The Planiverse: Computer Contact with a Two- Dimensional World Pdf, Epub, Ebook

Total Page:16

File Type:pdf, Size:1020Kb

The Planiverse: Computer Contact with a Two- Dimensional World Pdf, Epub, Ebook THE PLANIVERSE: COMPUTER CONTACT WITH A TWO- DIMENSIONAL WORLD PDF, EPUB, EBOOK A. K. Dewdney | 247 pages | 01 Nov 2000 | Springer-Verlag New York Inc. | 9780387989167 | English | New York, NY, United States The Planiverse: Computer Contact with a Two-dimensional World PDF Book Actually, if anyone wants to do the art for a game, I'm up for the programming side of things. Jan 02, J. Interestingly the book also gives you ways to imagine how the four dimensional world would behave. I recommend this book to anyone who enjoyed Edwin Abbott's "Flatland", which should be mandatory reading before tackling this book. Categories : Canadian novels science fiction novels Canadian science fiction novels Fictional dimensions Novels about mathematics. This purports to be an account of a computer programming project to simulate of a two- dimensional world. Buy Softcover. It seems that you're in Germany. Dewdny originally created a project for a class which would simulate a two dimensional world. To see what your friends thought of this book, please sign up. To go along with the fascinating worldbuilding there is a pretty gripping plot about a 2-dimensional being who befriends some 3-dimensional university students and takes th I think this is probably one of my all- time favorite books. If you were intrigued by Flatland, read this book. Friend Reviews. See if you dig a hole you have to put the material you remove somewhere. There were many little "aha" moments within it, and you can tell it was a ton of fun to develop. With this superiority and ease of understanding, we may extrapolate to the desire to acquaint ourselves with our higher dimensions, and possibly embolden ourselves to try such things as to "Know rather than to learn". Shelves: non-fiction , science , born-to-blush-unseen , science-fiction , humour. The Trek. Of course this book begs comparisons to Flatland An incredible piece of imagination. He is known for being able to disappear and then reappear in a different place, and it seems that the way in which he does this is by going into a third dimension and then coming back into two dimensions. This is when the class begins to really think about Arde differently from Earth. Couldn't resist. The Planiverse: Computer Contact with a Two-dimensional World Writer Recommended with any fan of world building! It's predecessors at least the two I previously mentioned dismiss these questions outright but Dewdney takes them on and really pushes my thinking about these concepts even further. The 2D world is in a computer. There were those who wanted to believe, despite the tongue-in-cheek subtext, that we had made contact with a two-dimensional world called Arde, a di- shaped planet embedded in the skin of a vast, balloon-shaped space called the planiverse. At times I felt the detail of the fiction was a little unnecessary but mostly I found the story of Yendred to be engaging and thought-provoking. Absolutely fascinating book. Dewdney put a lot of thought in the way a civilization must necessarily be set up in a two-dimensional world - how will the laws of physics affect these creatures and their world? Aug 16, Stoa rated it really liked it. The sophisticated simulation includes sentient beings, one of whom is able to communicate with the human investigators. The line between willing suspension of dis- lief and innocent acceptance, if it exists at all, is a thin one. A fascinating book which may be literature but also speculative science and even philosophy. If you can look past the paper thin plot that sets up Yendred's adventures in the Planiverse, you won't be disappointed. If you were intrigued by Flatland, read this book. Showing Friend Reviews. On the down side, I felt it was very little story and too much world building. A book has not excited me this much in a very long time. Flatland 's asshole sphere is traded for a bunch of college students and a teleprinter which is adorable , its top-down view for a more interesting side-scroller, and its endless confusion over dimensions for an exploration of the physical implications of a two-dimensional world. There are lots of asides and text boxes exploring some of the concepts touched upon, as well as appendices that give the Planiverse even more depth. The inhabinates of the world live underground, in homes that could not be built according to the weather they created without flooding. Community Reviews. See if you dig a hole you have to put the material you remove somewhere. In "The Planiverse," we have a frame story that wraps around a travelogue through a two-dimensional world. For this reason, I was forced to give it a 3 rating on "Math. He visits the Punizlan Institute for Technology and Science, where Arde's technology is explored in great detail. When Yendred first crosses paths with another Ardean, Tssil, one of them must lie down on the ground while the other walks over them in order to continue in their original directions since they cannot merely pass by each other. May 05, David Hibberd rated it it was amazing Recommends it for: Readers interested in computers, science, and technology. Feb 11, Kate rated it it was amazing Shelves: dude-writer , canadian-author , fiction , sci-fi , science. Eavesdropping on Yendred's conversation, the class learns that he is heading towards Vanizla, in search of something. The same happened with Flatland, the original "two-dimensional universe" narrative. This is when the class begins to really think about Arde differently from Earth. While embedded in a bit of a melodramatic story, the description of a universe of only two dimensions is interesting and much more detailed than the story in Flatland. Show all. The Planiverse: Computer Contact with a Two-dimensional World Reviews And I mean everything - biology, astrophysics, chemistry, weather, transport and traffic, painting, musical instruments, writing, computers, everything. I found the A little slow in the beginning, but a fascinating thought experiment in action. Contributed by anonymous This wasn't fiction was it? It seems that you're in Germany. An appendix explains various other aspects of two-dimensional science and technology which could not fit into the main story. This is a brilliant description of life in a two-dimensional world. Recreations, his column which appeared in Scientific American for more than eight years. However, YNDRD appears on the console a second day, and it becomes apparent that he is not a mistake, but