Lab 7: Coordinates, Projections, and Centers of Mass

This lab has several parts.

A. Tools

Building Coordinate and Lattice Tools

B. Finding barycentric coordinates in a lattice

In each case, make a Sketch that duplicates the problem on the web page and use your tools to check your answer.

Lattice Practice 1

In this exam question with a lattice, ignore the stuff about "harmonic" but find the barycentric coordinates with your tools.

C. Center of Mass

Follow verbal instructions and make a tool that will construct the center of mass of a two-mass system.

Then try this.

Take a triangle ABC..

• Find the location A’ of the center of the masses at B and C. Then find the location A’’of the center of mass of the mass at A and the mass 2+3 =5 at A’.
• Find the location B’ of the center of the masses at C and A. Then find the location B’’ of the center of mass of the mass at B and the mass 3+1=4 at B’.
• Find the location C’ of the center of the masses at A and B. Then find the location C’’of the center of mass of the mass at C and the mass 1+2=3 at C’.
  

D.. Ceva's Theorem

Find a statement of Ceva's Theorem on the web. See how the work on x, y, z shows that the theorm is true. There will be a discussion in lab.