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Mathematics Professor and Student Collaborate on Publication

Tian Liang
8/27/2006 —

Penn State McKeesport Professor of Mathematics, Zhibo Chen, and his former student, Tian Liang, have coauthored an article that has been accepted by the College Mathematics Journal. The article, "Converse of Viviani's Theorem, " is scheduled for November, 2006 publication.

Tian Liang was an Honors student at the campus from Fall 2002 through Summer 2004 and finished her major, Computer Engineering, at the University Park campus. Ms. Liang was chosen as student marshal for Computer Engineering at the Spring 2006 commencement ceremony. Currently she is enrolled in the University's Computer Engineering graduate program.
   
Dr. Chen and Ms. Liang collaborated in an undergraduate research program at Penn State McKeesport focusing on Viviani's Theorem.  Viviani's Theorem is a result of geometry discovered over 300 years ago.  The theorem states that inside an equilateral triangle, the sum of the perpendicular distances from a point P to the three sides is independent of P (and so equals the altitude of the triangle).

Through the use of vectors,  which Dr. Chen introduces in his Calculus and Vector Analysis class (MATH 230) as a tool, he and Ms. Liang established the converse of the theorem and extended the theorem to all regular polygons. The College Mathematics Journal, which accepted the resulting article, is a highly respected refereed journal.

Penn State McKeesport provides its students with opportunities for undergraduate research. Through these opportunities, students at Penn State are afforded the opportunity to work with a scholar to join in the pursuit of new knowledge.  By being an active researchers,  students are also introduced to the basic principles used to make new discoveries and develop theories.

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