Octant (solid geometry)

The geometry of the three-dimensional space is divided by the coordinate planes of a Cartesian coordinate system into 8 parts, called octants. Since the limiting levels coordinates typically include at any octant, indicate the sign of the respective coordinates of a point in three-dimensional space in which a point is to the eight octants.

Numbering

The first octant (I) consists of all points that have three positive coordinates. In the picture he is thus located above the rear right. The octant II to IV also have a positive coordinate, so the picture to remain in the upper half of the coordinate system, and is one of the octants counterclockwise with Roman numerals (I to IV). By this definition ensures that for the octant I to IV the same sign in the first two coordinates apply as for the quadrants I to IV in the plane. Accordingly, the procedure in the lower half (): The 5th octant (V ) is located directly below the first octant. Again, you continue counting counterclockwise with Roman numerals (V to VIII ).

Explicitly therefore result from the following octant sign of the coordinates - the order of the coordinates is here:

• I. octant:
• II octant:
• III. octant:
• IV octant:
• V. octant:
• VI. octant:
• VII octant:
• Octant VIII:

Octants in the two-dimensional space

Sometimes the two-dimensional space is divided into octants. Here, the four quadrants are divided on the straights and. The octant thus defined are numbered counterclockwise starting with the lower half of the first quadrant I to VIII.