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The Center of Gravity

CSEF · 2012 Mathematics & Software

Janet M.S. Liu · Abbott Middle School, San Mateo, San Mateo County

Overview

Objectives/Goals To define which crucial triangle point (incenter, centroid, orthocenter, circumcenter) is also the triangle#s center of balance or gravity. Methods/Materials I tested my theories with a scalene triangle, and plotted the four crucial triangle points necessary for my experiment by means of geometric construction methods. I tested my point which seemed to best balance the triangle by performing a balance test, then did the test again on paper versions of all four triangles. Results The crucial triangle point, the centroid, is the center of gravity for all four types of triangles. Conclusions/Discussion After I pondered my conclusion further, I was also able to better validate the conclusion mathematically and logically, not to mention the physical test I performed in this experiment. I believe I am fully convinced that the centroid is indeed the triangle#s center of balance. If I had to redo this experiment, I would also attempt to test and make certain the fact that the other three triangle points do not balance any of the other types of triangles.

Summary statement

My project is about validating the triangle's centroid as its center of gravity.

Help received

Father helped prepare heavy cardboard for project

Competition history

  • CSEF 2012 Mathematics & Software · Entry J1413

Resources

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Source: California Science & Engineering Fair public projects

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