Cut a line segment with a length of 15 cm into three segments so that the length of each segment is an integer. How many different triangles can be formed with these three segments? (Two triangles are said to be the same if and only if the three sides of the two triangles can be correspondingly equal.)
把一条长15cm的线段截为三段，使每条线段的长度是整数，用这三条线段可以组成多少个不同的三角形？(当且仅当两三角形的三条边可以对应相等时，我们称这两个三角形是相同的．)
<gadget id="calculator">4 + 2 + 1</gadget>
<output>7</output>

<result>7</result>