[Mathematics] a wooden rod with a length of L is randomly divided into three segments, and the three segments constitute the probability of a triangle.

1. Question

For example, if a wooden rod with a length of L is randomly divided into three segments, what is the probability that the three segments constitute a triangle?

2. Parsing

This is not so much a programming question as a mathematical question. It may be because you have never met or have never had such a problem-solving idea.(Well, I am familiar with it once again, and so on)

The lengths of the split three wooden bars are X, Y, and l-x-y.

(1) first, the length of the three sides is greater than 0.The following formula can be used:

As you can know, the area that meets the conditions is (1/2) * l, as shown below (that is, the area of the shadow area ):

(2) to form a triangle, the sum of any two sides must be greater than the third side.(That is, the difference between any two sides is smaller than the third side ). The following formula can be used:

As you can know, the area that meets the conditions is (1/8) * l, as shown below (that is, the area of the shadow area ):

 

From the above analysis, we can see that any split into three segments is based on the length of the three segments. Triangle composition accounts for 1/4 of all split cases.

So,Fold a wooden rod with a length of L into three segments at random, and the probability of a triangle consisting of three segments is 0.25..

[Mathematics] a wooden rod with a length of L is randomly divided into three segments, and the three segments constitute the probability of a triangle.