question

Albert Einstein - light did not travel in straight lines but had slight curves to them

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1. Name the scientist who revealed that the Universe was not flat. What did he do that demonstrated that the Universe was curved?

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Flatland - 1880 by Abbott Sphereland - 1960 by Burger

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2. Give the author and date for Flatland and Sphereland

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Square

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3. Who narrates Flatland?

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south

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4. The gravitational force in Flatland is in the direction called

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rain, north

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5. If someone loses his sense of direction and cannot sense gravity then he waits for _____ since it comes from the ___________

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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

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6. Describe the houses.

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When offspring's angle is 60°, he is certified as an equilateral and brought up by an equilateral couple.

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7. At what point is a child removed from his parents

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Adults - 11" long Women - straight line, almost no width Rank - more sides higher rank Men -- triangles or polygons Top angle contains brain Offspring's vertex angle increases until equilateral than offspring has one more side

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8. Discuss the shapes of people (men and women) in Flatland, how they are ranked in society and what shape offspring might be.

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priest, circles

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the ______class is made up of polygons with so many sides they resemble ______-

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equilaterals

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__________ make up the middle class

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isosceles triangles

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common worker's class

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they would kill each other off

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why do circles like for the lower class to be at war

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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

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13. What restrictions were originally placed on women in Flatland and what innovation changed these restrictions

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Hearing - voice of highly developed sounds more aristocratic (unreliable) Touch - carefully touching one of the anglesa Visual - more distant objects are hazy so sisdes of angle become less clear as they lead away (used by higher ranks, taught in school)

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14. Describe 3 ways that could be used by inhabitants of Flatland to recognize another's shape.

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pushing and pulling does not correct them, destroyed

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what hapapened to irregulars

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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

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16. What did some high ranking Polygons do to their children? What was the drawback of this and why was it tolerated?

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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.

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Who was Chromatistes and what happened as a result of his contribution?

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Head Circle

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18. Who was Pantocyclus?

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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

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19. On December 30, 2000, Square had a vision that he visited Lineland. Describe Lineland.

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hexagon

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20. What shape was Square's grandson

question

third dimension, granfather thought it was nonsense

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21. On December 31, 2000, while Square was discussing arithmetic and geometry with his grandson, his grandson speculated a ____

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Figure # of sides # of vertices Point 0 1 Line 2 2 Square 4 4 Cube 6 8

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22. On December 31, 2000, Square is visited by Sphere who discusses the progression from a point to a cube

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arithmetic; geometric

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sides form serioes of ______ progress while vertices form series of ___________

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23. In Flatland, describe what customarily took place at a turn of the century

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23. In Flatland, describe what customarily took place at a turn of the century

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the land 4 dimensions

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sphere got angry when square asked to visit ______________

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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

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25. On New Year's Day, what did Square do and what happened to him as a result?

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He deserted his grandfather. He would not listen to Square's discussion of 3rd dimension.

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why was the hexagon guilty

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Monument erected on market square surrounded by circle of 12 trees (represents highest wisdom)

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3. Describe what was done to honor Square

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Women can be smart Tantrums are a thing of the past Feeling of responsibility Innovation of the shoe

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4. Discuss the changes in women.

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Very straight, very slim, 2 step sisters; There was an official ball and a handsome 24 sided prince was to be there. A neighbor gave Cinderella a dancing shoe so she could go but told her that it would turn to jelly after 3 hours. The prince danced only with her until midnight when she ran for home and escaped through a ventilator which knocked her shoe off. The prince went searching for the owner of the shoe. He found Cinderella, they married and had many children

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5. Summarize the "Cinderella" fairy tale.

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Size of brain angle is not absolute measure of intelligence Increased freedom of association between sexes lessened class differences Not ashamed if married women of lower class and children had fewer sides Isosceles refused to let Caste Council take his equilateral sons

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6. Describe changes in attitudes towards class.

question

addresing him at one of his vertices

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7. How was disrespect shown to Equilaterals?

