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Between Measurement and Illusion
Euclid’s description of the Pythagorean theorem
Raphael, The School of Athens,1509, Fresco, Vatican, Rome
Detail showing Euclid with his students
Exterior view of the Pantheon
in modern day Rome
Interior view of the Pantheon
Giovanni Paolo Panini, c. 1750
Section showing pythagorean ratios at work in the Pantheon.
Brunelleschi devised a method of perspective for architectural purposes: he is said by Manetti to have made a ground plan for the Church of Santo Spirito in Florence on the basis of which he produced a perspective drawing to show his clients how it would look after it was built.
Alberti’s “fenestre” (window) or “velo”
A woodcut from Albrecht Dürer's treatise on measurement
Underweysung der Messung, 1527
Dürer's Perspectograph, early 16th c. (replica)
Elevation and plan of a typical Palladian villa.
vitruviusc. 90-20 B.C.E.
Hans Holbein, The Ambassadors, 1536
Francesco Borromini1599 - 1667
This architectural tromp l'oeil of an actual "perspective" collonade in the Palazzo Spada, was fashioned by Galileo's contemporary, Borromini in 1653. This is actually an illusion, played with the help of mathematical perspective. The trick is revealed in the image at the right where two figures of equal height show the perspective at work. The image in the center is a modern CAD rendering.
Diderot1713 - 1784
Contour plot . Map of Paris by L. L. Vauthier (1874), showing population density by contour lines, the first statistical use of a contour map. This approach to representing multivariate data arose from the use of contour maps in physical geography showing surface elevation (first published in 1752 by Buache), which became common in the early 19th century. It was not until 1843, however, that this idea was applied to data, when Léon Lalanne constructed the first contour plot, showing the mean temperature, by hour of the day and by month at Halle (lower left).
Lalanne's data formed a regularly-spaced grid, and it was fairly easy to determine the isolines of constant temperature. Vauthier generalized the idea to three-way data with arbitrary (x,y) values in his map of the population density of Paris.
This figure (showing the population of Sweden from 1750-1875 by age groups) by Luigi Perozzo, from the Annali di Statistica, 1880, is a very early example of a 3D stereogram. Perozzo's figure is also notable for being printed in color in a statistics journal, and in a way which enhances the perception of depth.
Etienne-Jules Marey, 1830-1906, was among the pioneers of dynamic graphics and the graphical representation of movement and dynamic phenomena. This image, from Marey's La méthode graphique dans les sciences experimentales (1876, p. 150) compares the time course of respiration of a person at rest and under exertion, using a pen-recording device to plot the traces over time.
Projection of one line
of one plane on another
Floor plan from a late Wright residence.