Science from Its Onset to the Present Has Been Pervaded by Geometry

Abstract

One hundred years after Euclid, the Greek mathematician Apollonius (c. 260–190 bc) of Perga (a Hellenistic city in Anatolia) wrote a treatise “On Conic Sections”. In it he showed that all major curves that are part of geometry can be derived from two cones being intersected by a single plane having different orientations. The resulting geometric figures are the circle, ellipse, parabola and hyperbola. This most original work represents the high peak of Greek geometry. His work demonstrated that a fundamental simplicity pervades geometry (Fig. 12.1).

Sources of Figures

Fig. 12.1 Ian, D. et al. 2002. The Cambridge Dictionary of Scientists. Cambridge University Press, Cambridge, UK (Fig. page 9).

Fig. 12.2 Romer, J. 2007. The Great Pyramid. Cambridge University Press (Fig. 30, page 65).

Fig. 12.3 (1) Waetzoldt, W. 1938. Tu y el Arte. Editorial Labor, Barcelona, Spain (Fig. 13, page 21). (2) Thompson, d’Arcy 1952. On Growth and Form, Vol. 2. Cambridge University Press, Cambridge, UK (Fig. 508, page 1053 and Fig. 510, page 1054). (3) da Vinci, Leonardo 1945. El Tratado de la Pintura. Spanish Version of the Edition of 1828, Buenos Aires, Argentina (Plate XVI).

Fig. 12.4 (1) Thompson, d’Arcy 1952. On Growth and Form, Vol. 2. Cambridge University Press, Cambridge, UK (Fig. 548, page 1082 and Figs. 550 and 551, page 1083. (2) Thompson, d’Arcy 1952. On Growth and Form, Vol. 2. Cambridge University Press, Cambridge, UK (Figs. 525 and 526, page 1064 and Figs. 523 and 524, page 1063).

Fig. 12.5 http://en.wikipedia.org/wiki/ Non-Euclidean geometry. 2011-08-15. (Fig. page 4).

Fig. 12.6 (1) WIKIMEDIA.org/WIKIPEDIA/commons (page 1). (2) Cabrera, A. 1935. Historia Natural, Vol. 1. Instituto Gallach, Barcelona, Spain (Fig. page 397).

Fig. 12.7 Wikipedia. Louvre Pyramid. Design and Construction (Fig. page 1).