兩題英文的數學請大大們幫我解答(不是要翻譯)

Question

1)Why can there be no parallel lines in elliptical (spherical) geometry?

2)How can you plant ten trees in five rows of four trees each?

謝謝

3) A recent report stated that all coffee grows within 2000 miles of the equator. The diameter of the earth is 7946.25 miles. Use only this information to determine the latitudes between which coffee grows.

4) A plane going from LAX to Frankfurt, Germany flies at 40000 feet above the Earth's surface for 11 hrs at 600 mph(The earth's diameter is 7946.25 miles)

a)How many degrees of the circumference does the plane cover?
b)Assuming that the plane could be refueled in the air, and wouldn't have to land cus of antsy passengers, how long would it take this plane to circumnavigate the earth?

c)Assuming all of the above, how many times could it go around the earth in 80 days?
(Hint: Flying above the ground will incraese radius)

5) A setellite flies 50 miles above the earth's surface. How fast must it be going to circum navigate the earth in 5 hrs?

下面的大大很感謝你回答我/...

不過我看得懂英文啦是題目...是數學讓我頭痛

Answer 1

Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p.Elliptic geometry, like hyperbolic geometry, violates Euclid's parallel postulate, which asserts that there is exactly one line parallel to L passing through p. In elliptic geometry, there are no parallel lines at all. The best way to picture this is to look at a globe. The lines of longitude are exactly next to each other, yet they eventually intersect. Elliptic geometry has other unusual properties. For example, the sum of the angles of any triangle is always greater than 180°.http://en.wikipedia.org/wiki/Elliptical_geometry
圖片參考：http://enciclopedia.us.es/images/3/3e/Latitudes_y_longitudes.png
Assuming Earth is a sphere (which it is not) circumference is pi*diameter=24961 miratio of distance * degree = 4000mi/24961mi*90degree=+14.42 degree to -14.42 degree5 40 000 feet = 7.575 757 576 mileWow I feel like an idiot. 7946.25 miles + 15.15 miles =  7961.40 miles11 hrs at 600 mph = 11 hr * 600 Mile/Hr = 6600 milesdegree ratio=flying miles/(diameter * pi)=6600 miles / (7961.40 miles*pi)360 degree in a sphere so... degree ratio * 360 = 95.00 degreecircumference = 25008 miles25008 miles / (600 miles/hr) = 41.68 hoursAhhhh not enough space to write more stuff.

Answer 2

還真強...佩服...

Answer 3

1) 橢圓(球面)幾何中為何沒有平行線?

2) 請問10棵樹要怎樣種成5排，而每排有4棵?

3) 最近的一篇報導說所有的咖啡都生長在赤道兩邊2000英哩以內。地球的直徑是7946.25英哩。請只使用以上的資料求出咖啡生長的緯度範圍。

4) 一架從洛杉磯飛往德國法蘭克福的飛機在地表上方4萬英尺的高空以時速600英哩的速度飛行11個小時，(地球的直徑是7946.25英哩)。
a) 這架飛機經過了多少圓周角度?
b) 假設飛機可以進行空中加油，而且因為沒有旅客，所以不用降落。請問這架飛機需要多久時間可以環繞地球一周?
c) 繼續前面的假設，在80天之內飛機可以繞地球幾周?
(提示: 在地表以上飛行會增加半徑。)

5) 一顆衛星在地表上方50英哩處飛行。請問這顆衛星要飛多快才可以在5小時之內環繞地球一周?

請參考 ^^

2006-06-02 18:20:35 補充：
已經幫你把題目解釋清楚了，剩下的功課要自己做。