Concurrent

Pronunciation: /kənˈkɜr ənt/ ?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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.org. http://www.allmathwords.org/en/c/concurrent.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

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.)