something beyond what was expected. The writing style is very economical and that this is all accomplished in such a concise fashion is a lesson to authors who take two or three times as many pages to achieve far less. This is science-fiction with lots of science in it. May 05, David Hibberd rated it it was amazing Recommends it for: Readers interested in computers, science, and technology. While this greatly worries Alice Little, Dewdney's course assistant, the class reaches the conclusion that it was most likely just a mistake caused by a misreading of bits because the FEC soon continues to behave normally. Paperback , pages. It is tempting to imagine that those who believed, as well as those who suspended disbelief, did so because of a persuasive consistency in the cosmology and physics of this in? It resonated a lot more than Flatland. Yendred lives! A book has not excited me this much in a very long time. Rating details. This book asked and answered questions before I even thought of them, and truly expanded the way I thought about the 2nd - and of course, the 3rd and 4th - dimension, as well as tackling ideas about philosophy, evolution, and intelligent ingenuity. Oct 03, Fred D rated it really liked it Shelves: science-fiction. There is some knowledge that Derbk possesses and that Yendred desires to know. They were unnecessary characters that didn't contribute to the story much. Games Workshop Issue 55 : The Planiverse: Computer Contact with a Two-dimensional World Read Online Other Editions If you can look past the paper thin plot that sets up Yendred's adventures in the Planiverse, you won't be disappointed. Moreover, many ideas are repeated Although Planiverse adds a great deal to the universe and is considerably different from that of Flatland. Refresh and try again. See if you dig a hole you have to put the material you remove somewhere. For instance, the chapter in which we view the two-dimensional shallow sea would have been a marvelous opportunity to discuss KdV solitons and Kelvin-Helmholz instabilities! View 1 comment. Maybe it's just me. An appendix explains various other aspects of two-dimensional science and technology which could not fit into the main story. It starts as an exercise in pure physics, mathematics and computer science, until their model som The Planiverse: Computer Contact with a Two Dimensional World by AK Dewdney The setting is a graduate program in the early 's. Oct 14, Adina rated it it was amazing. Simply put, it is easy to recognize a line as being one dimensional and a square as two dimensional. Very thoroughly researched. That is just 2 chapters into the book. Especially not as they learn about the two dimensional computer in the Punizlan Institute, only one of the more advanced engineering creations in Arde. Dewdney is great- right up there with Martin Gardner for making math, science, and more specific to him computer science interesting and fun. Far more detailed and thought out than, "Flatland", The Planiverse follows characters across their flat environment and explains how all their structures work.
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]
  • 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]
  • 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]
  • 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]
  • Spaceland Notes
    Rudy Rucker, Notes for Spaceland Spaceland Notes Notes written by Rudy Rucker for Spaceland (Tor Books, 2002). Copyright Rudy Rucker © 2002. I started writing Spaceland on August 24, 2000. These Spaceland Notes were last revised on July 16, 2001, when the final edit of Spaceland was mailed in. Document was put into PDF format on November 22, 2005. The Spaceland Notes are 37,000 words long. Writing Journal ....................................................................................................... 4 January 7, 2000. Preliminary Plans for my Next Novel. .................................... 4 June 22, 2000. Brussels, Hypercube on TV........................................................ 5 June 28, 2000. Joe’s view of Spazz. Joe’s Redemption. ................................... 5 June 30, 2000. Joe’s Astral Body. ..................................................................... 5 July 5, 2000. The cliff at the end of Sheepshead peninsula............................... 6 July 8, 2000. The two plots................................................................................. 7 July 18, 2000. T-shirts. ...................................................................................... 7 August 8, 2000. Hypervision. ............................................................................ 7 August 25, 2000. Started Writing. ..................................................................... 7 September 12, 2000. Underway. Calvino quotes.............................................. 7 September 15, 2000. Four Chapters,
    [Show full text]
  • The Story of Flatland: an Adventure in Many Dimensions
    The Story of Flatland: An Adventure in Many Dimensions By Suzanne Fox Buchele Adapted from the original story by Edwin A. Abbott Third Draft, May 8, 2009, minor revisions through August 10, 2010 ©2006 by Suzanne Fox Buchele Preface The classic story Flatland: A Romance of Many Dimensions by Edwin A. Abbott was first published in 1884. Both the original and this version of the story are written for a general audience, and tell the story of a two-dimensional figure who discovers three-dimensions and contemplates other dimensions as well. The story introduces and reinforces mathematical and especially geometric concepts, and also engages in social commentary, as part of a fantastical story. Abbott was a clergyman and educator whose passion was mathematics; I am a computer scientist, mathematician, and educator with an interest in spirituality. Abbott’s delightful story contains sociological and philosophical elements, particularly in his descriptions of Flatland society. Written when it was, in late 19th century England, the Flatland society Abbott describes is a strict caste system, with women at the bottom. In particular, the original book is quite derogatory in its descriptions of women in Flatland society, who are lines as opposed to closed figures, are hysterical, unable to reason, have to make a "peace-cry" when they are out in public, and more. While the social elements of Abbott’s version were apparently intended as a sharp critique of the place of women in Victorian England society, the depreciatory elements concerning women can be difficult to intellectualize as satire, especially for a younger audience or one not familiar with Abbott’s goals.
