SPHERE DUALITY
This image shows the relation existing between the blue, red and green geometries in their limiting flat Euclidian form. The duality of elements is not only shown as circles, triangles and points, but also as spherical surfaces, cubes, lines and points. It also shows the Fibonacci progression as a hint to scaling ratios.
BLUE, RED AND GREEN DUALITY
In this image I am trying to show the blue, red and green geometries relate to the unit circle, conics, projective geometry and hyperbolic geometry. I tried to show that a two dimensional plane through a cone, a sphere or another plane creates circles, lines, duality relations and other conic structures. Showing them in a three dimentional environment helps the understanding of the relation between blue, red and green geometries.
ARCHIMEDIAN DUALITY
A simpler version of the previous image.
ARCHIMEDIAN DUALITY
A simpler version of the previous image.
HYPERBOLIC PROJECTION
View of the cone/hyperbola from a very acute angle showing the projective relation of the hyperbola to the formation of an ellipse at infinity. Notice that the asymptote lines become the red geometry axis and cones.
PROJECTIVE CIRCLES
DUALITY IN THE FIBONACCI SPIRAL
Duality points created by the many spheres existing at every quarter turn of the Fibonacci spiral
APOLLONIO'S DUALITY AND CONICS
Animation of Apollonio's duality within conic projections