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Math Help - Ceva's Theorem

  1. #1
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    Ceva'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.
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  2. #2
    Senior Member pacman's Avatar
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    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

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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



    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.



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