DOCSLIB.ORG

Honors/Pre-AP Geometry Name______KEY______Sphereland (Through P

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Honors/Pre-AP Geometry Name______KEY______Sphereland (Through P Honors/Pre-AP Geometry Name_________KEY________________ Sphereland (through p. 26) Date_____________Period________ 1. Name the scientist who revealed that the Universe was not flat. What did he do that demonstrated that the Universe was curved? Pg ix Albert Einstein – light did not travel in straight lines but had slight curves to them 2. Give the author and date for Flatland and Sphereland. Pg vii Flatland – 1880 by Abbott Sphereland – 1960 by Burger 3. Who narrates Flatland? Pg 1 Square 4. The gravitational force in Flatland is in the direction called _south______. Pg 1 5. If someone loses his sense of direction and cannot sense gravity then he waits for __rain________ since it comes from the ____north___________. Pg 1 6. Describe the houses. Pg 2 Shaped like pentagons, wide door for men and narrow door for women, no windows Only military installations such as forts, powder magazines, barracks and certain government buildings are allowed to have sharper corners 7. At what point is a child removed from his parents? Pg 3 When offspring’s angle is 60°, he is certified as an equilateral and brought up by an equilateral couple. 8. Discuss the shapes of people (men and women) in Flatland, how they are ranked in society and what shape offspring might be. Pg 3 Adults – 11” long Women – straight line, almost no width Rank – more sides higher rank Men -- triangles or polygons Top angle contains brain 1 Offspring’s vertex angle increases 2 " until equilateral than offspring has one more side 9. The ___Priest___________ class is made up of polygons with so many sides they resemble ___circles_____________. Pg 4 10. ___Equilaterals_______ make up the middle class. Pg 4 11. The common workers’ class is made up of the ___Isosceles_____________. Pg 4 12. Why did the Circles like for the lower class to be at war? Pg 4 They would kill each other off. 13. What restrictions were originally placed on women in Flatland and what innovation changed these restrictions? Pg 5 – 6 Constant warning cry If disease with involuntary motions then destroyed immediately Endpoint in constant motion Eye and mouth constantly directed toward her lord and master 14. Describe 3 ways that could be used by inhabitants of Flatland to recognize another’s shape. Pg 7 . Hearing – voice of highly developed sounds more aristocratic (unreliable) . Touch – carefully touching one of the angles . Visual – more distant objects are hazy so sisdes of angle become less clear as they lead away (used by higher ranks, taught in school) 15. What happened to irregular children? Pg 8 If pushing and pulling does not correct them, they are destroyed. 16. What did some high ranking Polygons do to their children? What was the drawback of this and why was it tolerated? Pg 8 . They are reshaped at the state clinic (break frame in many places) . Dangerous – only a small percentage survive . Tolerated because fertility lessens with increase in sides & if not enough Circles are born then more must be made 17. Who was Chromatistes and what happened as a result of his contribution? Pg 9 – 10 Chromatistes was a Pentagon who invented the art of painting. By using many colors, Isosceles could look like Pentagons. As a result, there was a battle between classes. Painting was outlawed. 18. Who was Pantocyclus? Pg 9 Head Circle 19. On December 30, 2000, Square had a vision that he visited Lineland. Describe Lineland. Pg 10 – 14 Inhabitants were little lines, but not able to pass each other Longer line was king Women – dots, one voice (soprano or contralto) Men – lines, 2 mouths – bass and tenor Only saw dots Marriage – harmonizing of voices births of 2 girls and a boy Recognition – measuring time elapsed when calling 20. What shape was Square’s grandson? Pg 15 Hexagon 21. On December 31, 2000, while Square was discussing arithmetic and geometry with his grandson, his grandson speculated a _____third dimension____. How did Square react? Pg 16 Square said it was nonsense. 22. On December 31, 2000, Square is visited by Sphere who discusses the progression from a point to a cube. Fill in the following chart: Pg 20 Borders Figure # of sides # of vertices Point 0 1 Line 2 2 Square 4 4 Cube 6 8 The number of sides forms a series called a ___arithmetic____________ progression. The number of vertices forms a series called a ____geometric_________ progression. 23. In Flatland, describe what customarily took place at a turn of the century. Pg 21 A creature from Spaceland visits the States Conference to argue for the existence of a third dimension 24. Sphere got angry when Square asked to visit __the land of 4 dimensions______. Pg 23 25. On New Year’s Day, what did Square do and what happened to him as a result? Pg 26 At a gathering of the Natural Sciences Association he told about the Sphere’s visit and about his own trip to Spaceland. “upward but not northward” arrested and sentenced to life imprisonment .
