Hi guys, I''ve been seraching around the internet for a long time in search of an answer of how we use this theorem in life today? If any of you guys could help me. Thanks. (Hi)

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- October 29th 2009, 03:51 PMJubblyCeva's Theorem
Hi guys, I''ve been seraching around the internet for a long time in search of an answer of how we use this theorem in life today? If any of you guys could help me. Thanks. (Hi)

- October 29th 2009, 09:43 PMpacman
Jubbly: "I''ve been seraching around the internet for a long time in search of an answer of how we use this theorem in life today?"

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**Ceva's theorem**is a well-known theorem in elementary geometry. Given a triangle*ABC*, and points*D*,*E*, and*F*that lie on lines*BC*,*CA*, and*AB*respectively, the theorem states that lines*AD*,*BE*and*CF*are concurrentif and only if

http://upload.wikimedia.org/math/7/7...864fe0bb5c.png

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the theorem pertains to elementary geometry, and its application is wide and many. theorem has also been generalized to triangles on other surfaces of constant curvature - Masal'tsev, L. A. (1994) "Incidence theorems in spaces of constant curvature."*Journal of Mathematical Sciences*, Vol. 72, No. 4

If you want it locally, it can be used in. . .**land area measurement**

- Grünbaum, Branko; Shephard, G. C. (1995),"Ceva, Menelaus and the Area Principle",*Mathematics Magazine***68**(4): 254–268

http://upload.wikimedia.org/wikipedi...hs_theorem.png

Take a look at the familiar figure above, find the ratio of the pink triangle with the outside triangle if a,b, and c are 1/3 of lengrth of its side?

Ceva's theorem kills this off.

Yet, another proof without words of that line is even better.

http://www.randi.org/images/02-09-01...esolution2.gif

ok

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