Determina\c{c}\~ao do centro de massa de uma pe\c{c}a triangular por meio de parti\c{c}\~oes a partir da mediana

TL;DR

This paper discusses the classical geometric method for finding a triangle's center of mass using medians, highlighting its historical development by Archimedes and its connection to calculus concepts.

Contribution

The paper revisits the traditional method of locating the triangle's center of mass and presents a new approach inspired by calculus principles.

Findings

Historical analysis of Archimedes' method

Development of a calculus-inspired approach

Confirmation of the median intersection as the center of mass

Abstract

It is well known the method of determining the center of mass of a triangular piece in which it is hanged from each one of its vertices while drawing from the vertice its verticals. The intersection of the three verticals is considered as the center of mass, verified by equilibrating the piece over a point object. But not everybody knows that the method was developed by Arquimedes 2,300 years ago, determining the geometrical elements to the medians of the triangle. He demonstrated theoretically its result and, inspired on his demonstration we developed another one, which lends to the ideia and methods of the differential and integral calculus.