Load more

Recommended publications
  • Flatterland: the Play Based on Flatterland: Like Flatland Only More So
    Claremont Colleges Scholarship @ Claremont HMC Senior Theses HMC Student Scholarship 2012 Flatterland: The lP ay Kym Louie Harvey Mudd College Recommended Citation Louie, Kym, "Flatterland: The lP ay" (2012). HMC Senior Theses. 27. https://scholarship.claremont.edu/hmc_theses/27 This Open Access Senior Thesis is brought to you for free and open access by the HMC Student Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in HMC Senior Theses by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Flatterland: The Play based on Flatterland: Like Flatland Only More So by Ian Stewart Kym Louie Arthur Benjamin, Advisor Art Horowitz, Advisor Thomas Leabhart, Reader May, 2012 Department of Mathematics Copyright c 2012 Kym Louie. The author grants Harvey Mudd College and the Claremont Colleges Library the nonexclusive right to make this work available for noncommercial, educational purposes, provided that this copyright statement appears on the reproduced ma- terials and notice is given that the copying is by permission of the author. To dis- seminate otherwise or to republish requires written permission from the author. Abstract This script is an adaptation of the popular science novel Flatterland: Like Flatland, Only More So by Ian Stewart. It breathes new life into mathemat- ical ideas and topics. By bringing math to the stage, this script presents concepts in a more friendly and accessible manner. This play is intended to generate new interest in and expose new topics to an audience of non- mathematicians. Preface I was first introduced to Flatterland by Sue Buckwalter while I was at Phillips Academy.
    [Show full text]
  • ___Booknotes for Flatland Authorial Background: Edwin
    ____________ Booknotes for Flatland Authorial Background: Edwin Abbott Abbott was born in 1838, in a time when the nineteenth-century middle class had begun to rise up from social oppression in Britain. A highly distinguished head schoolmaster, English clergyman, and Shakespearean scholar, he was more interested in the fields of theology and classic literature than in mathematics. Because he sought to express concern over the social problems of the period, he recognized his motivation for writing Flatland; the book was published in 1884 under the pseudonym A. Square to protect himself from attack by those he satirizes in the book. However, although he held his interests in theology and classic literature, his presentation of geometrical concepts earned him acclaim for his intricate barbed satire of the hierarchical Victorian age. For eighty-eight years he lived; in 1926 he died, renowned and remembered for his treatise on mathematical fiction and the power of knowledge. Literary Period/Country: Victorian Period, Great Britain. Setting: The social context of the satire was during the 1800s, when socioeconomic and political changes began to create a flux of new ideas, rebellion, and tense order. The satire takes place in the two-dimensional space Flatland, where lines and shapes move “freely about, on or in the surface” (1). A hierarchical dominion exists in Flatland: Circles are priests, figures having the greater number of sides comprising the higher class, isosceles and irregular triangles are shunned from society, and women--only pinlike lines--are considered the lowliest class of all. This hierarchy emulates exactly the social order of Britain at the time.
