1. The mathematical model of the hyperboloid twist drill was introduced.

2. The authors show that the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

3. According to our method, hyperboloid catadioptric omnidirectional imaging systems and paraboloidal catadioptric omnidirectional imaging systems have been designed and been set up.

4. The authors showthe hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

5. The roof of Beijing Capital Airport T 3 Terminal Building adopted large - span hyperboloid steel grid structure.

6. The cutting edge the drill is the intersection the hyperboloid and the spiral rake face.