Even one (mathematics)

One Even one is in that more in two dimensions . Usually one means in that used Euclidean level, more in two dimensions is.

To Description one level (level equation) there are different possibilities:

• Koordinatendarstellung : <math>a_1 \cdot x+a_2 \cdot y+a_3 \cdot z=b</math>
• Parameter form : <math>\vec r = \vec r_0 + \lambda \cdot \vec u + \mu \cdot\vec v</math> (one point and two directions)
• : <math>(\vec r - \vec A) \cdot \vec n = 0</math>
• : <math>\vec r \cdot \vec n_0 = d</math> ( and one perpendicularly to the level)
• Axis intercept form : <math>{x \over A} + {y of \over b} + {z of \over C} = 1</math>
• three points, which lie in the level

Even one in the three-dimensional area

cartesian coordinates

The x-y plane, the y-z-level and the z-x-level are cuts or illustrations of the three-dimensional area, with those the axles occurring in each case in the name of the are visible. They are usually infinitely far expanded.

Polar coordinates

Exactly the same leave themselves in levels form. One can do it with one Cake explain:

• The computer centre-even describes the level, Piece of cake from the cut side shows. (one sees the cream filling and the paste layers). Thus one can very well rotationssymetrische Bodies represent and z. B. three-dimensional fields, forces, etc.. compute simplified. (a rotation of this level around the Z-axis around 2? results in then the rotationally symmetric body.) the computer centre-even is infinitely far ausgedent in z-direction, in r-direction however only from r=0 to?, therefore it is actually only one Half plane. Became one the whole Cake in 2 halves cut, would left be everything from the center a reflection of the right side, therefore one who-turns only one half plane.
• The r-?-level (also plane of rotation) one sees those Cake from above, or one cuts something off with the measurer from above and sees the cut by a layer from above. It is expanded infinitely far and does not differ not from one level in cartesian coordinates, if one it to x-y planes redefined (the Z-axis shows then further from the levels out). The r-?-level knows z. B. to the zweidimensinalen representation and computation one to be used.
• A smaller meaning is attached to the?-z-level. It became z. B. that completed Edge that Cake show and lie in the intervals z=[?,?] and?=[0,2? ].

See also , Spurgerade, Affine level