高斯的故事

来源：百度知道 编辑：UC知道 时间：2024/05/16 23:18:32
高斯最出名的故事就是他十岁时，小学老师出了一道算术难题：“计算1＋2＋3…＋100＝？” 。这可难为初学算术的学生，但是高斯却在几秒后将答案解了出来，他利用算术级数（等差级数）的对称性，然后就像求得一般算术级数和的过程一样，把数目一对对的凑在一起：1＋100，2＋ 99，3＋98，……49＋52，50＋51 而这样的组合有50组，所以答案很快的就可以求出是： 101×50＝5050。不过，这很可能是一个不真实的传说。（关于这个故事的英文文章，大约2—3分钟读完
)

The famous story about Gauss , and one that has evolved in the telling, has it that in primary school his teacher, J.G.

The famous story about Gauss , and one that has evolved in the telling, has it that in primary school his teacher, J.G. Büttner tried to occupy pupils by making them add up the integers from 1 to 100. The young Gauss produced the correct answer within seconds by a flash of mathematical insight, to the astonishment of all. Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050. But this may not be real.

Gauss most famous is the story of his 10-year-old, a primary school teacher from an arithmetic challenge : "Calculation 1 +2 +3 ... +100=?. " This can be hard when a mathematics student, but Gauss will have the answer in a few seconds out of the solution, He used the arithmetic progression (arit