John Na is a rising junior from Winchester, Massachusetts. His current academic interests lie in mathematics, computer science, and physics, which he seeks to pursue in the future. He is especially attracted to electrostatics, and hopes to learn Mathematica in order to apply it in this field. At school, John is the vice-president of his class and participates in various math competitions. In his spare time, he enjoys playing basketball casually, competing at tae kwon do tournaments, and playing the piano and the drums. Currently, he is pursuing his third-degree black belt, and he aspires to perform well at the USA Taekwondo National Championships.
This Demonstration allows the user to rotate the unit 3-sphere (a four-dimensional hypersphere) around its six directional planes. Shown is the stereographic projection of its parallels, meridians, and hypermeridians onto a three-dimensional space. Although the circles seen in 3D seem to intersect themselves when the hypersphere is rotated, in 4D, the 3-sphere does not self-intersect.