Properties of Cyclide Dyupen and Their Application. Part 1

2015 ◽  
Vol 3 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Nineteenth Century ◽  
Contact Line ◽  
Classical Problem ◽  
Descriptive Geometry ◽  
Practical Application ◽  
Surfaces Of Revolution ◽  
Early Nineteenth Century ◽  
Focal Surface ◽  
Lines Of Curvature ◽  
And Task

In the training course in descriptive geometry we consider the class of surfaces formed by circles and named "Circular surface. Within this class of surfaces is the so-called kanalowe surface. Under a lie cyclide belong to canalave surfaces, but in the course of descriptive geometry, their formation is not considered. Under a lie cyclide were discovered by Pierre Charles Francois Dyupen in the early nineteenth century and named in his honor. He dyupen was a disciple of Gaspard Monge, like many great scientists in France at that time. Under a lie cyclide usually represented as envelopes of a family of spheres tangent to three given. Under a lie – the only surface whose focal surface degenerates into a line, and all lines of curvature are circles. Particular cases of ticlid cyclide is a torus, and conical and cylindrical surfaces of revolution. The paper discusses the analytical representation of the focal lines for the General case of a job under a lie cyclide. It is analytically proved that the contact line inscribed in cyclide spheres are circles, and degenerate in the focal curve on the surface is a curve of the В учебном курсе начертательной геометрии из- учается класс поверхностей, образованный окруж- ностями и названный «Циклические поверхности» [5; 8; 12]. Внутри этого класса поверхностей есть так называемые каналовые поверхности. Циклиды Дюпена принадлежат к каналовым поверхностям, более того, они являются частным случаем [2–4; 6] этих поверхностей, но в курсе начертательной гео- метрии их формирование не рассматривается. Циклиды Дюпена были открыты Пьером Шарлем Франсуа Дюпеном (1784–1873) в начале XIX в. и названы в его честь [14]. Дюпен (рис. 1) был учени- ком Гаспара Монжа, как и многие великие ученые Франции того времени, и являлся почетным членом Петербургской академии наук c 20 декабря 1826 г. second order. Identified some (nine) properties of this surface. As a practical application of ticlid cyclide solved such well-known classical problem as the problem of Apollonius (about Casa-NII three circles fourth) and task Farm (touch four spheres fifth) using again the classic way – with a ruler and a compass. In the first part of the article is only three ways to solve the problem of Apollonius solely by means of compass and ruler, using the properties of cyclide Dyupen.

Properties of Dupin Cyclide and Their Application. Part 4: Applications

2016 ◽  
Vol 4 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Dense Packing ◽  
Descriptive Geometry ◽  
Practical Application ◽  
Surfaces Of Revolution ◽  
Special Cases ◽  
Dupin Cyclide ◽  
Different Diameters

In the first and second parts of the work there were considered mainly properties of Dupin cyclide, and given some examples of their application: three ways of solving the problem of Apollonius using only compass and ruler, using the identified properties of cyclide; it is determined that the focal surfaces of Dupin cyclid are degenerated in the lines and represent curves of the second order – herefrom Dupin cyclide can be defined by conic curve and a sphere whose center lies on the focal curve. Polyconic compliance of these focal curves is identified. The formation of the surface of the fourth order on the basis of defocusing curves of the second order is shown. In this issue of the journal the reader is invited to consider the practical application of Dupin cyclide’s properties. The proposed solution of Fermat’s classical task about the touch of the four spheres by the fifth with a ruler and compass, i.e., in the classical way. This task is the basis for the problem of dense packing. In the following there is an application of Dupin cyclide as a transition pipe element, providing smooth coupling of pipes of different diameters in places of their connections. Then the author provides the examples of Dupin cyclide’s application in the architecture as a shell coating. It is shown how to produce membranes from the same cyclide’s modules, from different modules of the same cyclide, from the modules of different cyclides, from cyclides with the inclusion of other surfaces, special cases of cyclides in the educational process. The practical application of the last problem found the place in descriptive geometry at the final geometrical education of architects in the "Construction of surfaces". Here such special cased of cyclides as conical and cylindrical surfaces of revolution.

THOMAS CHALMERS, THE ‘GODLY COMMONWEALTH’, AND CONTEMPORARY WELFARE REFORM IN BRITAIN AND THE USA

2014 ◽  
Vol 57 (3) ◽  
pp. 845-868 ◽  
Author(s):  
JAMES J. SMYTH
Keyword(s):  
Nineteenth Century ◽  
Welfare Reform ◽  
Voluntary Sector ◽  
Practical Application ◽  
Early Nineteenth Century ◽  
The Poor ◽  
The Usa ◽  
Charity Organization ◽  
The Uk ◽  
The Church