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Hexagon, Nonagon, Dodecagon "Do-Decay"

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8. List the shapes of the sons of the Isosceles triangle who surgically changed their shapes. Also list the nicknames given to one of them.

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indicates exactly how ther person in question acquired his many-sidedness

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9. What does the linealogy registers record

question

New ideas could be considered

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10. What were the consequences of the "quiet revolution

question

They were inhabited by the same creatures that were living with them and they were at the same levels of development and culture

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11. Up until this time, what was thought about all inhabited countries

question

The pointed Isosceles had killed all the higher ranks They resolved to keep it that way Good at warfare but arts & sciences were missing

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12. Describe the country where the vertical angle of the men was never more than 10

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few Isosceles were left and those that were had a vertical angle of more that 50° Lots of Polygons and Circles Border nation was jealous and attacked killing most and taking possession of the resources

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13. Describe the country where the inhabitants had only been interested in intellectual development.

question

Thought to be all females but they kept men confined Isosceles were killed at birth because of potential threat Men rebelled but angles weren't sharp enough and were mostly destroyed Amazon nation started raiding other nations and capturing men Neighboring states joined together to try to defeat the Amazons

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14. Discuss who the Amazon tribe was, what they did, and what became of them

question

BELLAFORTA

answer

QUEEN OF THE AMAZONS

question

He was a general and a decagon. He led the army against the Amazons.

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16. Who was Prince Armatus and what did he do

question

edged her between 3 trees; changed into a Dodecagon and made a nobleman

answer

17. How did Quadratus capture the queen of the Amazons and how was he rewarded for his heroic deed?

question

Somewhat rounded; seeds form on surface and pop off and take root Dissolve in air

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18. What shape were trees, how did they propagate, and what happened to them when they died?

question

Fresher green color on north side (because of rain)

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19. How did adults use trees to maintain their orientation

question

Rough surface with ribs or scales; snout, eye, appendages

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20. Describe the "dragons" found in the southern woods.

question

gravitational pull, air pressure, higher, more luxurious

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21. When traveling south, the ______ and _________ increase and the temperature is ________ and plant growth _________.

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Became victims of tropical disease "dengue" Dizzy, ringing in ears, no longer think clearly

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22. What often happened to those who traveled to the far south

question

Sharp Isosceles Came upon a sea where rainwater was collected Saw creatures at upper line of sea (fish)

answer

23. Who were the trail hackers and what was learned from the expedition that they were on?

question

hermetically sealed boat; rock or stone "Rock bottom limit" of the world - What was beneath the rock?

answer

24. What was used to explore below the ocean's upper line and what was found at the bottom of the ocean?

question

They competed for "most traveled" Mr. Occidentalis went west and Mr. Orientalis went east. The two returned 3 years later together. Mr. Orientalis had had an accident & was taken in by a village. They regarded him as a great medicine man and when he recovered they would not let him leave. Mr. Occidentalis met him there. Mr. Orientalis announced Mr. Occidentalis the winner. People were amazed that one could head out due west and return from the east.

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25. Discuss the bet that two members of the "Club of Squares", Mr. Orientalis and Mr. Occidentalis had and what resulted

question

Scientist - earth is round

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26. Who was Dr. X. Pert and what was his contribution?

question

professor who said that gravity is attributed to the earth's center

answer

27. What was Dr. Newton?

question

Athletic lady; catapulted to investigate upper atmosphere; saw other worlds but did not know if they were inhabited

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28. Who was Aerosalta and how did she explore the "north?" What was determined as a result of her trips?

question

Snow White was a slimmer line than her stepmother who could curve her body sharply to become a witch. The Prince had 12 sides.

answer

29. Summarize the fairy tale "Snow White and the Seven Dwarfs."

question

Shape # of Vertices # of Edges # of lateral faces Square 4 4 1 Cube 8 12 6 Overcube 16 32 24

