Geometric constructions is one of the most historical and most educational subjects in Mathematics. Till now, this subject has been limited to plane geometry. But why not in three-dimensional space?
This is an introductory paper on the new subject, geometric constructions in three-dimensional eulidean space or in n-dimensional space as well. At first, new construction tools substituting the ruler and the compass for high-dimensional spaces are introduced. And after some exercises, we prove some extended versions of well-known basic theorems about the constructible points and the equivalence of old and modern compass. And then, finally, we prove two main results of this paper about some implications between those classical construction tools. One of them is the implication of high-dimensional compasses by the orginal two-dimensional compass. And the other is an extended version of Mohr-Mascheroni theorem considering the constructions with high-dimensional compass only.