ABSTRACTCurrent prescriptions for welfare reform and increased reliance on the voluntary sector often base their appeal on the lessons of history, in particular the apparent successes of Victorian philanthropy in combating ‘pauperism’. This article looks at how this message has become influential in the USA and the UK among the ruling parties of right and left through the particular prism of the neo-conservative appreciation of the work of Thomas Chalmers, the early nineteenth-century Scottish churchman and authority on poverty. The attraction of Chalmers, both to the Charity Organization Society then and neo-conservatives today, lies in the practical application of his idea of the ‘godly commonwealth’ in Glasgow and Edinburgh where voluntary effort, organized through the church, replaced the statutory obligations of the poor law. While Chalmers, and his followers, declared his ‘experiments’ to be great successes, modern Scottish historians have revealed these claims to be false and his efforts failures. Only by completely ignoring the evidence presented by this historiography and continuing to rely on Chalmers's own writings and earlier hagiographies can the neo-conservative approbation of Chalmers be sustained. Such wilful neglect raises questions both about their approach to history and their proposed remedies for tackling poverty today.

A history of some fruit models in wax and other materials: scientific teaching aids and courtly table decorations

2003 ◽  
Vol 30 (2) ◽  
pp. 299-316 ◽  
Author(s):  
Hans-JüRgen Lechtreck
Keyword(s):  
Nineteenth Century ◽  
Fruit Trees ◽  
Visual Aids ◽  
Early Nineteenth Century ◽  
Teaching Aids ◽  
Scientific Teaching ◽  
Glass Marble ◽  
History Of ◽  
By Products ◽  
Wax Models

Two early nineteenth century texts treating the production and use of wax models of fruit reveal the history of these objects in the context of courtly decoration. Both sources emphasise the models' decorative qualities and their suitability for display, properties which were not simply by-products of the realism that the use of wax allowed. Thus, such models were not regarded merely as visual aids for educational purposes. The artists who created them sought to entice collectors of art and natural history objects, as well as teachers and scientists. Wax models of fruits are known to have been collected and displayed as early as the seventeenth century, although only one such collection is extant. Before the early nineteenth century models of fruits made from wax or other materials (glass, marble, faience) were considered worthy of display because contemporaries attached great importance to mastery of the cultivation and grafting of fruit trees. This skill could only be demonstrated by actually showing the fruits themselves. Therefore, wax models made before the early nineteenth century may also be regarded as attempts to preserve natural products beyond the point of decay.

Disease and Civilization: A Scottish Atlantic Network of Physicians in the Enlightenment

2017 ◽  
Vol 10 (2) ◽  
pp. 197-216
Author(s):  
Sarah Irving-Stonebraker
Keyword(s):  
Nineteenth Century ◽  
Native Americans ◽  
Early Nineteenth Century ◽  
The Enlightenment ◽  
Historical Progress ◽  
Practice Of Medicine ◽  
Benjamin Rush ◽  
American Physician ◽  
The Relationship ◽  
A Current

Through an examination of the extensive papers, manuscripts and correspondence of American physician Benjamin Rush and his friends, this article argues that it is possible to map a network of Scottish-trained physicians in the late eighteenth and early nineteenth-century Atlantic world. These physicians, whose members included Benjamin Rush, John Redman, John Morgan, Adam Kuhn, and others, not only brought the Edinburgh model for medical pedagogy across the Atlantic, but also disseminated Scottish stadial theories of development, which they applied to their study of the natural history and medical practices of Native Americans and slaves. In doing so, these physicians developed theories about the relationship between civilization, historical progress and the practice of medicine. Exploring this network deepens our understanding of the transnational intellectual geography of the eighteenth and early nineteenth century British World. This article develops, in relation to Scotland, a current strand of scholarship that maps the colonial and global contexts of Enlightenment thought.

The Township, the Pregnant Girl and the Church: Community Dynamics, Gender and Social Control in Early Nineteenth-century Scotland

2019 ◽  
Vol 10 (1) ◽  
pp. 41-67
Author(s):  
Elizabeth Ritchie
Keyword(s):  
Nineteenth Century ◽  
Rural Communities ◽  
Social Control ◽  
Community Dynamics ◽  
Church Discipline ◽  
Sexual Offences ◽  
Early Nineteenth Century ◽  
Female Community ◽  
The Church ◽  
Unmarried Girl

In 1814 in a small Highland township an unmarried girl, ostracised by her neighbours, gave birth. The baby died. The legal precognition permits a forensic, gendered examination of the internal dynamics of rural communities and how they responded to threats to social cohesion. In the Scottish ‘parish state’ disciplining sexual offences was a matter for church discipline. This case is situated in the early nineteenth-century Gàidhealtachd where and when church institutions were less powerful than in the post-Reformation Lowlands, the focus of most previous research. The article shows that the formal social control of kirk discipline was only part of a complex of behavioural controls, most of which were deployed within and by communities. Indeed, Scottish communities and churches were deeply entwined in terms of personnel; shared sexual prohibitions; and in the use of shaming as a primary method of social control. While there was something of a ‘female community’, this was not unconditionally supportive of all women nor was it ranged against men or patriarchal structures.

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