Flatland Worksheet

Honors Geometry – Flatland

Flatland Worksheet

Have complete, the following sections for the next three (3) classes in your notebook1. Complete questions on pages 2 to 32. Complete questions on pages 4 to 53. Complete questions on pages 6 to 7

Title Page....................................................................................................................................................................................2

Dedication..................................................................................................................................................................................2

Contents......................................................................................................................................................................................2

Limitations..................................................................................................................................................................................2

Chapter 1: Of the Nature of Flatland..........................................................................................................................................2

Chapter 2: Of the Climate and Houses in Flatland.....................................................................................................................2

Chapter 3: Concerning the Inhabitants of Flatland....................................................................................................................2

Chapter 4: Concerning the Women............................................................................................................................................3

Chapter 5: Of Our Methods of Recognizing One Another........................................................................................................3

Chapter 6: Of Recognition by Sight...........................................................................................................................................4

Chapter 7: Concerning Irregular Figures....................................................................................................................................4

Chapter 8: Of the Ancient Practice of Painting..........................................................................................................................4

Chapter 9: Of the Universal Colour Bill....................................................................................................................................4

Chapter 10: Of the Suppression of the Chromatic Sedition.......................................................................................................4

Chapter 11: Concerning Our Priests...........................................................................................................................................5

Chapter 12: Of the Doctrine of Our Priests................................................................................................................................5

Chapter 13: How I Had a Vision of Lineland...........................................................................................................................5

Chapter 14: How I Vainly Tried to Explain the Nature of Flatland..........................................................................................6

Chapter 15: Concerning a Stranger from Spaceland.................................................................................................................6

Chapter 16: How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland..........................6

Chapter 17: How the Sphere, Having in Vain Tried Words, Resorted to Deeds......................................................................6

Chapter 18: How I Came to Spaceland, and What I Saw There...............................................................................................6

Chapter 19: How, Though the Sphere Shewed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of

It..................................................................................................................................................................................................7

Chapter 20: How the Sphere Encouraged Me in a Vision........................................................................................................7

Chapter 21: How I Tried to Teach the Theory of Three Dimensions to My Grandson, and with What Success.....................7

Chapter 22: How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result....................7

Burgeson, Joel. (2001). Retrieved February 25, 2007 from http://www.newmanu.edu/fs/pages/burgesonj/FlatlandWS.htm of 7

http://www.newmanu.edu/fs/pages/burgesonj/FlatlandWS.htm


Title Page

In the title what does the word “romance” mean?

Who is the author? Who (what) is the narrator?

Dedication

To whom and for what purposes is the book dedicated?

Contents

Given the titles of the two sections and the 22 chapters, write a three or four sentence summary of what you think this book will be about.

Limitations

According to Isaac Asimov what are the “limitations” of Flatland, the book? Even though it is flawed, why should we read it anyway?

Chapter 1: Of the Nature of Flatland

What is Flatland and who are its residents?

What problem do Flatlanders have in recognizing one another?

Chapter 2: Of the Climate and Houses in Flatland

A Law of Nature is that there is a constant attraction to the _____. Rain always comes from the _____. Side walls of houses run _____ and _____.

Why are there no windows in Flatland? What do you think is the origin of light in Flatland?

What has the Legislature done about investigating the origin of light? Whom do you think the author is satirizing and what is he saying about them?

The most common shape of house is _____. The south side is usually _____. The small door for _____ is on the _____ side. The larger door for _____ is on the _____ side. Why are square and triangular houses disallowed?

Chapter 3: Concerning the Inhabitants of Flatland

The largest inhabitant of Flatland is _____. _____ are straight lines. _____ and the lowest classes of workers are _____ triangles. The middle class is composed of _____. Squares and pentagons are _____ and _____. The author, who is a square, is therefore a _____. The nobility have _____ sides. The priestly class is _____. From the first six paragraphs of this chapter, what can you deduce about class-consciousness in Victorian England?Burgeson, Joel. (2001). Retrieved February 25, 2007 from http://www.newmanu.edu/fs/pages/burgesonj/FlatlandWS.htm

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The usual Law of Nature is that the father of a (male) hexagon is a _____. There is a lengthy discussion of how rare it is that an isosceles triangle will be the father of an equilateral triangle, much less a square. What do you think the author is saying about moving up into the middle class of Victorian England?

What is the Law of Compensation? Give both a geometrical and a sociological answer.

Why do you think regular polygons are held in greater esteem?

Make a guess about how you think women will be portrayed in Flatland. Hint: The book is a satire of Victorian England, and one tool of the satirist is exaggeration.

Chapter 4: Concerning the Women

What geometrical term describes the shape of Flatland women?

How can they make themselves nearly invisible?

What “power of Fashion” or “natural instinct” counteracts this invisibility?

What is St. Vitus’ Dance?

What do you think the “Peace cry” is?

According to the narrator how intelligent are women in Flatland? How violent are they? What do you suppose the author’s point is?

Chapter 5: Of Our Methods of Recognizing One Another

What are the three methods Flatlanders use to recognize each other?

Why is “feeling” one angle enough to determine a polygon’s class? Give an example and use one of our formulas from chapter #7.

Explain the narrator’s grandfather’s tragedy in having his brain reduced from 5930’ to 58. Give a geometrical and a societal answer.

According to the narrator, how do children in Flatland learn to discriminate between the small angles? What is the author’s point?




Chapter 6: Of Recognition by Sight

What is Fog? How does it help Flatlanders to discriminate distances? Use the narrator’s example of the Merchant Triangle and the Physician Pentagon in your explanation.

What is meant by the phrase “task the angularity of the most intellectual”?

What does the narrator mean by “to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself”? What does the author mean?

In your opinion, is the author really opposed to deaf people using sign language?

