How To Determine The Number Of Octants | The Science

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# How to determine the number of octants

The orthogonal coordinate system defines a plane, each pair of axes, which divides the space into two equal halves. In three-dimensional space of three mutually perpendicular planes, and all the coordinate space divided them into eight equal regions. These areas are called "octants" - for designation of eight Latin.

## Instruction how to determine the number of octants

Step 1:

Octant designated by Roman numbers, starting with one and ending with eight. If you want to properly enumerate all of them, mark the unit that is in the positive area of ​​each of the coordinate axes. In the first octant includes a set of points in which all three coordinates (abscissa, ordinate and applicate) are determined by a number from zero to infinity.

Step 2:

Roman deuce mark the octant, a set of points which has positive coordinates along the z-axis and the y, but negative along the horizontal axis. The spatial position of the octant is such that it has a common border with the first, third and sixth octants.

Step 3:

The third octant consider a region of space, composed of dots that have only positive applicate and the abscissa and the ordinate are in the negative range. This spatial region has a common border with the second, fourth and seventh octants.

Step 4:

Roman Quartet mark the set of points whose coordinates along the x-axis and z-positive, and along the vertical axis - negative. This area of ​​the coordinate space has common borders with the first to third and eighth octants. All of these four steps octants have a common property - positive applicate. As usual we definitely we would say that all of them together are the top of the coordinate space, and four follow-up - down. But in an orthogonal coordinate system, those designations are not used, so they can only be used to better understand and remember the correct numbered octants.

Step 5:

The set of points with positive coordinates along the axes of abscissa and ordinate, but negative on the Z-axis, call the fifth octant. It has common borders with the first, sixth and eighth octants.

Step 6:

Sixth call octant space area, which lies in the positive area of ​​the Y-axis values, but in the negative values ​​of the x-axis and the z. This region has a common border with the fifth, seventh and second octants.

Step 7:

If all coordinates of the points of a certain area of ​​negative space, then call her seventh octant. It has common borders with the sixth, eighth and third octants.

Step 8:

Eighth octant call the area of ​​the coordinate space, the set of points which has positive abscissa, but the negative ordinate and applicate. This region has a common border with the fourth, fifth and seventh octants.