# 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.