基本介紹
![球心](/img/a/95d/wZwpmL0YzNyQTN0gTMzEzM1UTM1QDN5MjM5ADMwAjMwUzL4EzLzUzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
以半圓的直徑為軸,把半圓鏇轉360°所成的曲面,叫做 球面。半圓的圓心叫做 球心(圖中的 )。連結球心和球面上任意一點的線段,叫做 球的半徑(圖中的OA)。連結球面上的兩點並且經過球心的線段。叫做 球的直徑(圖中的AB)。鏇轉過程中,在各個位置上的半圓,叫做 球面的母線(子午線)。半圓上的點鏇轉形成的圓,叫做 球面的平行圓。被經過球心的截面截得的圓叫做 大圓。被不經過球心的截面截得的圓,叫做 小圓 。
![圖1 球](/img/2/a7e/wZwpmLwgTN2kTN0MzMzATN1UTM1QDN5MjM5ADMwAjMwUzLzMzLwAzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
球面的方程
球面是與一定點的距離是定長的空間點的軌跡。此定點叫 球心,定長叫 半徑 。
![球心](/img/a/c02/wZwpmL3ETMwYjN5cjNxMzM1UTM1QDN5MjM5ADMwAjMwUzL3YzL1UzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![球心](/img/4/10f/wZwpmL2IzNxgjN0MDOwADN0UTMyITNykTO0EDMwAjMwUzLzgzLzYzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
①以 為球心, 為半徑的 球面方程 的向量形式為:
![球心](/img/7/4d8/wZwpmLwITO1gDM0UjMzATN1UTM1QDN5MjM5ADMwAjMwUzL1IzLxAzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
坐標形式為:
![球心](/img/e/737/wZwpmL2cTM4gjNxMzMzATN1UTM1QDN5MjM5ADMwAjMwUzLzMzL3AzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
球面方程的一般形式也可以寫成
![球心](/img/a/4cb/wZwpmLyMzMxcDN3EjMzATN1UTM1QDN5MjM5ADMwAjMwUzLxIzL1YzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
②三元二次普遍方程:
![球心](/img/6/819/wZwpmL2IjN1QTNygjMzATN1UTM1QDN5MjM5ADMwAjMwUzL4IzL3gzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
表示一個球面的充要條件是
![球心](/img/2/7c2/wZwpmL4QzNzgzN2YzMzATN1UTM1QDN5MjM5ADMwAjMwUzL2MzLyEzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![球心](/img/3/ef5/wZwpmLyUDMwMzNwkjMzATN1UTM1QDN5MjM5ADMwAjMwUzL5IzL4UzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
球心是 ,半徑是
![球心](/img/4/7bf/wZwpmL2czNzUDMxkTMzATN1UTM1QDN5MjM5ADMwAjMwUzL5EzL0EzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![球心](/img/1/be2/wZwpmL0IjMxAzNzkjMzATN1UTM1QDN5MjM5ADMwAjMwUzL5IzLzYzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![球心](/img/3/ef5/wZwpmLyUDMwMzNwkjMzATN1UTM1QDN5MjM5ADMwAjMwUzL5IzL4UzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![球心](/img/0/4a8/wZwpmL2IDO5YTNwAjMzATN1UTM1QDN5MjM5ADMwAjMwUzLwIzLyAzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
當 時,則表示一個點 ,當 時,則沒有實軌跡。
![球心](/img/a/717/wZwpmL2MzMxADMxAzMzATN1UTM1QDN5MjM5ADMwAjMwUzLwMzL3UzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
③已知四個不共面的點 ,過此四點的球面方程是
![球心](/img/4/7bf/wZwpmL2czNzUDMxkTMzATN1UTM1QDN5MjM5ADMwAjMwUzL5EzL0EzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)