# How to define numbers of octants

In the orthogonal system of coordinates each couple of coordinate axes sets the plane which divides space into two equal half. In three-dimensional space of such mutually perpendicular planes three, and all coordinate space is divided by them into eight equal areas. These areas are called "octants" - on designation of the eight in Latin.

## Instruction

1. Octants are designated by the Roman numbers, since unit and finishing with the eight. If it is required to number correctly each of them, then by unit designate what lies in the positive area of each of coordinate axes. The set of points at which all three coordinates (an abscissa, ordinate and z-coordinate) are defined by number from zero indefinitely enters the first octant.

2. By the Roman two designate that octant which set of points has positive coordinates along ordinate axes and z-coordinates, but negative along abscissa axis. The spatial provision of this octant such is that it has the general border with the first, third and sixth octants.

3. The third octant consider the area of space made of points at which only z-coordinate is positive and an abscissa and ordinate lie in the negative range of values. This spatial area has the general border with the second, fourth and seventh octants.

4. By the Roman four designate a set of points which coordinates along abscissa axes and z-coordinates are positive, and along ordinate axis - are negative. This area of coordinate space has the general borders with the first the third and eighth octants. All octants listed in four steps have the general property - positive z-coordinate. By definitions habitual to us we would tell that all of them together designate top of coordinate space, and the four of the subsequent - a bottom. But in the orthogonal system of coordinates such designations are not used therefore they can be applied only in order that it is better to present and correctly to remember numbering of octants.

5. Call a set of the points having positive coordinates on axes of abscissa and ordinates, but negative on an axis of z-coordinates the fifth octant. It has the general borders with the first, sixth and eighth octants.

6. The sixth octant call the area of space lying in the positive area of values of ordinate axis, but in negative areas of values of abscissa axes and z-coordinates. This area has general borders with the fifth, seventh and second octants.

7. If all coordinates of points of a certain area of space are negative, then call it the seventh octant. It has the general borders with the sixth, eighth and third octants.

8. The eighth octant call that area of coordinate space which set of points has a positive abscissa, but negative ordinate and z-coordinate. This area has general borders with the fourth, fifth and seventh octants.

Author: «MirrorInfo» Dream Team