# B3D-Chapter 2

## Irene Klein

Chapter 2, in B3D, mainly addressed the issue of volume in the context of dimension. Basically, the chapter starts out by building up to discuss the volumes of hyperfigures by beginning with two dimensions and progressing up to four and above. Then, it continues on with the binomial theorem, Pascal's triangle, the Egyptians, and fractals.

In this chapter, I noticed a few interesting facts that I had not known before. For instance, though I knew that the Egyptians excelled in geometry(especially concerning pyramids), I never knew that they developed the formula for the volume of the incomplete pyramid.

Another part of the chapter that I found interesting was the discussion of diagonals of cubes in different dimensions. Though I see the relationship of diagonals of cubes in different dimensions, I began to wonder if there is a similar correlation for rectangular shapes in different dimensions.

The last part of the chapter that I found interesting was the discussion of fractals. Up until this point, the book has only talked about dimensions in relation to classical geometry. However, fractals bring in "non-classical" geometry into the aspect of dimension. I wonder if the study of fractals could aid in the study of higher dimensions.