    [Show full text]
  • Activity Overview
    Grade level: middle/secondary Subject: mathematics Time required: 45 to 90 minutes + TI-Nspire Activity: Flatland: A Romance of Many Dimensions By: Tammy L. Jones [email protected] Activity Overview "[The universe] is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures..." -- Galileo Galilei In this document, students are asked questions about their reading of the book Flatland by Edwin Abbott. The handheld skills required are minimal with the exception of the last problem. The students are asked as they progress through the questions to draw some of the characters from the book. This can be easily done with the shapes tool on a geometry page. The students are also asked to begin to think about hyperspace, the fourth dimension. This activity is an extension of a LearningCheck I created for the TI- 84/Navigator several years ago. Concepts • Basic Geometric concepts • Literacy Connections to mathematics • Socio-historic lessons that are still relevant today NCTM Standards addressed: Geometry: Precisely describe, classify, and understand relationships among types of two- and three- dimensional objects using their defining properties. Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Connections: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Representations: Use representations to model and interpret physical, social and mathematical phenomena. Tennessee State Standards addressed: 0606.1.9, 0706.1.9, 0806.1.9 Use age-appropriate books, stories, and videos to convey ideas of mathematics. GLE 0606.4.1 Understand and use basic properties of triangles, quadrilaterals, and other polygons.
    [Show full text]
  • Final Project
    Chris Gregg CS 208E October 30, 2018 Project Ideas When you learn about programming, you don’t get very far by reading books or listening to lectures. You have to sit down at the computer and write a few programs on your own. Recognizing the intellectual dimension of computer science takes a similar investment of time and energy. You have to wrestle with the ideas. For this reason, I expect that most of you will get even more out of the work you do for the class project than you do from the material I present in class. The project deliverables are as follows: • A 35-45 minute oral presentation to the class. The goal of the presentation is to give your classmates an overview of your topic area, illustrate the topic with some simple examples, and offer a sense of why that topic is intellectually exciting. You are encouraged to use projection technology to illustrate your presentation— presumably including parts of the web site described below—but it is important to avoid becoming so wrapped up in the technology that the main points are lost. As shown on the syllabus, the presentations will take place during the 12:15 to 3:15P.M. final exam slot on Monday, December 10. • A web site that gives a more detailed presentation of the topic. Your web site should include a top-level general introduction along with links to more detailed information, some of which will be part of your site and some of which will be resources elsewhere on the web.
    [Show full text]
  • Human Four-Dimensional Spatial Intuition in Virtual Reality
    Psychonomic Bulletin & Review 2009, 16 (5), 818-823 doi:10.3758/PBR.16.5.818 BRIEF REPORTS Human four-dimensional spatial intuition in virtual reality MICHAEL S. AMBINDER, RANXIAO FRANCES WANG, JAMES A. CROWELL, AND GEORGE K. FRANCIS University of Illinois, Urbana-Champaign, Illinois AND PETER BRINKMANN City College, New York, New York It is a long-lasting question whether human beings, who evolved in a physical world of three dimensions, are capable of overcoming this fundamental limitation to develop an intuitive understanding of four-dimensional space. Techniques of analogy and graphical illustration have been developed with some subjective reports of suc- cess. However, there has been no objective evaluation of such achievements. Here, we show evidence that people with basic geometric knowledge can learn to make spatial judgments on the length of, and angle between, line segments embedded in four-dimensional space viewed in virtual reality with minimal exposure to the task and no feedback to their responses. Their judgments incorporated information from both the three-dimensional (3-D) projection and the fourth dimension, and the underlying representations were not algebraic in nature but based on visual imagery, although primitive and short lived. These results suggest that human spatial representations are not completely constrained by our evolution and development in a 3-D world. Illustration of the stimuli and experimental procedure (as video clips) and the instruction to participants (as a PDF file) may be downloaded from http://pbr.psychonomic-journals.org/content/supplemental. Representations of space and time are deeply rooted in (1965; Abbott, 1991) explained how a 4-D creature can human thinking, reasoning, and perception of the world enter a 3-D locked closet from the fourth dimension by (Abbott, 1991; Bork, 1964; Durrell, 1938; Gardner, 1975; describing how a 3-D creature enters a two-dimensional Kant, 1881/1896; Reichenbach, 1958; Rucker, 1984).