    [Show full text]
  • In Between Psychology Table Topic for Scientific Investigation, and the Re-Discovery of the Role of Unconscious P.N
    _NA_ru__ ~_v_o_L_n __ ~_~ __ R,_L_•~-----------------------S~NGBQQKS·--------------------------------------- 7~ related, revolutions in American psycho­ logy: the recovery of the mind as a respec­ In between psychology table topic for scientific investigation, and the re-discovery of the role of unconscious P.N. Johnson-Laird mental processes. Bruner began by setting a new fashion in In Search of Mind: Essays in Autobiography. By Jerome Bruner. the study of perception, the so-called Harper & Row: 1984. Pp.306. $19.25, £14. "New Look". He and his colleagues carried out a series of experiments showing THE imaginary line that divides the two less trust in the testimony of his father. that people's desires, attitudes and expec­ cultures runs through the middle of Bruner with hindsight also offers a tations can affect the way they see the psychology. On one side lies a science that Freudian interpretation of his experiment, world. For example, children over­ aims to explain the mechanisms underlying though it may be significant that he later estimate the size of coins, and children behaviour and the mind. Its practitioners ran into trouble at college for refusing to from poor homes make a greater error than propose explicit theories, often modelled in attend compulsory chapel. those from affluent ones. Other studies the form of computer programs or axiom­ Few people of Bruner's generation showed that an emotionally charged word atized within a formal calculus, sometimes takes very much and attempt to test them in longer to recognize than a more controlled experiments on neutral word - as though the human beings or animals.
    [Show full text]
  • A Non-Linear Take on the Flatland and Sphereland Films
    MEDIA COLUMN Over-Sphere in the fourth dimension is voiced by Kate Mulgrew, who played Captain Janeway on Star Trek: Voyager, In addition to longer reviews for the Media Column, we invite and the minor character Captain Aero is voiced by Danica you to watch for and submit short snippets of instances of women McKellar, who studied mathematics at UCLA and is a force in mathematics in the media (WIMM Watch). Please submit to for encouraging girls to like and do math. In this day and the Media Column Editors: Sarah J. Greenwald, Appalachian age of excessive narcissism, I especially appreciated Tony State University, [email protected] and Alice Silverberg, Hale’s rendition of the King of Pointland; in a bonus inter- University of California, Irvine, [email protected]. view, Hale refers to this character as “just a sad emasculated point.” It’s great that such prominent celebrities were A Non-Linear Take on the enthusiastic about giving their all for some short animated educational math films. Flatland and Sphereland Class stratification was a major theme of Flatland. Films York reminds us in an actor interview that Abbott anticipated a number of political and sociological trends. Circles were Alice Silverberg superior. As stated in the Flatland film, “The more sides you have, the greater your angles, so the smarter you are.” Irregular I enjoyed the delightful 35 minute animated film polygons were viewed as monsters who could be “cured” by versions of the classic Flatland and its lesser known quasi- surgery, or executed. sequel Sphereland. They were released directly to DVD in Abbott’s Flatland society was blatantly sexist, though 2007 and 2012, respectively.
    [Show full text]
  • Contemporary Reviews of Flatland We Have Made a Few Very Minor
    æ Contemporary reviews of Flatland We have made a few very minor editorial changes in these reviews including making (mathematical) word usage current and correcting obvious typos and misspellings. The footnotes are from the original articles; the endnotes contain our commentary. 1. The Academy (November 8, 1884), p. 302. 2. The Athenaeum No. 2977 (November 15, 1884), p. 622. 3. The Athenaeum No. 2978 (November 22, 1884), p. 660. (Abbott unmasked.) 4. The Athenaeum No. 2980 (December 6, 1884), p. 733. (Abbott’s reply to No. 2977.) 5. Nature (November 27, 1884), pp. 76–77. 6. The Spectator (November 29, 1884), pp. 1583–1584. 7. New York Times (February 23, 1885), p. 3. 8. The Literary News (March 1885), p. 85. 9. The Literary News(April 1885), p. 123. (Abbott identified by name.) 10. Science (February 27, 1885), p. 184. 11. Science (April 3, 1885), pp. 265–266. 12. The Literary World (March 21, 1885), p. 93. 13. Lippincott’s Magazine (May 1885), p. 528. 14. City of London School Magazine 8(December 1885), 217–221. 15. Nature(February 12, 1920), p. 629. (Excerpt of Garnett’s letter.) 16. Saturday Review of Literature (October 30, 1926), p. 254. 17. Reviews we’d like to have. 1. The Academy (November 8, 1884), p. 302. Flatland is a world inhabited by beings whose experience of space is limited to two dimensions. In this book a native of this strange region has undertaken to describe its peculiarities to us dwellers in ‘Spaceland.’ It seems the male Flatlanders are plane rectilineal figures, varying in shape according to their position in the social scale, or, what in Flatland is the same thing, to their degree of intellectual development; the lowest class being isosceles triangles, and the highest class, or priesthood, being polygons which have so many sides that they are accounted circles.
