about the 3-Dimensional Circle
A 3D Circle consists of 6 consecutive quarter circles, each plane rotated by 90° relative to the plane of the previous quarter circle. When you draw a quarter circle on one face of a cube, you can continue the circle on the next face with another quarter circle. The sixth quarter circle completes the resulting 3D Circle.
How the construction of a 3D circle works is shown in pictures...
In contrast to the classical circle, which is defined as the set of all points in a plane equidistant from the center of the circle and therefore two-dimensional, in the 3D Circle, all points are symmetrically arranged in three-dimensional space and equidistant from the circle's center.
To define the 3D Circle, in addition to the property that all points on the circle have the same distance from the circle's center, the property of a uniformly curved line must be added. Otherwise, any scribble on a sphere would be a 3D Circle, as all points on the surface of a sphere also have the same distance from the sphere's center.
One fascinating characteristic of the 3D Circle is its angular size. Instead of the usual 360° degrees, the 3D Circle astonishingly encompasses 540° degrees. This unique property adds an extra dimension to the 3D Circle and opens up new possibilities for mathematical and geometric applications.
Orthogonal views of the 3D circle are identical to the top view or their mirror images. The similarity of the sides illustrates the symmetrical arrangement of the 3D circle in space. Views from a 45-degree angle differ and have opposing mirror image sides.
Without support, the 3D circle tilts by 54.74 degrees and comes to rest.
In a lying position, the 3D circle rests on three low points and has three high points.
Multiple stacked 3D circles create an elastic and stable structure.
By filling in the spaces between the circle and the center, alternating convex and concave surfaces can be generated.
Naturally, a 3D circle fits perfectly onto a sphere and appears as a uniformly curved line with an equal distance from the center of the sphere.
The circle also closes when a semicircle is drawn per cube face. Since the circle does not pass through all 6 cube faces, the 3D circle constructed in this way does not look the same from all sides and is therefore excluded for now in this consideration.
An interesting aspect of the 3D circle is that it also remains closed when a ¾ circle is drawn from center to center on each cube face, and this process is repeated on each cube face. This results in a circle with 1620 degrees.
¾ 3D circles with different radiuses on Top of each other
