions ◽  
Symbolic Calculation ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Calculation System ◽  
The Stability

The eight-body Newtonian problem is studied. Applying the symbolic calculation system Mathematica the stationary solutions, their stability in numerical form and the geometric characteristics of the stability domain are studied.

scholarly journals An application of the MEFM to the modified Boussinesq equation

2018 ◽  
Vol 9 (1) ◽  
pp. 11-17
Author(s):  
Tolga Akturk
Keyword(s):  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
3D Graphics ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Wolfram Mathematica ◽  
Modified Boussinesq Equation ◽  
Mathematica Software ◽  
2D And 3D

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ) equation are obtained by using the modified expansion function method (MEFM). When the obtained solutions are commented, trigonometric functions including hyperbolic features are obtained. The 2D and 3D graphics of the solutions have been investigated by selecting appropriate parameters. All the obtained solutions provide the MBQ equation. In this work, all mathematical calculations are done with Wolfram Mathematica software. 

Symbolic Calculations

2021 ◽  
pp. 277-310
Keyword(s):  
Dynamical System ◽  
Shear Stress ◽  
Laplace Transform ◽  
Symbolic Calculation ◽  
Lubrication Film ◽  
Algebraic Expressions ◽  
Mathematical Expressions ◽  
Symbolic Calculations ◽  
The Laplace Transform ◽  
Scale Shear

The chapter is devoted to symbolic calculations in which the variables and commands operate on mathematical expressions containing symbolic variables. The representation of a symbolic expression, its simplification, the solution of algebraic expressions, symbolic differentiation and integration, and conversion of the symbolic numbers to their decimal form are described. ODEs solutions are also presented. The final sections of the chapter give examples of the symbolic calculation implementation for some mechanical and tribological problems that were solved numerically in previous chapters, namely lengthening a two-spring scale, shear stress in a lubrication film, a centroid of a certain plate, and two-way solutions of the ODE describing the second order dynamical system – traditional and using the Laplace transform.

The Computational Sublime in Nick Montfort's ‘Round’ and ‘All the Names of God’

CounterText ◽  
2015 ◽  
Vol 1 (3) ◽  
pp. 348-365 ◽  
Author(s):  
Mario Aquilina
Keyword(s):  
Computer Code ◽  
Computer Programs ◽  
Literary Text ◽  
Text Generation ◽  
Mathematical Concepts ◽  
Literary Space

What if the post-literary also meant that which operates in a literary space (almost) devoid of language as we know it: for instance, a space in which language simply frames the literary or poetic rather than ‘containing’ it? What if the countertextual also meant the (en)countering of literary text with non-textual elements, such as mathematical concepts, or with texts that we would not normally think of as literary, such as computer code? This article addresses these issues in relation to Nick Montfort's #!, a 2014 print collection of poems that presents readers with the output of computer programs as well as the programs themselves, which are designed to operate on principles of text generation regulated by specific constraints. More specifically, it focuses on two works in the collection, ‘Round’ and ‘All the Names of God’, which are read in relation to the notions of the ‘computational sublime’ and the ‘event’.

Planned Man-Hour Calculation System in High-Mix Assembly Products

2020 ◽  
Vol 140 (11) ◽  
pp. 1286-1294
Author(s):  
Fumiya Shimizu ◽  
Masataka Tanaka ◽  
Kohei Haruta ◽  
Motonobu Saito
Keyword(s):  
Calculation System

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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