Math 325

Spring 04

 

Reading Questions/Notes for Flatland: Part 1.

 

            These are questions/notes to help you think about the book as you are reading.  You don’t have to write up formal answers to them, but you might wish to jot down some notes.

 

Chapter 1:

            1.  How does the set-up of Flatland relate to what we’ve discussed about the intrinsic point of view?

            2.  Try out the experiment with the penny.  How would it change if you looked at a toothpick instead?  A penny standing on its edge?

 

Chapter 2:

            3. How are the symmetries of the plane different in the North and the South of Flatland?  In each region, would Flatland look different under rotation?  reflection?  translation?

            4.  What if the light in Flatland came from the plane of Flatland (like the rain does)?  What kinds of shadows would there be?

            5.  Do you see the visual pun in the drawing of the pentagon?

 

Chapter 3:

            6.  Much of this chapter satirizes ideas of the Victorian upper class about social rank, inheritance, etc.  Think about it in the context of things you might know about the theory of evolution, natural selection, social Darwinism, phrenology, etc.

 

Chapter 4:

            7. How can a Flatland woman make herself invisible?  Relate to question 2.

            8. This chapter is also quite satirical about the role of women in Victorian England in general, and about their access to education in particular.  What do you know about this time and place?  From that knowledge, what do you think Abbott’s true opinions were?

 

Chapter 5:

            9.  Relate the information about how Flatlanders “feel” angles to how we discern shapes in three dimensions, when our retinas are essentially two-dimensional.

            10.  Explain why all Flatlanders would eventually become circles under the inheritance scheme described here.  Where do isosceles triangles come from?  Are we entering the territory of theology?

 

Chapter 6:

            11.  Do you think Abbott’s use of Fog is a good solution to solving the dilemma in this chapter?  Can you see other ways that Flatlanders could recognize each other?

 

Chapter 7:

            12.  Is it possible for a polygon to have equal angles, but unequal sides (try starting with a hexagon  maybe play with Sketchpad)?  Is it possible to have equal sides, but unequal angles?  How does Abbott’s use of angles to determine sight recognition in Flatland affect his notion of who is irregular?

            13.  Think about what Abbott might be satirizing in this chapter.

 

Chapter 8:

            14.  Is Abbott’s notion that women and priests both have no sides valid mathematically?  What is he trying to do in terms of the narrative?

            15.  Can color be thought of as another dimension?

 

Chapter 9:

            16.  Is this chapter consistent with what Abbott has said previously about Flatland women’s intelligence?  What might his satirical meaning be?

 

Chapter 10

            17.  Here Abbott is also commenting on the concept of “universal rights,” which was spreading during the Victorian era and also on some of the politics (including the use of military force against subjects) of the British Empire.

            18.  Think about ways that color is currently used in mathematics to illustrate deep concepts.

 

Chapters 11-12

19.    Keep thinking about the social satire Abbott is making here.

Chapter 17

            1. Note that Abbott was serious about his religion, but he also was willing to make jokes about it too.

            2. What does a locked closet look like in Flatland? How is it that the Sphere has access to it (and to A. Square's stomach)? Get a picture for yourself, and then try to imagine an analogy with 3 and 4 dimensions, instead of 2 and 3. Is it surprising that A. Square thinks the Sphere is a magician?

Chapter 18

            3. Would A. Square, whose brain evolved in 2 dimensions, see solid objects the same way we do?

            4. Looking at the map of A. Square's house, think of how strange it would look to him. Imagine what things might look like if you were transported to a fourth spatial dimension.

            5. What's your response to the theological discussion here? To the comments about women? The different punishments for different offenders?

            6. Taking away the policemen is a reference to the way the British Empire kept secrets from the general public.

 

Chapter 19

            7. What does A. Square see in figure 2, and how is it related to a cube?

            8. Note that A. Square wants to go to higher dimensions and note the Sphere's reaction. Moving to a higher dimension is one of the reasons Abbott wrote this book.

            9. A. Square describes a four dimensional cube. Try to figure out how many 3D cube faces, 2D square faces, and edges such a cube would have. What about a SD cube?

            10. Does A. Square's reasoning mean such a fourth spatial dimension exists?

Chapter 20

            11. What is Pointland like? What satire is Abbott making?

Chapter 21 .

            12. Why can't A. Square explain his math discoveries to his grandson?

Chapter 22

            13. Does A. Square's plight remind you of that of any historical figures?

 

   Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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