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Editorial Version
Chapter 1 : Introducing Dimensions
Study Questions and Projects
- Find some pictures of amoebas and other organisms that live in a
virtually planar environment. What kinds of sense impressions do they
receive that are different from ours? What would correspond to an eye for
an amoeba?
- In what ways is the amoeba world not really two-dimensional? What would
happen if we picked an amoeba up and held it vertical?
- Would an amoeba have any sense of gravity? How would it be diffferent
from our notions of weight or mass?
- We speak naturally of height, a distinguished direction. What would it
be like to live as an amoeba? Would there be anything in its world
corresponding to height?
- Do you think it is unusual that Edwin Abbott Abbott was a schoolmaster
and a priest? Schools for girls in England were separate from those for
boys. Was the education they received any different?
- What does the term "Victorian England" refer to? When did the Victorian
Era begin and when did it end?
- Study the cover of the first edition of "Flatland" and not the numbers
hidden in he cloud at the top. How many dimensions is the author inviting
us to consider? (Recently physicists have been working on theories using
that same number of dimensions! Find a news story or magazine article that
treats dimensions in physics.)
- There are two quotations on the front page, both by the same author.
Can you find out where they came from?
- The price of the first edition was Half-a-crown. The current edition in
England costs seven pounds. How many times greater is the price today?
- What does Abbott mean by "A Romance of Many Dimension?"
- The author of the first edition was listed as "A Square" (with no
period after the "A"). Not long afterwards it was revealed that the author
was Edwin Abbott Abbott. Why was that an appropriate pseudonym?
- What are some examples of professions that depend on making accurate
measurements? Often a professional will want to know several numbers before
making a decision. Give some cases where someone would like to have more
information in terms of numbers in order to make a better choice.
- Make up a "dimensional story", where someone becomes conscious of
dimensional limitation and wishes for more dimensional freedom.
- Collect some data from family members, such as the hat size, or
distance from the elbow to the end of the fingers, or the span measured
from the tip of the thumb to the tip of the little finger.
- How does an oculist view a patient? What numbers does a cardiologist care about?
- Given two views of a tool or a building, under what circumstances can
we predict other views?
- In the sequence of pictures at the bottom of page 9, how many corners
are there in each? How many segments?
- Find out more about Galileo, van Leeuwenhoek, and Roentgen. What
countries did they live in? When did they live?
- Give some other examples of modern visualization tools.