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30. Hexagon's son discussed with him the concept of the third dimension and then Hexagon posed the question of a fourth dimension. Fill in the following table with the numbers that they discussed. Pg 71 - 72

question

1) eat dough circles 2) fairy tale 3) visit from Sphere

answer

31. What three things were traditionally done by Hexagon's family on New Year's Eve?

question

Cross section of Over-Sphere was a sphere. He punched Sphere gently inside his stomach, because Spaceland lies entirely open for Over-spaceland. Over-Sphere removed objects out of a tightly shut closet. Also loosened a knot while bothe ends were held and unhooked closed chain links.

answer

32. Describe Sphere's visit by the Over-Sphere.

question

Animal with one snout, eye, ear, 2 bumps and 2 legs (not needed for movement) Lived in southern jungles, woods and forests of more temperate zones

answer

1. Describe a "wolf" and where they lived?

question

"dogs" they are exactly the same except the mongrel faces right and pedigree faces left (they are symmetric)

answer

2. What do mongrels and pedigrees have in common and what makes them different?

question

Agatha had a mongrel pup and her friend Chromosa had a pedigreed dog. Pentagon had been interested in Agatha (Hexagon's daughter) but turned his attention to Chromosa when her dog had 7 puppies, 3 of which were pedigreed. Hexagon bought Agatha a pedigree and had puppies (12) all mongrels. Chromosa and Pentagon got married.

answer

3. Summarize who Agatha, Chromosa, and Pentagon were and the story of the dogs

question

Little disobeyed her mother & took the shortcut through the woods to get to her grandmother's. She encountered a wolf and they had a race to get to grandmother's house. The wolf won and gulped grandmother in one bite. Little got there and questioned the appearance. The wolf gulped Little. In the process, Little lost her shoe. She was so frightened that she was vibrating violently in the wolf's stomach and that pierced a hole and Little was able to get out. Little's father had heard the noise and was able to get grandmother out. Little knew how to defend herself against the wolf. Considered patroness of feminist movement.

answer

4. Summarize the fairy tale, "Little Red Riding Shoe." Why was it considered the fairy tale for girls?

question

Because it was irregular

answer

5. Why did the Sphere think that the dog was a criminal

question

Homo sapiens - considers itself justified in killing and eating lesser creatures Constantly at war with each other Had to prevent something worse Women differ little from men except by clothes 2 feet which are symmetrical

answer

6. Sphere told of some of the domesticated animals that were in Spaceland but there was one in particular that he considered odd. Which one was this? Describe the "creature's" behavior.

question

Lifted a mongrel out of the plane and turned him over to become a pedigree

answer

7. What was the "magic trick" that Sphere performed?

question

symmetry

answer

8. Sphere used the "magic trick" to demonstrate congruence and

question

Hexagon talked to the King about turning around so that he looked the other way. Hexagon lifted out of his line shaped world and turned him around. He didn't know where he was. The king thought the world had turned.

answer

9. Describe Hexagon's vision of Lineland. (symmetry)

question

1) afraid the value of the pups would be questioned 2) afraid that it would become commonplace to turn mongrels into pedigrees 3) thought it was more impressive to act mysteriously

answer

10. List three reasons why Agatha was evasive as to how she had acquired such a magnificent set of pedigreed dogs.

question

Mr. Vertato was a businessman who Sphere had turned around. The world seemed backwards. If he looked in a mirror, things seemed normal. Music gave him the courage to live. Note: He became "sick" on New Year's Eve

answer

11. Who was Mr. Vertato and what happened to him? What restored his courage to live?

question

Princess lived in castle in impenetrable forest. The density of the trees had reduced the amount of fresh air and the people in the castle went into a state of sleep. After a time (more than 100 years), a 12-sided prince penetrated the forest. He was enchanted by the princess, kissed her and she woke. A wedding followed, the forest was thinned out, the castle was spruced up, and they lived happily ever after.

answer

12. Summarize the fairy tale "Sleeping Beauty."

question

political books then actual people ( left handed ones) - He was unhappy. He could not read his own writing (it was mirror writing) from before. His new writing he could read but no one else could. During a walk, he moved out of the way of an oncoming vehicle but because his left and right were reversed he was struck and died.

