Concurrent

Pronunciation: /kənˈkɜr ənt/ ?
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Manipulative 1: Points of concurrency. Created with GeoGebra.

Two or more geometric figures are concurrent at a point if they share that point[1][2]. The shared point is called the point of concurrency. A point of concurrency the same thing as an intersection.

Manipulative 1 shows several figures. Points where the figures are concurrent are red. Click on the blue points in manipulative 1 and drag them to change the figure. If the red points disappear, the figures are not concurrent.

Concurrent lines

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Manipulative 2: Concurrent lines. Created with GeoGebra.
Two straight lines have either 0 or 1 concurrencies. If two lines have 0 concurrencies, the lines are parallel. If they have 1 concurrency, the lines are not parallel. Click on the blue points in manipulative 2 and drag them to change the figure. Note that the two lines might intersect outside of the view window of manipulative 2.

Discovery

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Manipulative 4: Concurrent objects. Created with GeoGebra.

Use manipulative 4 to find the answers to the following questions.

  • What is the least number of concurrencies of an arbitrary circle and an arbitrary square?
  • What is the greatest number of concurrencies of an arbitrary circle and an arbitrary square?

References

  1. concurrent. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=concurrent&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 7. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/concurrent.
  3. Hart, C. A.; Feldman, Daniel D.. Plane Geometry, pg 72. American Book Company, 1911. (Accessed: 2010-01-18). http://www.archive.org/stream/geometryplane00hartrich#page/72/mode/1up/search/concurrent.

Cite this article as:


Concurrent. 2010-01-18. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/concurrent.html.

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Revision History


2010-01-18: Added "References" and removed section on concentric circles. (McAdams, David.)
2009-12-21: Added reference to Euclid's Elements; Expanded table of angle classes. (McAdams, David.)
2008-11-19: Expanded from just lines to geometric figures (McAdams, David.)
2008-07-09: Added More Information (McAdams, David.)
2008-04-25: Initial version (McAdams, David.)

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