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 in a net, the angles in one 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. told Hexagon and Mr. Puncto that was actually a _spherical surface______. Pg 156

12. What was Sphere’s advice? Pg 160 Not to make everything they knew public because it would not be accepted.

13. How did Hexagon’s grandson line up his toy soldiers and why did he say that he moved them one at a time? Pg 164 Marching in a They don’t hear all at the same time - commander’s voice moves past the row of soldiers

14. Where does Hexagon visit in his dream. Pg 167 Flatland

15. What does he notice about the world that he is seeing? Pg 168 It is curved and it is not infinite.

16. What did he observe about light rays? Pg 169 They cannot leave their so they follow the curve of that space.

17. What did Hexagon do that made Sphere angry? 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 either. Hexagon said that if Sphere did not realize that then Hexagon was much wiser than Sphere.