    [Show full text]
  • Flatland Og Dimensioner” – Et Indblik I Viktoriansk Samfund & Kultur Og Om Forståelse for Eksistensen Af Flere Dimensioner Af Lise Danelund
    10. april 2007 Oplæg til studieretningsprojekt i matematik og engelsk ”Flatland og Dimensioner” – Et indblik i viktoriansk samfund & kultur og om forståelse for eksistensen af flere dimensioner af Lise Danelund Introduktion Dette oplæg tager udgangspunkt i romanen ”Flatland – A Romance of Many Dimensions” fra 1884 af Edwin Abbott Abbott. Værket, som er en fantastisk rejse ind i en 2-dimensional verden, giver på fremragende vis læseren indsigt i konceptet om fler-dimensionale verdener, men fungerer samtidig som en social satire over det viktorianske samfund i England i slutningen af 1800-tallet. Matematikken fungerer i relation til sidstnævnte som et utroligt virkemiddel og analysemulighederne af romanen er talrige. Samtidig øges læserens matematiske bevidsthed, og med henblik på at beskæftige sig med eksempelvis 3. dimensionelle objekter i 2 dimensioner (skæringer mellem rumlige objekter og planen), fraktaler (ikke heltallige dimensioner) og lign., er bogen en fantastisk indføring i dimensionskonceptet og incitament til den, i sådanne relationer, til tider nødvendige abstrakte tænkning. Faglige forudsætninger (Matematik A/B) De faglige forudsætninger afhænger naturligvis af valget af matematisk emne, men generelt må det siges at være en fordel, hvis eleverne har kendskab til: • Trigonometri • Plangeometri • Logaritmer og komplekse tal (ved fokus på fraktaler) Faglige forudsætninger (Engelsk A) Generelt kendskab til: • Tekstanalyse - herunder sprogbrug, kompositionsopbygning, symbol- og metaforbrug, • Britiske samfundsforhold / evt. amerikanske samfundsforhold, hvis der ønskes perspektivering til eksempelvis filmen Flatland the Movie. • Teksten kræver en god sproglig basis Faglige mål (Matematik) Nedenstående faglige mål er naturligvis afhængige af det matematiske fokus, man vælger at anlægge i opgaven; men nogle muligheder er: • At give eleverne kendskab til keglesnit (geometrisk og analystisk tilgang) • At give eleverne kendskab til fraktaler fx mandelbrot, julia mgd’er mv.
    [Show 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_____________.
    [Show full text]
  • Flatland, Sphereland, and Beyond: a Journey Through Two-Dimensional Universes
    Flatland, Sphereland, and Beyond: A Journey Through Two-Dimensional Universes Maxime Fortier Bourque University of Glasgow September 4, 2019 Flatland, Sphereland and Beyond We get a cube: Gluing squares together What happens if we take several identical squares and glue them along their edges so that 3 meet at each vertex? Gluing squares together What happens if we take several identical squares and glue them along their edges so that 3 meet at each vertex? We get a cube: We get an infinite plane: Gluing squares together What happens if we take several identical squares and glue them along their edges so that 4 meet at each vertex? Gluing squares together What happens if we take several identical squares and glue them along their edges so that 4 meet at each vertex? We get an infinite plane: We get a tetrahedron: Gluing triangles together What happens if we take several identical equilateral triangles and glue them along their edges so that 3 meet at each vertex? Gluing triangles together What happens if we take several identical equilateral triangles and glue them along their edges so that 3 meet at each vertex? We get a tetrahedron: We get an octahedron: Gluing triangles together What happens if we take several identical equilateral triangles and glue them along their edges so that 4 meet at each vertex? Gluing triangles together What happens if we take several identical equilateral triangles and glue them along their edges so that 4 meet at each vertex? We get an octahedron: We get an icosahedron: Gluing triangles together What happens
    [Show full text]