Astronomical Images : Helix

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 shows the plan and elevation of a complex helical structure, comprised of a cylindrical helix on which a conical helix is seated. The relationship between the two projections is emphasised by the vertical lines drawn between corresponding numbered points on each diagram; thus point α at the peak of the elevation (top) would appear in the middle of the ground-plan (i.e. when viewed from above). The points on the circumference of the helix are also projected onto the vertical axis of the elevation, as shown by the horizontal lines. Though it is not obvious in this figure, the resulting division of the vertical axis is such that the cylindrical part is comprised of equal subdivisions, while the conical part is comprised of unequal subdivisions, the intervals increasing with the height of the axis. Thus, the helix becomes increasingly steep. This model seems to reflect a practical application: if applied, for example, to the construction of a spiral staircase in the spire of a tower, the length of the steps must be progressively reduced as the stairs rise. Thus, the helix is conical, and the steps will become progressively steep as the height of the tower increases. This results in the subdivision of the vertical axis as presented in Duerer's figure. This consideration of practical experience suggests that Duerer was not merely concerned with the construction of an abstract mathematical object, but its physical construction in a visual space.</p>