    [Show full text]
  • FLATLAND: a Romance of Many Dimensions - E
    FLATLAND: A Romance of Many Dimensions - E. Abbott Published in 1884 FLATLAND: A Romance of Many Dimensions Edwin A. Abbott Table of Contents Preface to the Second and Revised Edition, 1884. By the editor PART 1: THIS WORLD Of the Nature of Flatland Of the Climate and Houses in Flatland Concerning the Inhabitants of Flatland Concerning the Women Of our Methods in Recognizing one another Of Recognition by Sight Concerning Irregular Figures Of the Ancient Practice of Painting Of the Universal Colour Bill Of the Suppression of Chromatic Sedition Concerning our Priests Of the Doctrine of our Priests PART 2: OTHER WORLDS How I had a Vision of Lineland How I vainly tried to explain the nature of Flatland Concerning a Stranger from Spaceland How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland How the Sphere, having in vain tried words, resorted to deeds file:///E|/moe/HTML/Abbott/Abbott_contents.html (1 of 2) [10/27/2003 5:15:19 PM] FLATLAND: A Romance of Many Dimensions - E. Abbott How I came to Spaceland, and what I saw there How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it How the Sphere encouraged me in a Vision How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result file:///E|/moe/HTML/Abbott/Abbott_contents.html (2 of 2) [10/27/2003 5:15:19 PM] FLATLAND: A Romance of Many Dimensions - E.
    [Show full text]
  • From Flatland to Fractaland: New Geometries in Relationship to Artistic and Scientific Revolutions
    FROM FLATLAND TO FRACTALAND: NEW GEOMETRIES IN RELATIONSHIP TO ARTISTIC AND SCIENTIFIC REVOLUTIONS RHONDA ROLAND SHEARER 62 Greene Street, New York, NY 10012 Fax: {212}925-0459 Internet: [email protected] ' Abstract Abbott's 19th century book, Flatland, continues to be popularly interpreted as both a social commentary and a way of visualizing the 4th-dimension by analogy. I attempt here to integrate these two seemingly disparate readings. Flatland is better interpreted as a story with a central theme that social, perceptual, and conceptual innovations are linked to changes in geometry. In such cases as the shift from the two-dimensional world of Flatland to a three­ dimensional Spaceland, the taxonomic restructuring of human importance from Linnaeaus to Darwin, or the part/whole proportional shift from Ptolemy's earth as the center of the universe to Copernicus's sun, new geometries have changed our thinking, seeing, and social values, and lie at the heart of innovations in both art and science. For example, the two greatest innovations in art the Renaissance with geometric perspective, and the birth of modern art at the beginning of this century with n-dimensional and non-Euclidean geometries were developed by artists who were thinking within new geometries. When we view the history of scientific revolutions as new geometries, rather than only as new ideas, we gain direct access to potential manipulations of the structures of human innovation itself. I will discuss the seven historical markers of scientific revolutions (suggested by Kuhn, Cohen, and Popper), and how these seven traits correlate and can now be seen within the new paradigm of fractals and nonlinear sc1ences.• 617 618 R.
