The paper explores the historical development of perspective in art and its intersection with mathematics, focusing on key figures such as Leon Baptista Alberti, Albrecht Dürer, and D'Arcy Wentworth Thompson. It discusses how these artists and mathematicians contributed to the understanding of visual representation, using techniques that combined geometric principles with artistic expression. The text emphasizes the idea that mathematics reveals the underlying structure and beauty of nature, ultimately paving the way for modern concepts in computer graphics.

The Roman Accademia dei Lincei, founded in 1603 by Federico Cesi and three friends, is often credited for being the first modern scientific academy. In their scientific projects the Linceans emphasized observation and experimentation; they focused on the so-called ‘lesser known sciences’, such as mathematics, natural history, and natural philosophy; and they were fanatic supporters of Galileo, who became a member himself in 1611. Another striking feature of this academy is the fact that Cesi and his fellow academicians commissioned large amounts of drawings and prints, often of a high quality, for their scientific projects. These artistic images played a role in processes of knowledge acquisition and divulgation. However, it remains unclear what the exact functions of these drawings were in the scientific practices of the Linceans. How did these drawings – and the artists who produced them – aid the scientists in acquiring knowledge from the natural world? One promising perspective from which this question can be answered is Federico Zuccari’s theory of Disegno, as this was presented in the Accademia di San Luca in Rome. Zuccari was the first president of this art academy and in 1594 he laid down the theoretical principles for the lectures and practical training of young artists (published in 1604). More than other art theorists, Zuccari explicitly connects the process of artistic production to that of knowledge acquisition. He does so with the help of the notion of Disegno. According to Zuccari, Disegno is not only the foundation and starting point for the production of artistic images, but it also is that what enables man to gain knowledge of the natural world. Moreover, his proposal for the art academy’s curriculum describes the steps by which young artists can and should improve their Disegno. This paper attempts to show how Zuccari’s double-layered notion of Disegno and his proposal for the academic curriculum can further our understanding of the functions of the drawings that were commissioned by the Linceans in the context of their scientific practices. It argues that these 'disegni' and the artists who produced them functioned as instruments for the scientists.

Endeavour, 24, 2000

Observation, depiction and description are active forces in the doing of science. Advances in observation and analysis come with advances in techniques of description and communication. In this article, these questions are related to the work of Leonardo da Vinci, 16th-century naturalists and artists like Conrad Gessner and Teodoro Ghisi, and 17th-century micrographers like Robert Hooke.

Leonardo da Vinci and Optics, ed. by Francesca Fiorani & Alessandro Nova, (Studi e Ricerche, 10), Venezia 2013, pp. 9-27

Giambattista Nolli and Rome: Mapping the City before and after the Pianta Grande, 2014

Physis. Rivista internazionale di storia della scienza 45 (2008), 29-55, 2008

This paper examines the hypothesis that early perspective paintings were drawn arithmetically, without vanishing points. The best argument for this hypothesis is that the division of two parallel lines by straight lines intersecting each other at the vanishing point (geometrical method) is equivalent to the division of those parallel lines in proportional parts (arithmetical method). If an arithmetical method had been used, then the vanishing points exhibited ex post should be purely fortuitous. But the lack of multiples and submultiples of measurement units, the absence of proportionality ratios, the length of the operating series, and the correspondence of vanishing points to visible loci of the painting offer sound objections to this hypothesis. The use of optics and geometrical method is more probative–though it does not mean that painters were using concepts of linear perspective, which would be an anachronism.

The science born of art proved to be an art. (Kline, pp 641) The history of projective geometry is revealing to the ways practical knowledge and theoretical knowledge relate and interact. This historical thread interwove more than 600 years of art, philosophy, mathematics and physics. From Greek and Arab philosophy concerning sight and light, through the invention of linear perspective by in the early 15th century, the first theorems of projective geometry formulated in the 17th century and rediscovered in the 19th, and eventually leading to Paul Driac developing his famous equation in 1928 (Farmelo, 2005). It is a fascinating example, where the needs of renaissance art resulted in a measuring devices and a body of geometrical knowledge, designed and formulated to be used by the artisan, not the mathematician. A new geometry was formulated, and its first theorems were added as appendices to technical art books. This geometry was forgotten for almost two centuries, and its rediscovery gave rise to a new way of thinking about geometry and mathematics – and physics. The development of perspectival drawing had another effect on science. In his influential 2008 book van-Fraassen uses perspective drawing, and especially Durer’s work on measurement, as a fundamental example to his theory of representation, a major discussion in current philosophy. In the scope of this work, which regretfully is mostly an outline for future research, I will offer a brief review to the history of perspective drawing and projective geometry, focusing mainly on the character of Albrecht Dürer (1471-1528). Durer studied the basic tools of perspective drawing and mathematical art in Italy, and brought them to Germany, publishing “four books on measurement”, and treatise on human proportion, bringing this practical knowledge to his own countryman. In some points along the narrative I will stop to point the relations between the theoretical a practical knowledge, each deserving a detail analyses.

