Axis

Pronunciation: /ˈæk sɪs/ ?

--plural axes

An axis is a line that is used as a reference for drawing a figure.[1] This line can exist in two dimensional and three or more dimensional space. It can also be used as a reference for geometric reflections.

Common Axes

x-Axis

2 dimensional Cartesian plane with the horizontal x-axis highlighted.
Figure 1: x-axis on a 2-D Cartesian plane
3 dimensional Cartesian plane with the horizontal x-axis highlighted.
Figure 2: x-axis on a 3-D Cartesian plane

The x-axis is the horizontal axis on a two variable Cartesian graph. This axis is typically assigned to the input of the function being represented. This also means that the x-axis typically represents the independent variable.

y-Axis

2 dimensional Cartesian plane with the vertical y-axis highlighted.
Figure 3: y-axis on a 2-D Cartesian plane
3 dimensional Cartesian plane with the vertical y-axis highlighted.
Figure 4: y-axis on a 3-D Cartesian plane

The y-axis is the vertical axis on a two variable Cartesian graph. The y-axis is typically assigned to the output of the function being represented. This also means that the y-axis typically represents the dependent variable.

On a three-variable Cartesian system, the y-axis typically represents an independent variable.

z-Axis

3 dimensional Cartesian plane with the vertical z-axis highlighted.
Figure 5: z-axis on a 3-D Cartesian plane

The z-axis is the third axis on a three variable Cartesian graph. The z-axis is typically assigned to the output of the function being graphed. This also means that it shows the dependent variable.

Axis of Symmetry

Graph of y = (x - 1)^2 - 1 with the axis of symmetry x = 1 highlighted.
Figure 6: Axis of symmetry of a parabola
Graph of y=x^3 and its inverse with the axis of symmetry y = x highlighted.
Figure 7: Axis of symmetry of a function and its inverse.

An axis of symmetry is the line around which a curve is symmetrical.[4] For parabolas this is a line which passes through the vertex (see figure 6).

Functions and their inverses can also be drawn using the axis of symmetry, which is the line with the equation y = x (see figure 7).

Real Axis

Figure 8: A complex coordinate system with the real axis highlighted.
Figure 8: A complex coordinate system with the real axis highlighted.

In the complex plane, the real axis, on which real numbers are represented, is the horizontal axis.[3]

Imaginary Axis

Figure 9: A complex coordinate system with the imaginary axis highlighted.
Figure 9: A complex coordinate system with the imaginary axis highlighted.

In the complex plane, the imaginary axis, on which imaginary numbers are represented, is the vertical axis.[3]

Axis of Rotation

Figure 10: Diagram of the earth showing the axis of rotation.
Figure 10: Diagram of the earth showing the axis of rotation.

An axis of rotation is a line about which a geometric object rotates.[5] The earth is an example of a rotating sphere. The line from the north pole to the south pole is the axis of rotation as show in figure 10. The earth spins, or rotates, about the axis of rotation.

References

  1. axis. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=axis&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Author unknown. The Elements of the Conic Sections with the Sections of the Conoids, 3rd edition, pp 1-18. Published by J. Deighton and Sons, 1826. (Accessed: 2010-01-07). http://www.archive.org/stream/elementsofconics00hastuoft#page/1/mode/1up/search/axis.
  3. Turnbull, H. W., M.A. F.R.S.. Theory of Equations, 4th edition, pp 6-7. Oliver and Lloyd, 1947. (Accessed: 2010-01-08). http://www.archive.org/stream/theoryofequation029153mbp#page/n23/mode/1up/search/axis.
  4. axis of symmetry. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=axis&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  5. axis of rotation. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=axis&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  6. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 49-50. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n66/mode/1up/search/axis.

Cite this article as:


Axis. 2010-01-08. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/axis.html.

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Revision History


2010-01-08: Added "References" (McAdams, David.)
2008-06-19: Corrected imaginary axis text, added hot link to complex plane (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-03-11: Added vocabulary links. Corrected typo in y-axis (McAdams, David.)
2007-08-10: Initial version (McAdams, David.)

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