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The graphic statics of the systems of space by Benjamin Mayor
Published in Ine Wouters, Stephanie Van de Voorde, Inge Bertels, Bernard Espion, Krista De Jonge, Denis Zastavni, Building Knowledge, Constructing Histories, 2018
Spatial problems can be compared to classic problems in a plane by considering projections on planes. A possible approach is based on the use of descriptive geometry which allows the correlated study of the two system planes obtained by orthogonal projections of the system of the space. An example of this type of approach is mentioned by Mayor (1926, 41) through a case developed in the book of Föppl (1900) for the calculation of three-dimensional structures. Mayor points out that graphical approaches associating graphic statics and descriptive geometry enable to solve spatial problems but do not constitute a real extension to the space of the planar graphic statics. Mayor’s quest was the research for a spatial approach whose the graphic statics in the plane would be a special case. Starting from the preponderant role played by the rights in the theory of the systems of forces, Mayor chose, from 1896, to support his approach on the theory of ruled geometry. This choice is also motivated by the dualistic character associated with this geometry (Mayor 1926, 1). In the plane, the dualistic character of the graphic statics is characterized by the relationships between the funicular polygons and the force polygons. This character is not extended to space by the use of descriptive geometry. The ruled geometry allows to introduce a form of duality by the construction of reciprocal figures under certain conditions. The fundamental concepts of this theory and its application to systems of forces in space are outlined in this part in order to give the necessary notions to the understanding of Mayor’s approach.
What Is Engineering Science?
Published in Diane P. Michelfelder, Neelke Doorn, The Routledge Handbook of the Philosophy of Engineering, 2020
Largely in response to this development, the first civilian school for engineering was founded in Paris in 1794. It is commonly known under the name École Polytechnique (Grattan-Guinness 2005). It was led by Gaspard Monge (1746–1818), who was an able mathematician and also a Jacobin politician. He considered mathematics and the natural sciences, including mechanics, to be the most important subjects (Hensel 1989a: 7). About a third of the curriculum hours were devoted to mathematics (Purkert and Hensel 1986: 27, 30–35). He also developed a new discipline, called descriptive geometry, which is a mathematically precise form of technical drawing that is particularly useful as a tool for machine construction (Lawrence 2003; Klemm 1966).
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Published in Stephen P. Radzevich, Theory of Gearing, 2018
As early as 1842, a monograph by Theodore Olivier† (Figure 1.14) on the theory of gearing [88] was published. This monograph (Figure 1.15) is the first monograph ever to be titled Geometric Theory of Gearing (Théorie Géométrique des Engrenages). In the monograph, the first and second principles of the generation of enveloping surfaces are proposed. Later on, both these principles received wide usage by gear scientists. Graphical methods developed in descriptive geometry are used by Olivier in this book [88].
Mathematics teaching pedagogies to tertiary engineering and information technology students: a literature review
Published in International Journal of Mathematical Education in Science and Technology, 2022
Fouzeh Albeshree, Malik Al-Manasia, Charles Lemckert, Shuangzhe Liu, Dat Tran
Rubio et al. (2010) highlighted the significance of web-based application in descriptive geometry learning. They argue that computer-aided learning (CAL) is central to enhancing teaching and learning. Technology is indeed increasingly taking centre stage in the domain of teaching, especially in STEM subjects. CAL has proved effective in terms of helping undergraduate students learn descriptive geometric learning. Karr et al. (2003) expounded on the effectiveness of online learning to enhancing teaching mathematics. While mathematics is a crucial subject, a large number of students pursuing it have failed to record appealing results because of ineffective teaching/ learning strategies. The fact that the online delivery model reported better results is a clear indication that online-based systems are central to enhancing achievement in technical subjects like engineering, IT, and mathematics.
A critical inquiry into the hyperreality of digitalization in construction
Published in Construction Management and Economics, 2021
Visual abstraction is at its most useful in design drawings as was described in the last section. The building drawing shown in Figure 3 is a conventional example that could have been produced by hand or by various forms of computer aided drafting. It is a plan which is a horizontal section through the imagined building, thus, it is a projection of important features onto a 2D plane. It follows the rules of technical drawing based on descriptive geometry (Bafna 2008). This output then has a number of characteristic abstractions. Firstly, the main abstraction is geometric and this is iconic in that it is a scaled representation of the space created by walls. These walls are themselves iconic but their representation is less complete than the geometry; for example, the internal composition has been idealized and does not show internal surfaces such as plaster. Items such as stairs are partly a representation of reality but follow an agreed syntax for such technical drawings. Many other features are extremely abstract or have been omitted.
An assessment of geometry teaching supported with augmented reality teaching materials to enhance students’ 3D geometry thinking skills
Published in International Journal of Mathematical Education in Science and Technology, 2020
Emin İbili, Mevlüt Çat, Dmitry Resnyansky, Sami Şahin, Mark Billinghurst
The coexistence of virtual objects and real environments using AR allows students to visualize complex spatial relationships and abstract concepts [27]. AR teaching environments enable students to learn more deeply by increasing the attention and motivation of the students and by providing a different perspective for the systems or objects that are difficult to learn [28,29]. AR teaching environments improve the spatial skills of students, give students practical application skills, and provide conceptual and inquiry based understanding [30]. Geometry teaching with mobile Augmented Reality systems improves the spatial skills of students and their ability to understand descriptive geometry [31]. AR helps students to perform spatial visualization tasks, such as mentally manipulating, rotating and inverting objects [32]. AR enhances spatial visualization and mental rotation skills. In addition, natural interaction reduces cognitive load and helps the user to establish a connection between the visualization and rotation skills [33]. Cognitive activities that are not directly related to the learning goal create an extra cognitive load. For example, interacting with virtual manipulators by using a mouse and keyboard in geometry teaching creates an extra cognitive load and can reduce learning outcomes. However, AR may allow natural sensory interaction with virtual contents through actions that mirror real-world interaction such as motion, body language, sound, gaze, touch and so on. The extra cognitive load that prevents students from using the system is reduced by using natural interaction interfaces [34]. Such interfaces may enable the user to feel the interaction between the environment, the user and the system as a natural interaction while performing a certain task [35].