The Geometry of an Art. The History of Perspective from Alberti to Monge

Andersen, Kirsti

doi:10.1007/978-3-0346-0518-2_10

Cited by 14 publications

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“…Some notes on Lambert's life and work may be found in [1]. For further biographical information and details of Lambert's contributions to the mathematical theory of perspective see [2].…”

Section: Origin Of the Lambert W Functionmentioning

confidence: 99%

“…When considering a special case of his series solution to (2) Euler introduced a function w that satisfies…”

Section: Origin Of the Lambert W Functionmentioning

confidence: 99%

“…Some notes on Lambert's life and work may be found in [1]. For further biographical information and details of Lambert's contributions to the mathematical theory of perspective see [2].In 1758 Lambert derived a series solution to the trinomial equationIn 1779 Euler studied the following transformed version of (1)When considering a special case of his series solution to (2) Euler introduced a function w that satisfiesA related function W (z) that solves …”

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Analytic Root Locus and Lambert W Function in Control of a Process with Time Delay

Cogan¹,

Paor²

2011

Journal of Electrical Engineering

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Recently, the Lambert W function has arisen in the analysis of many systems including a restricted class of time-delay systems. An alternative approach to this analysis, based on the well-established root locus method, is shown here to contain the Lambert W function as a special case.As a purely illustrative example of the equivalence between the Lambert W function and analytic root locus a system comprising a Proportional controller with a time-delay process is analysed. Controller designs based on rightmost eigenvalue location and the dominant eigenvalue method are described.K e y w o r d s: Lambert W function, root locus, time-delay system, stability, eigenvalues ORIGIN OF THE LAMBERT W FUNCTIONJohann Heinrich Lambert (1728-1777) was a multitalented scientist and philosopher who produced important work in fields such as number theory, optics, meteorology, and astronomy -to name but a few. Some notes on Lambert's life and work may be found in [1]. For further biographical information and details of Lambert's contributions to the mathematical theory of perspective see [2].In 1758 Lambert derived a series solution to the trinomial equationIn 1779 Euler studied the following transformed version of (1)When considering a special case of his series solution to (2) Euler introduced a function w that satisfiesA related function W (z) that solves ANALYTIC METHOD FOR DRAWING ROOT LOCUS PLOTS FOR SYSTEMS WITH TIME DELAYIf the process G(s) has time delay L > 0 the characteristic polynomial of the system in Fig. 1 iswhere N (s) and M (s) are polynomials of degree n and m respectively, with m ≤ n, s = σ + jω and the gain k is a real number. The roots of (5) are the eigenvalues of the system. In root locus terminology, the poles and zeros of the root locus are given by the roots of N (s) = 0 and M (s) = 0 , respectively. The root locus of (5) consists of the paths traced out in the (σ, ω) plane by the roots of (5) as k varies and these paths are called the root locus branches. As for the delay-free case, the root loci for time-delay systems are symmetrical about the real axis, but unlike the delay-free case, the number of root locus branches is infinite. Setting k = 0 , these branches start at the poles (roots of N (s) = 0 ) and at σ = −∞; setting k = ±∞, these branches terminate at the zeros (roots of M (s) = 0 ) and at σ = +∞. Root locus branches that do not terminate at a zero approach σ = +∞ along asymptotes. These asymptotes are infinite in number and parallel to the real axis. A geometric method, consisting of rules for drawing the root locus of (5) when L = 0 may be found in standard texts such as [12]. An extended set of these rules for drawing the root locus of (5) with L > 0 may be found in [13][14][15]. Alternatively, when L = 0 there is an analytic method [16,17] for drawing the root locus of (5). This method consists of deriving an equation for the root locus curves. A root locus equation for L > 0 will now be derived. In the following the real and imaginary parts of the polynomial P are written as ReP and ImP ...

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“…Some notes on Lambert's life and work may be found in [1]. For further biographical information and details of Lambert's contributions to the mathematical theory of perspective see [2].…”

Section: Origin Of the Lambert W Functionmentioning

confidence: 99%

“…When considering a special case of his series solution to (2) Euler introduced a function w that satisfies…”

Section: Origin Of the Lambert W Functionmentioning

confidence: 99%

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confidence: 99%

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Analytic Root Locus and Lambert W Function in Control of a Process with Time Delay

Cogan¹,

Paor²

2011

Journal of Electrical Engineering

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“…Art history, mathematics, descriptive geometry, drawing, architecture, stage design and other more technical fields of knowledge have applied geometric principles to the solution of practical problems such as architectural photogrammetry and cartographic representations. Since its theorisation at the dawn of the Renaissance, thousands of pages have speculated about and then proven the mathematical bases, forming a valuable body of technical-scientific literature, and then described and explained the applications to drawing and architecture, studying the works and treatises in a historical-critical body of literature that is so ramified that it might lead us to think that there can be nothing new to say (Andersen 2007). This is not the case: the topic continues to attract scholars for various disciplines, constantly revealing new aspects with respect to both traditional approaches and possible applications to design.…”

Section: Introductionmentioning

confidence: 99%

Architectural Perspective Between Image and Building

Rossi¹

2016

Nexus Netw J

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Perspective is an important example of ''cultural heritage'' in Western figurative culture. This issue provides an overview of the applications of perspective to architecture and their current validity in design. The sequence of topics underlines the relationships between historical literature and coeval realisations, and the connection with other applications, such as cartography. The affirmation of a shared rule of perspective was the result of a long process of practical experimentation. The starting point was the classical principles of optics in the applications to the wall paintings of Pompeii, where the fascinating story of architectural perspective began. Thus, in this context, the term 'architectural perspective', also refers to the set of perspective constructions realised on the surfaces of a wall or room to simulate a different space than those actually built. Several ''real scale'' examples document the broad experimentation of projective devices in which the image interacts with the space and representation becomes architecture, offering suggestions are still valid today for its possible applications in design.

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“…The plane representation of three-dimensional objects was an issue discussed since ancient times, and for this reason artists found different solutions based on empiricism. Only during the Renaissance there was a change towards the elaboration of precise rules for the representation of reality: Leon Battista Alberti (1404-1472) in his De Pictura, was the first who wrote about perspective and presented a true perspective representation model [2], extending the ideas of his predecessor Brunelleschi (1377-1446). Later, Piero della Francesca (1416-1492), in his De perspectiva pingendi, investigated in deep this argument using mathematical and geometrical subjects.…”

Section: Introductionmentioning

confidence: 99%