今天,我要给大家讲的题目是——三角形的内角和不一定是180度
例如,在圆中。
首先,我们先要知道球的表面积是4πr²
那么,作一个半径为1的球
设圆上2条线的夹角为A,易知当A=2π时,两条线围成的面积为4π,且两线所围成的面积与A成正比,所以两线所围成的面积=2A
所以,如图。延长三角形ABC的三边,使其交于圆的另一边,记做A’,B’,C’
所以 ,
又因为三角形ABC面积不为0,所以A+B+C>π,即A+B+C>180度
My presentation is the sum of the three interior angles of a triangle may not equal to 180 degrees such as a triangle on a ball.
First of all, we should know that the superficial area of a ball is equal to 4π times the radius of a ball squared.
Then, let’s make a ball whose radius is 1 and define an angle A which is between two segments on the ball.
It is easy to know that if A’s measure is equal to 2π, the superficial area between two segments is equal to 4πand the A’s measure has a direct proportion with the superficial area between two segments.
So, the superficial area between two segments equals 2 times A.
And, look at this picture. There is a triangle ABC and lengthen three segments, AB, AC, BC which meet at another side on the ball. We call that A’ B’ C’. So
And
So, add this three equations, we can see that and we can know .Because the superficial area of a triangle isn’t 0, so, A plus B plus C is greater than 180 degrees.
其实中间还有证明过程的插图,没法直接复制,所以就这些了…………
各种翻译器出来的不要,宁可看分没了…………
希望达人帮忙挑错,今天就要!!!
So(有式子)
And(有式子)
So, add this…………
we can see that (有式子) and we can know(有式子)
由于式子是插图,不用管的说