The Spherical Spiral. By Chris W ilson And Geoff Zelder. History. Pedro Nunes , a sixteenth century Portuguese cosmographer discovered that the shortest distance from point A to point B on a sphere is not a straight line, but an arc known as the great circle route.
The Spherical Spiral
Pedro Nunes, a sixteenth century Portuguese cosmographer discovered that the shortest distance from point A to point B on a sphere is not a straight line, but an arc known as the great circle route.
Nunes gave early navigators two possible routes across open seas. One being the shortest route and the other being a route following a constant direction, generally about a 60 degree angle, in relation to the cardinal points known as the rhumb line or the loxodrome spiral.
M C Esher (1898-1972), known for his art in optical illusions drew the Bolspiralen spiral, which is the best representation of Nunes’ theory
Gerardus Mercator (1512-1594), used Nunes’ loxodrome spiral which revolutionized the making of world maps
Map makers have to distort the geometry of the globe in order to reproduce a spherical surface on a flat surface
Plotting the spiral
In this case we let run from 0 to k , so the larger k is the more times the spiral will circumnavigate the sphere. We let , where controls the spacing of the spirals, and controls the closing of the top and bottom of the spiral.
Another use is a high definition 3-D projection technique to produce many 2-D images in different directions so the image could be viewed from any angle, this creates a sort of fishbowl effect.
We let . We end up with this.