These objects are the fibers in the Hopf fibration of a four-dimensional sphere. The fundamental group of these objects is isomorphic to the integers 
These objects are the fibers in the Hopf fibration of a four-dimensional sphere. The fundamental group of these objects is isomorphic to the integers under addition. Descartes' theorem gives a quadratic relation between the sizes of four of these objects. A torus is the Cartesian product of two of these entities. Calculus of variations can prove that these shapes enclose the maximal area for a given perimeter. An ellipse is one of these figures if its eccentricity is zero, which implies that these figures have equal major and minor axes. For 10 points, identify these two-dimensional figures which are the set of all points located exactly a certain distance from another one, whose area equals pi-r-squared.
These objects are the fibers in the Hopf fibration of a four-dimensional sphere.
circles