    [Show full text]
  • Sphereland Name______Part III – Curved Worlds Date______Period______
    Sphereland Name______________________________________ Part III – Curved Worlds Date________________________Period_________ 1. What was the purpose of the Trigonometric Service? Institute established for the purpose of mapping the world accurately by means of trigonometry. 2. What happened that caused Mr. Puncto to lose his job as director of the Trigonometric Service? While measuring triangles in a net, the angles in one triangle added to more that 180°. One who dares to consider such results is not fit for the position. 3. What were some reasons that the deviations were not found sooner? Pg 133 – 134 . Improved instruments . Errors were seen as observational errors . Old way – net of small triangles 4. Mr. Puncto determined that the discrepancy from 180 increased with __the increase in size of the triangles___. 5. What did Hexagon’s grandson suggest that would explain Mr. Puncto’s data? A triangle whose sides are curved 6. Who was Ergo and how did he respond to Mr. Puncto? Professor of mathematics - would not accept explanation that refuted science facts (180°) Up to investigators to find error 7. Who was Professor Supposo and how did he respond to Mr. Puncto? Professor of physics - principles of math were being attacked Considered peculiar triangle and explained why it wouldn’t work 8. What argument did Professor Supposo give that caused him to reject Hexagon’s explanation for the unusual triangle? Pg 145 If side curve out in one triangle, then they curve in in another. 9. While contemplating his dilemma, Hexagaon sees Lineland as _____Circleland__________. Pg 148 10. Which direction did Hexagon believe that the sides of the triangle were curved? in a third direction invisible to him 11.
    [Show full text]
  • Discover Magazine
    MinD Games By Scott Kim FLATHOUSE 1. On the left is an image from Flatland: The Movie showing Arthur Square (the blue square) at home with his wife (the ma- genta square). Notice that Arthur and his wife are both facing to the right and that each has an eye and a mouth. What problem does this present if they want to kiss each other? How do you think the filmmakers solved this problem? 2. Find the objects listed below in the picture at left. Can you explain their peculiar appearances and how they work? a. bed d. plant b. patio chair e. refrigerator c. dining table f. book 3. In some cases, the filmmakers took artistic license, including objects that are familiar to us but which would be illogical in a two- dimensional world, like the chimney. In Flatland, this chimney would not work correctly because it lacks a hollow channel through which smoke can flow.W hy is the weather vane similarly illogical? SLICES The Flatlanders live in a two- In each case the shape moves (7). M dimensional world that is much straight up at a constant speed I K like the surface of a pond. without rotating. Can you iden- TT O SC Since they are trapped inside tify each of the 3-D shapes? their world, they cannot see rtesy an entire three-dimensional OU C ; solid all at once. Instead they 1. S see only a 2-D cross section ION CT U of a solid where it crosses the D O R FLATLAND planes of their world.
    [Show full text]
  • Flatland a Romance of Many Dimensions with Illustrations by the Author, a SQUARE (Edwin A
    Flatland A romance of many dimensions With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926) To The Inhabitants of SPACE IN GENERAL And H. C. IN PARTICULAR This Work is Dedicated By a Humble Native of Flatland In the Hope that Even as he was Initiated into the Mysteries Of THREE Dimensions Having been previously conversant With ONLY TWO So the Citizens of that Celestial Region May aspire yet higher and higher To the Secrets of FOUR FIVE OR EVEN SIX Dimensions Thereby contributing To the Enlargement of THE IMAGINATION And the possible Development Of that most rare and excellent Gift of MODESTY Among the Superior Races Of SOLID HUMANITY CONTENTS PART 1: THIS WORLD 1. Of the Nature of Flatland 2. Of the Climate and Houses in Flatland 3. Concerning the Inhabitants of Flatland 4. Concerning the Women 5. Of our Methods in Recognizing one another 6. Of Recognition by Sight 7. Concerning Irregular Figures 8. Of the Ancient Practice of Painting 9. Of the Universal Colour Bill 10. Of the Suppression of the Chromatic Sedition 11. Concerning our Priests 12. Of the Doctrine of our Priests PART II: OTHER WORLDS 13. How I had a Vision of Lineland 14. How I vainly tried to explain the nature of Flatland 15. Concerning a Stranger from Spaceland 16. How the Stranger vainly endeavoured to reveal to me in words the mysteries ofSpaceland 17. How the Sphere, having in vain tried words, resorted to deeds 18. How I came to Spaceland and what I saw there 19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it 20.
