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高中必修5“数列的概念和简单的表示法”中引用了这样一段话:传说古希腊毕达哥拉斯学派的数学家经常在沙滩上研究数学问题,他们在沙滩上画点或用小石子表示数,比如,他们研究过1,3,6,10(如图1),由于这些数都可用三角形点阵表示,他们就将其称为三角形数.类似地,1,4,9,16,…,被称为正方形数.一、三角形数的计算方法读者一定知道怎样计算三角形数,但本文要说的是另一种方法.图2是一个正方形,其总点数可用正方形面积公式S=a~2计算,a是边长,也就是边上的点
High School Compulsory 5 “Concepts of Numbers and Simple Representations” quoted the following passage: Legend has it that mathematicians at the Pythagorean school of ancient Greece often study math problems on the beach, draw or use on the beach For example, they have studied 1, 3, 6 and 10 (Figure 1), and since these numbers are all represented by a triangular lattice, they are called triangles. Similarly, 1,4,9 , 16, ..., is called the square number. A triangle number calculation method The reader must know how to calculate the number of triangles, but this article is to say is another method Figure 2 is a square, the total number of points available square area formula S = a ~ 2 calculation, a is the side length, that is, the edge of the point