Astronomical Images : Cochlea

Albrecht Duerer

Astronomical Images

<p style='text-align: justify;'>Albrecht Duerer (1471-1528), now widely famed for his painting, engraving and printmaking, was interested and proficient in the mathematical arts. In his <i>Institutiones geometricae</i> he married the mathematical art of geometry to the art of perspective and drawing, bringing Euclidean principles to bear on the theory and practices of visual representation. This image demonstrates the principles used by Duerer to divide the vertical axis of a helical structure. In the lower figure, arc be is divided into equal parts. This is then projected onto a vertical tangent, ba, by extending radial lines through the points on the circumference to the vertical tangent. As the figure clearly shows, when projected onto this vertical axis, the equal divisions of the arc become unequal, the intervals increasing as height increases. Thus, the corresponding helix derived from this plan would become increasingly steep, as seen in the top figure. Duerer offers several examples of the application of this dividing technique, notably the construction of a spiral staircase in the spire of a tower, in which the steps must reduce in length and therefore become increasingly steep as one ascends. This method was also applied by Duerer to the decoration of columns, such that the increasing intervals would appear equal to a viewer at the base of the column, and hence any decorative pattern would appear uniform.</p>