Rome - Colosseum
- Author:
- chris cambré
an oval with 6 centers
On the drawing of the Colosseum below one can clearly see the radii and the centers of circular arcs.
In the construction of the ovaal, one can see that is doesn't have 4 but 6 centers.
- The centers of the green circular arcs are on the long (horizontal) axis.
- The centers of the yellow circular arcs are on the short (vertical) axis.
- The centers of the red circular arcs are the intersection points of the radii that limit the yellow circular arches and the extended radii that limit the green circular arcs.
- As the centers of the red circular arcs are as well on the radii of the yelloww circular arcs as on the extended green circular arcs the tangents at the transition points coincide. As a result of this you get a nice continuous oval.
In his online article Camillo Trevisan even goes further and speaks about 8 centers.
The technique to draw curved lines out of connected circular arcs is frequently used in Islamic architecture. I collected a serie of constructions I found in Iranian books in the GeoGebrabook Iranian arcs and vaults.
connecting circular arcs
The technique is based on de property that in a point on a circle the tangent is perpendicular to the radius of the circle.
Next applet illlustrates the technique:
- Draw a random circular arc ending at a random (green) point.
- Extend the of the circular arc and define a second (yellow) ppoint on it.
- Starting from the green point construct a circular arc with the yellow point as center.
- Now in the green point the tangents to the the two circular arcs will coincide while the green point and the centers of the two circular arcs are collinear.