IASLonline Lessons in NetArt, 2015

The development of the use of computers and software in art from the Fifties to the present is explained. As general aspects of the history of computer art an interface model and three dominant modes to use computational processes (generative, modular, hypertextual) are presented. The "History of Computer Art" features examples of early developments in media like cybernetic sculptures, computer graphics and animation (including music videos and demos), video and computer games, reactive installations, virtual reality, evolutionary art and net art. The functions of relevant art works are explained more detailed than usual in such histories. The German version was completed in December 2012. The last chapter of the English translation was published in June 2014. First update: September 2015 (English version as PDF, 16 MB, 384 p., c. 300 ill.: http://iasl.uni-muenchen.de/links/GCA.pdf).

Digital Imaging for …, 2011

AI

The Journal Biuletyn of Polish Society for Geometry and Engineering Graphics, 2012

The paper presents an extract of forming the principles of perspective construction, construction which had formidable influence on the development and course of shaping European painting. It deals with Albrecht Dürer, his output as an art theorist and one of the greatest artists of the north.

Palgrave Handbook of Images Studies, 2021

Contemporary digital media are correlated to spatial GPS (Global Positioning Satellite) coordinates. Spatial information is itself knit together according to absolute coordinates, which may be viewed in conformity with the principles of projective geometry. Such a mode of viewing-relatively recent-has now become completely natural to most electronics users. It is natural to assume that such digital technologies, whose algorithms include projective geometrical processing according to a mobile viewpoint, are descended from the history of western art in the Renaissance. But that genealogy is much contested. Renaissance art, particularly in Italy (and later in Northern Europe), pioneered the convincing depiction of space in painting. The refinements of space led to a series of pictorial innovations related to linear perspective or the technique of coordinating space according to a number of (sometimes contradictory) geometrical rules. Later, through refinements of projective geometry in the seventeenth century (Guidobaldo del Monte and Jean-Pierre Nicéron) and finally true projective geometry in the work of Gaspard Monge in the eighteenth century, the fully realized geometrical system was articulated. In the meantime, natural philosophers and then physicists explained the practical application of such geometric principles in the working of a number of instruments like the camera obscura.

By the sixteenth century geometry had been important to the crafts for a long time. Yet the geometry of the medieval craftsman fundamentally differed from the geometry taught within the educational circle of the liberal arts. The latter was defined as the ‘art of measurement.’ It constituted as a theoretical art that focused on the teaching of Greek mathematicians such as Euclid and a practical one that dealt with the computation of lines, surfaces and bodies. From the High Middle Ages onwards both aspects interacted in many ways. The geometry of the crafts, on the other hand, involved neither mathematical rigour nor mathematical proofs. Equally, it did not use computations, but consisted solely of ‘the construction and physical manipulation of simple geometrical forms’ in order to ‘solve technical problems of design and building’ (Shelby, 1972, p. 409). Lon Shelby has demonstrated its simple and non-mathematical character by examining the booklets of two German craftsmen, the stonemason Matthäus Roriczer (c. 1440-95) and the goldsmith Hans Schmuttermayer (last mentioned 1518). Both wrote about the construction of gablets and pinnacles and neither of them gave the slightest indication that they knew of the existence of any kind of geometry other than their own. Thus, the constructive geometry of the craftsman was cut off from the theoretical and practical geometry of the educated world. It was the sixteenth century that saw the first attempt to cross this border when Albrecht Dürer published two geometrical books.

Optics in Our Time, 2016

Human Vision and Electronic Imaging V, 2000

Science Museum Group Journal, 2023

is a CDP PhD student at the Science Museum Group and the History of Art Department at Birkbeck, University of London. His research project explores the connections between art and science in the SMG Collection. He has worked variously as a curator, librarian, and university lecturer. He is on Twitter @suryabowyer Media in article

XXV Annual Colloquium-SIEPM, Porto IF-FLUP Per cognitionem visualem. The Visualization of Cognitive and Natural Processes in the Middle Ages., 2021

The purpose of this colloquium is to deepen understanding of the Medieval visual tools that represented and demonstrated philosophical and scientific knowledge and, to an extent, the accumulation of empirical data with a focus on medieval Latin, Greek, Arabic and Jewish traditions. While some sought to outline physical phenomena, others depicted cognitive processes such as deduction or inference, for instance, arbor porphyriana, astronomical diagrams, or geometrical illustrations of physical motion. In addition to this, various kinds of graphics, charts, and diagrams supported the dissemination of legal knowledge, prognostic methods, genealogical records, moral schemes, division of sciences, and medical practices.

The Renaissance period was not only a new era of Humanism, but also a revival of Platonism in which mathematics was the key for understanding the universe. This belief was manifested by Kepler’s model of the solar system and Vincenzo Galilei’s twelve-tone equal temperament.

In Europe, the commonly named "scientific revolution" reached its maximum development in 17 th century, with the complete overtaking of one of the most heavy heritages of the classic age, the separation between theory and practice. In this context, it is necessary to underline the connection between graphic description and mechanics development: in the 16 th century Tartaglia formerly bore witness to the fundamental role of the drawing, on one side an instrument for evaluating and developing projects, on the other a tool for modelling and studying physical phenomena. Galileo and his apprentices, protagonists of the subsequent development of the theoretical studies, completed their written dissertations with very precise and clear drawings, in comparison with the drawings in the older scientific texts. The technical drawings of the 19 th century are still far away, but it is interesting to find drawings with technical value, in representing devices and machines, also in the...

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