B3D Chapter 2 Summary
Chapter 2 deals primarily with scaling and measurement. In the chapter such ideas as exponent patterns for basic building blocks and volume patterns for pyramids are discussed at length. The wide variety of techniques used to proceed from one dimension to another is the key theme of this chapter.
What interested me the most was the very end of the chapter that dealt with scaling and growth exponents. The Sierpinski gasket and the Koch snowflake are two very intreging examples. The various properties that these strange objects exhibit are helpful in understanding the nature of dimensionality. What I am curious about though is perhaps 3-dimensional equivalents to these objects. Are there objects that could exhibit these same strange qualities (such as Koch's snowflake's perimeter being 4/3rds the time of the last perimeter)?
Some good problems that would be helpful at the end of the chapter could deal with the mathematics of some of these dimensionality techniques. Solving for common equations or deriving from those equations even more information about certain objects in different dimensions could be beneficial to a better understanding of the chapter.