    [Show full text]
  • Flatland: a Romance of Many Dimensions Part I Summary Edwin A
    Flatland: A Romance of Many Dimensions Part I Summary Edwin A. Abbott, 1884 Chapter 1: A. Square, the narrator and protagonist, starts the book by introducing to his readers this world of Flatland, which he compares to a sheet of paper on which straight lines, triangles, squares, pentagons and other figures roam about. - The narrator immediately starts the book with an analogy to help the reader-like landscape of his world to what will later look a lot like Victorian Britain. - This very mathematical world, governed by geometrical concepts and theories, shows that reason and logical thinking will be an important theme throughout the work. - Religion, Divinity, and the Unknown - Reason vs. Emotion - Knowledge and Truth vs. Dogma - Analogy as Satire, which leads to allegories. A. Square says that Flatlanders, lacking the ability to distinguish each other by sight, only see each other as straight lines, much in the way one sees the side of a penny from the edge of a table. He includes 3 figures that illustrate how a triangle appears from above, close to the level of a table, and at the level. - Abbott’s inclusion of actual images suggests that analogy may be limited if only conducted through words. - The fact that Flatlanders all see each other as lines will later prove ironic, since they distinguish each other by more absurd means. - Social hierarchy and Oppression - Analogy as satire Chapter 2 A. Square continues to illustrate his world by describing its physical environment. Flatland is organized by four cardinal directions (N, S, E, W), and by a “Law of Nature” there is a constant attraction to the South, which functions as a compass to Flatlanders.
    [Show full text]
  • Geometry, Relativity, and the Fourth Dimension
    %* GEOMETRY, RELATIVITY AND THE FOURTH I I DIMENSION •^ ^^f!^ 1 DOVER BOOKS ON RELATIVITY AND RELATED AREAS Methods of Quantum Field Theory in Statistical Physics, A.A. Abriko- sov, et al. (63228-8) $6.00 The Evolution of Scientific Thought from Newton to Einstein, A. d'Abro. (20002-7) $6.00 The Rise of the New Physics, A. d'Abro. (20003-5, 20004-3) Two-volume set $12.00 Introduction to the Theory of Relativity, Peter G. Bergmann. (63282-2) $4.50 Relativity and Common Sense, Hermann Bondi. (24021-5) $3.00 Einstein's Theory of Relativity, Max Bom. (60769-0) $4.50 The Restless Universe, Max Bom. (20412-X) $6.00 Causality and Modern Science, Mario Bunge. (23728-1) $6.95 Investigations on the Theory of the Brownian Movement, Albert Ein- stein. (60304-0) $2.75 The Principle of Relativity, Albert Einstein, Hendrik Lorentz, H. Min- kowski, and Hermann Weyl. (60081-5) $3.50 Differential Geometry, Heinrich W. Guggenheimer. (63433-7) $6.00 The Physical Principles of the Quantum Theory, Wemer Heisenberg. (60 1 1 3-7) $3.50 Atomic Spectra and Atomic Structure, Gerhard Herzberg. (60115-3) $4.00 Speculations on the Fourth Dimension, C. H. Hinton. (23916-0) $4.00 The Domain of Natural Science, E.W. Hobson. (21966-6) $3.50 The Strange Story of the Quantum, Banesh Hoffmaim. (20518-5) $4.25 The Nuclear Properties of the Heavy Elements, Earl K. Hyde, et al. (62805-1, 62806-X, 62807-8) Three-volume set, Clothbound $45.00 Crucibles: The Story of Chemistry, Bernard Jaffe. (23342-1) $5.50 The Absolute Differential Calculus, Tullio Levi-Civita.
    [Show full text]