Showing Revision 1 created 06/27/2012 by Amara Bot.

1. タイトル：
   01-44 Solving for Alpha
2. 概説：

3. 0 0:00 - 0:06
   Now, we can go back to the original problem--the thing we've been trying to solve this whole unit.
4. 6000 0:06 - 0:12
   As you remember we have the sun's rays striking perpendicular to the earth here at Syene.
5. 12000 0:12 - 0:19
   We've seen that these rays all came in parallel like what's around here and here in Alexandria
6. 19000 0:19 - 0:25
   which is north of Syene, the rays no longer strike the earth perpendicular to the surface of the earth.
7. 25000 0:25 - 0:27
   They strike at this angle α.
8. 27000 0:27 - 0:31
   We showed before that must be equal to this angle α as well.
9. 31000 0:31 - 0:38
   And by comparing the full angular measure of the circle 360 degrees to this portion α, we will
10. 38000 0:38 - 0:44
    define that if we knew d and we knew α, we can calculate the circumference of the earth.
11. 44000 0:44 - 0:51
    We got d by timing a camels distance from Syene to Alexandria. Now we just need to find α.
12. 51000 0:51 - 0:56
    To determine this angle α, let's imagine what it would be like to be standing here in Alexandria.
13. 56000 0:56 - 1:00
    Well, if I were actually standing there, I can now say the earth is flat
14. 60000 1:00 - 1:04
    because I don't notice the curvature of the earth on a daily basis
15. 64000 1:04 - 1:08
    and I can imagine sticking some sort of pole into the ground.
16. 68000 1:08 - 1:10
    And maybe I know the length of this pole.
17. 70000 1:10 - 1:13
    Now I know the sun's rays are coming in at a certain angle.
18. 73000 1:13 - 1:17
    I'm going to draw the rays in red just to make it a little easier to see.
19. 77000 1:17 - 1:24
    So here comes the sun's rays, you can tell they're being blocked by the pole in some places.
20. 84000 1:24 - 1:31
    So when the pole blocks the sun's rays, we get a shadow--here's the pole shadow.
21. 91000 1:31 - 1:35
    And now you can see we're almost there. You can see the right triangle that's emerged.
22. 95000 1:35 - 1:40
    We have the sun's ray that just barely missed the edge of the pole,
23. 100000 1:40 - 1:44
    we have the shadow of the pole, and we have the pole itself forming a right triangle.
24. 104000 1:44 - 1:50
    Now from this drawing, you can actually see that the angle we called alpha.
25. 110000 1:50 - 1:54
    If I imagine making a perpendicular line here perpendicular to the earth,
26. 114000 1:54 - 1:56
    this is the angle we called alpha.
27. 116000 1:56 - 2:01
    There's no problem. That's also equal to this angle α and now we're almost there.
28. 121000 2:01 - 2:09
    So here's our triangle with three sides--one, two, three, opposite, adjacent to α, and hypotenuse
29. 129000 2:09 - 2:12
    and we just need to know what this angle is.
30. 132000 2:12 - 2:16
    Now that we have a right triangle, we just need to consult the trigonometric table
31. 136000 2:16 - 2:21
    and we should be able to figure out what alpha is and what's the circumference of the earth is.
32. 141000 2:21 - 2:24
    So we set up the experiment.
33. 144000 2:24 - 2:29
    We have our vertical bar with its shadow and what Eratosthenes data may have looked like
34. 149000 2:29 - 2:32
    with the length of the bar would have been something around 1 meter
35. 152000 2:32 - 2:39
    and the length of the shadow about 0.126 meters which is 12.6 cm.
36. 159000 2:39 - 2:44
    He, of course, has access to his trigonometric tables and here's a portion of one such table.
37. 164000 2:44 -
    Now, can you put yourselves in Eratosthenes' shoes and tell me what is the value of alpha?