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