The one-band hyperboloid represents a rotation figure. To construct it, it is necessary to follow a certain technique. At first half shafts, then, hyperboles and ellipses are drawn. Connection of all these elements will help to make already spatial figure.
It is required to you
- - pencil,
- - paper,
- - mathematical reference book.
Instruction
1. Represent a hyperbole in the Xoz plane. For this purpose draw two half shafts coinciding with axis y (valid half shaft) and with axis z (imaginary half shaft). Construct on the basis of them a hyperbole. After that set a certain height of h of a hyperboloid. In end at the level of this assigned altitude draw straight lines which will be parallel to Ox and cross at the same time the schedule of a hyperbole in two points: lower and top.
2. Repeat the above actions in other plane – Oyz. Here construct a hyperbole in which the valid half shaft passes through axis y, and imaginary - coincides with with.
3. Construct a parallelogram in the Oxy plane. For this purpose connect points of schedules of hyperboles. Then draw a throat ellipse taking into account that it fitted into the parallelogram constructed earlier.
4. Repeat the above actions at creation of other ellipses. Finally the drawing of an odnopolostny hyperboloid will be created.
5. The Odnopolostny hyperboloid is described by the represented equation where an and b – valid, with – imaginary half shafts. I.e. its coordinate planes are at the same time also the symmetry planes, and the beginning of coordinates represents the center of symmetry of this spatial figure.