answer

13. The Over-Sphere demonstrated the "turning around" of objects in Spaceland by first turning around

question

Institute established for the purpose of mapping the world accurately by means of trigonometry.

answer

1. What was the purpose of the Trigonometric Service?

question

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.

answer

What happened that caused Mr. Puncto to lose his job as director of the Trigonometric Service?

question

Improved instruments Errors were seen as observational errors Old way - net of small triangles

answer

3. What were some reasons that the deviations were not found sooner?

question

the increase in size of the triangles___.

answer

4. Mr. Puncto determined that the discrepancy from 180 increased with

question

triangle whose sides are curved

answer

5. What did Hexagon's grandson suggest that would explain Mr. Puncto's data?

question

Professor of mathematics - would not accept explanation that refuted science facts (180°) Up to investigators to find error

answer

6. Who was Ergo and how did he respond to Mr. Puncto?

question

Professor of physics - principles of math were being attacked Considered peculiar triangle and explained why it wouldn't work

answer

7. Who was Professor Supposo and how did he respond to Mr. Puncto?

question

If side curve out in one triangle, then they curve in in another.

answer

8. What argument did Professor Supposo give that caused him to reject Hexagon's explanation for the unusual triangle?

question

Circleland

answer

9. While contemplating his dilemma, Hexagaon sees Lineland as

question

in a third direction invisible to him

answer

10. Which direction did Hexagon believe that the sides of the triangle were curved?

question

spherical surface

answer

11. Sphere told Hexagon and Mr. Puncto that Flatland was actually a

question

Not to make everything they knew public because it would not be accepted.

answer

12. What was Sphere's advice?

question

Marching in a circle They don't hear all at the same time - commander's voice moves past the row of soldiers

answer

13. How did Hexagon's grandson line up his toy soldiers and why did he say that he moved them one at a time?

question

Flatland

answer

14. Where does Hexagon visit in his dream. (circularity)

question

It is curved and it is not infinite.

answer

15. What does he notice about the world that he is seeing?

question

They cannot leave their space so they follow the curve of that space.

answer

16. What did he observe about light rays?

question

Hexagon said that Sphere must realize that his 3-D space is curved in a direction invisible to him and that light rays were not straight in Spaceland either. Hexagon said that if Sphere did not realize that then Hexagon was much wiser than Sphere.

answer

17. What did Hexagon do that made Sphere angry?

question

trigonometry

answer

1. After visiting the Space Station, Hexagon noted that because of the great distances to the other worlds the only reliable way to obtain dependable results would be by means of

question

second space station

answer

2. Mr. Puncto convinced the government to build

question

the distances of the various worlds (charting the space).

answer

3. Mr. Puncto got a new job measuring

question

After time all distances increased, some more than others.

answer

4. What kind of discrepancies did Mr. Puncto find this time?

question

Used radar beams that would "bounce" off an object and then measured the distance by using the time it took the radar signal to go and come back

answer

5. What different method of measuring did Mr. Puncto and Hexagon use to verify the discrepancies?

question

The radar method coincided with the trig and showed that the worlds were moving further away and at different speeds Speed of withdrawal increased with the distance

answer

6. What conclusions did they arrive at?

question

They saw a circular object being filled with gas. As the object expanded, the inscribed letters got larger and the distances between them increased. If you look at them from the top, the close letters appear to move away slower.

answer

7. What did Mr. Puncto and Hexagon observe on their way home that made them understand what was happening to their world?

question

The forest became penetrable between since the world was expanding. The distance between the trees increased.

answer

8. What change did Hexagon make to the fairy tale "Sleeping Beauty?"

question

He wrote a book and left the manuscript sealed with the city librarian. He put a label on it saying to open when the theory of the expanding universe is accepted.

answer

9. What did Hexagon do with the amazing revelation about his world?

question

agent for the internal revenue service

answer

10. What new job did Mr. Puncto get

question

Four Stages in Problem Solving 1) observing 2) checking 3) concluding 4) sharing

answer

11. What are the four stages in the search for the solution to a mathematical problem?

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