Chapter 7: Concerning Irregular Figures

What benefit do Flatlanders who “feel” derive from all Figures having congruent angles?

What does the narrator say is true of those who suffer from “Irregularity of Figure”? What are the consequences? What does the author mean? (Hint: What is the narrator’s Via Media?)

Chapter 8: Of the Ancient Practice of Painting

What is the author’s joke in the first paragraph where he writes, “nor would I deny that the strange mixture of the problems of life and the problems of Mathematics, continually inducing conjecture and giving the opportunity of immediate verification, imparts to our existence a zest”?

What is the name of the Pentagon who started the Colour Revolt? What does his name mean?

What is the meaning of the motto of the Colour Revolt? What is the objection of the priests and women?

Why was one illustrious Circle led to become an artist?

Chapter 9: Of the Universal Colour Bill

Describe three ways in which the “intellectual Arts” declined.

What was the Soldiers and Artisans argument for equal rights?

What was the half-red, half-green coloring proposal? How could a priest then be mistaken for a woman? Why is the skill of Sight Recognition important here?

Give two reasons that society was in danger of anarchy from this proposal.

Chapter 10: Of the Suppression of the Chromatic Sedition

What catastrophe led to the “Suppression of the Chromatic Sedition”?




Who was Pantocyclus? What does his name mean? What did he do?

Now that Colour has been outlawed, where is the only place it still exists in Flatland?

The author may have been using the Universal Colour bill to satirize an actual series of events in 19th Century England. Do some research into this question and report on your findings.

Chapter 11: Concerning Our Priests

What are some of the topics the narrator does not discuss?

Explain the sentence “[t]hree feet being the average Perimeter it follows that, in a Polygon of three hundred sides each side will be no more than the hundredth part of a foot in length, or a little more than the tenth part of an inch.”

What are the “two antagonistic decrees affecting Circular propagation”?

What is the Circular Neo-Therapeutic Gymnasium? What are the rewards and the risks of sending an infant there?

Chapter 12: Of the Doctrine of Our Priests

Explain the saying “Attend to your Configuration.” What was the teaching of Pantocyclus concerning praise for a job well done? Why are right and wrong meaningless ideas then? Is free will related?

What is the “system of female non-education”? What is the rationale for it? What dilemma results and how is it resolved?

What does the narrator fear might happen? What is the author’s point?

Chapter 13: How I Had a Vision of Lineland

What is Lineland and who are its inhabitants? Describe them.

What is the Law of Nature for marriage and offspring in Lineland? Why are two girls born for every boy?

Why does the narrator have to ask so many questions? What does the King of Lineland think of this?




Chapter 14: How I Vainly Tried to Explain the Nature of Flatland

Explain the King’s claim that space and length are the same.

How is the sense of hearing used to approximate length in Lineland?

What difficulty does the narrator have in describing himself to the King?

Explain the narrator’s two demonstrations of two dimensions to the King.

Why does the King think the narrator is a woman? What is the narrator’s reaction? Then what happens?

Chapter 15: Concerning a Stranger from Spaceland

How does the narrator explain the meaning of 32? What is the narrator’s geometrical meaning of 33? What is yours?

Compare the narrator’s reaction to his grandson to the King of Lineland’s reaction to the narrator.

Who (or what) is the visitor? Describe what the Narrator and his wife see. Why does the visitor’s size change?

Chapter 16: How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland

Compare the narrator’s claim that in Lineland the idea of space is incomplete with the visitor’s claim that in Flatland the idea of space is incomplete.

Describe the visitor’s two methods of explaining the third dimension to the narrator. Compare them, and their results, to the narrator’s two methods of explaining two dimensions to the King of Lineland.

Explain the Analogy. Sketch a segment moving to become a square and a square moving to become a cube. What is the narrator’s reaction to the Analogy? What do you suppose the narrator’s grandson’s reaction would have been? What might the author have been saying about the younger generation?

Chapter 17: How the Sphere, Having in Vain Tried Words, Resorted to Deeds

What did the sphere do to convince the narrator? Describe how a four dimensional burglar could be very “successful” if an analogous procedure could be followed.

What does the narrator do? What is the sphere’s reaction?

Chapter 18: How I Came to Spaceland, and What I Saw There

What is “omnividence”? Why does the narrator ask if it is an attribute of God?




What does the narrator overhear in the High Council? What is the author’s point?

Chapter 19: How, Though the Sphere Shewed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It

Who was Prometheus? Why the narrator think of himself as a second Prometheus? What was his fate?

How does the narrator offend the sphere? Describe his request and his analogy.

Compare the sphere’s reaction to the possibility of four dimensions to the narrator’s earlier reaction to the idea of three dimensions and the King of Lineland’s to two dimensions. What is the author’s point?

Chapter 20: How the Sphere Encouraged Me in a Vision

Explain what is meant by “Upward, and yet not Northward.” Write your own four dimensional analogue to “Upward, and yet not Northward.”

What is a “blue-bottle” and why does it hum?

What effect do the narrator’s words have on the King of Pointland?

What is an Extra-Solid? a Double Extra-Solid? Make a table with these analogues.

How do the sphere’s actions at the end of this chapter differ from those at the end of Chapter #19? What is the author’s point?

Chapter 21: How I Tried to Teach the Theory of Three Dimensions to My Grandson, and with What Success

Upon his return to Flatland, what does the narrator do? What danger does he face? Why does he do it then?

What is the narrator’s grandson’s reaction? Is this different than your prediction in Chapter #16? Why is it different?

Chapter 22: How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result

After his failure with his grandson, what is the narrator’s next course of action? Explain the title of his treatise.

What does the narrator do to get arrested?

Answer the two questions the President puts to the narrator.

How many converts does the narrator make? What is his state of mind?



Flatland Worksheet

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