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蜚声全球的力学家、数学家牛顿曾以诗歌形式提出了一个数学问题：要栽九棵树,请你来帮忙,每行栽三棵,恰好成十行.这就是著名的牛顿栽树问题.要解决这一问题,颇有难度,因为按题中要求,似乎需要30棵树才行.常规思路不通,怎么办?让我们先降低难度,看一看较为简单的情况：9棵树栽成8行,每行3棵,怎么栽?分析：很自然地画图试试,每行3棵,先画3行,已经9棵(如图1),树不能增加了,行数能否增加呢?联想正方形的性质,易知,将9棵树栽在正方形的四个顶点、四边中点及中心9个位置,便成8行,且每行3棵.再进一步试验：9棵树栽成9行,每行3棵,怎么栽?这样我们就会想,能不能利用图1作些调整,即移动1棵或几棵树的位置后,增加1行呢?
Newton, a global mechanic and mathematician, has proposed a mathematical problem in the form of poetry: To plant nine trees, ask for help. Three trees in each row, exactly ten lines. This is the famous Newton tree planting problem. To solve this problem, it is quite difficult, because according to the requirements in the question, it seems that it takes 30 trees to do it. The conventional thinking is unreasonable. What should we do? Let’s lower the difficulty first and take a look at the simpler situation: 9 trees planted 8 rows, 3 rows per row, how to plant? Analysis: Naturally try painting, 3 rows per row, first draw 3 rows, already 9 trees (Figure 1), the tree can not increase, can increase the number of rows The nature of Lenovo Square, easy to know, will be 9 trees planted in the four vertices of the square, the four midpoints and the center of the nine positions, it will be eight rows, and three per row. Further tests: 9 trees planted 9 lines, 3 lines each, how to plant? So we will think, can you use Figure 1 to make some adjustments, that is, after moving a tree or several trees, add 1 line?