MATLAB or Mathematica

1) Start with these four points S = {{1.14412, -0.371748}, {0.511667, -0.371748}, {0.707107, -0.973249}, {1.33956, -0.973249}}

Make a picture.

2) Rotate the points in S by five multiples of 2Pi/5 around the last point in S

angles 0, 2Pi/5, 4Pi/5, 6Pi/5, and 8Pi/5

Make separate pictures of these points.

3) Translate the points in S by these offsets, using a single matrix multiplication for each point in S.

offsets = {{-2.995, 0.973}, {-1.851, -0.6015}, {-1.851, 2.548}, {0, 0}, {0, 1.9465}}

Make a picture of the resulting points.

4) Rotate the points in (3) by five multiples of 2Pi/5 around the last point in S

Make a picture of these points altogether. What do you observe? Do you think this pattern can be extended?

5) Make a matrix for all integer 3D coordinates where the entries range from -3 to 3 and call it M

6) For these three vectors T = {{-1, -1, 0}, {1, -1, 0}, {0, 1, -1}} calculate all integer combinations with coefficients from -3 to 3 using M from (5) and a single matrix multiplication.

7) Create a 2D graphic of all of these points from (6) using the technique of perspective explained in the textbook. Use the point of view {3,2,1} centered on {0,0,0} If you are using software with 3D capabilities, do not use the 3D capabilities, just the 2D rendering.