No you guys, most shapes do not have a center of mass with this property (but some do)

The video explores the misconception that any plane through the center of mass of a 3D object cuts it in half. While this is true for objects with obvious symmetry like circles and squares, it does not hold for equilateral triangles or tetrahedrons. The video provides a mathematical analysis and proof using an equilateral triangle to demonstrate that no such point exists where any line through it will bisect the triangle. The conclusion extends this finding to other shapes, emphasizing that not all objects have a magical point for bisecting planes.

What is the significance of the center of mass in relation to cutting objects in half?

Explain why the property of cutting an object in half through its center of mass does not hold for an equilateral triangle.

Describe the method used to find the area of the upper piece of the triangle when a horizontal line is drawn.

What conclusion can be drawn about the assumption that every shape has a point where any plane through it cuts in half?

Discuss the implications of the findings regarding the tetrahedron and pyramid in relation to the center of mass.