从一颗小种子开始：一座小镇和一个大梦想
第一章：从一颗小种子开始——一座小镇和一个大梦想
Chapter 1: From a Little Seed — A Small Town and a Big Dream
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杭州的春天总是来得特别温柔。
Hangzhou's spring always arrives especially gently.
当冬天的最后一丝寒意悄悄溜走，西湖边的柳树便迫不及待地抽出了嫩绿的新芽。那些细长的枝条轻轻垂落在湖面上，像是爱美的姑娘在对着镜子梳理自己的长发。断桥边的桃花也开了，一朵朵粉色的花瓣像是小朋友的脸颊，红扑扑的，可爱极了。
When the last trace of winter's chill quietly slips away, the willows by West Lake can't wait to sprout tender green shoots. Those slender branches hang gently over the lake's surface, like beautiful girls combing their long hair before a mirror. The peach blossoms by Broken Bridge also bloom, their pink petals like little children's cheeks—rosy and adorable.
这座城市有一千多年的历史了。传说中，白娘子曾经在这里遇见了她心爱的人，苏东坡爷爷在这里留下了无数美丽的诗篇，马可·波罗旅行到中国时，也特意来这儿看过，说它是“世界上最美丽华贵之城”。
This city has over a thousand years of history. Legend has it that the White Snake once met her beloved here, Grandfather Su Dongpo left countless beautiful poems here, and when Marco Polo traveled to China, he made a special trip to see it, calling it "the most beautiful and magnificent city in the world."
就是在这样一个美丽的地方，在一个普通的居民小区里，住着一个叫黄峥的小男孩。
It was in such a beautiful place, in an ordinary residential community, that a little boy named Colin Huang lived.
那一年，小黄峥才七岁。
Little Colin was only seven years old at the time.
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小小数学迷
The Little Math Enthusiast
“你怎么又在看数学书啊？”
"Why are you reading that math book again?"
黄峥的妈妈站在门口，看着自己的儿子，忍不住轻轻叹了口气。窗外的阳光正好，小区里的孩子们正在楼下追逐打闹，笑声一阵一阵地传上来。可是七岁的小黄峥却坐在书桌前，捧着一本比他的脸还大的数学书，看得津津有味。
Colin's mom stood at the doorway, looking at her son, and couldn't help but sigh softly. The sunshine outside was perfect, and the children in the neighborhood were running and playing downstairs, their laughter floating up in waves. But seven-year-old Colin sat at his desk, holding a math book bigger than his face, reading it with complete absorption.
“妈妈，”小黄峥抬起头，眼睛里闪着光，“你知道吗？我发现了一个特别好玩的事情！”
"Mom," little Colin raised his head, his eyes sparkling with light, "do you know? I discovered something really fun!"
妈妈走过来，在他身边坐下，好奇地问：“什么事情呀？”
Mom came over and sat beside him, asking curiously, "What is it?"
小黄峥把书翻到一页，指着上面的题目说：“你看，1加到100，如果一个一个加，要算好久好久。但是有一个特别聪明的方法——就是用头尾配对！1加100等于101，2加99也等于101，一共有50对，所以答案就是101乘以50，等于5050！”
Little Colin flipped the book to a page, pointing to the problem and saying, "Look, adding 1 to 100, if you add them one by one, it takes forever. But there's a really clever method—pairing from the ends! 1 plus 100 equals 101, 2 plus 99 also equals 101, there are 50 pairs, so the answer is 101 times 50, which equals 5050!"
说着说着，他拿起旁边的草稿纸，飞快地写下：
Saying this, he grabbed the draft paper beside him and quickly wrote:
$$1 + 2 + 3 + \cdots + 100 = \frac{(1+100) \times 100}{2} = 5050$$
妈妈看着儿子兴奋的小脸，忍不住笑了。她伸手摸了摸黄峥的头，说：“你真是个小数学迷！以后一定可以成为一个很厉害的人！”
Mom looked at her son's excited little face and couldn't help but smile. She reached out and patted Colin's head, saying, "You're really a little math enthusiast! You're sure to become someone really remarkable someday!"
小黄峥笑了，露出两颗小虎牙：“妈妈，我以后要发明很多厉害的东西，帮助很多人！”
Little Colin smiled, showing his two little tiger teeth, "Mom, when I grow up, I want to invent lots of amazing things and help many people!"
那时候，他还不知道自己的梦想有多大。
Back then, he had no idea how big his dream would become.
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帮邻居解决问题的孩子
The Boy Who Helped Neighbors Solve Problems
黄峥住的小区叫“翠苑小区”，这里住着很多很多人家。隔壁住着王奶奶，她今年已经七十多岁了，儿女都在外地工作，平时就她一个人住。
The residential community where Colin lived was called "Cuiyuan Community," home to many, many families. Next door lived Grandma Wang, who was already over seventy years old. Her children all worked in other cities, so she lived alone most of the time.
这一天，小黄峥放学回家，看见王奶奶坐在楼下的长椅上，愁眉苦脸的。
One day, little Colin came home from school and saw Grandma Wang sitting on the bench downstairs, looking worried.
“王奶奶，您怎么啦？”小黄峥跑过去，关心地问。
"Grandma Wang, what's wrong?" Little Colin ran over and asked with concern.
王奶奶叹了口气说：“唉，小峥啊，我遇到难题了。你看我每个月要交水电费，电力公司寄来的单子写得密密麻麻的，什么'峰时段'、'谷时段'，我一个老太婆哪里看得懂啊！这个月电费特别贵，我都不知道是怎么回事。”
Grandma Wang sighed and said, "Ah, Xiao Zheng, I've run into a difficult problem. Look at these electricity bills the power company sends every month—filled with tiny print, with things like 'peak hours' and 'off-peak hours.' An old woman like me can't understand any of it! This month's electricity bill is especially high, and I don't know what happened."
小黄峥想了想，说：“王奶奶，您把单子给我看看，好吗？”
Little Colin thought for a moment and said, "Grandma Wang, could you let me take a look at the bill?"
王奶奶把水电费通知单递给了他。小黄峥仔细看了看，发现王奶奶家的电费确实比上个月高了不少。他仔细研究了一下，发现问题出在用电时间上——王奶奶习惯晚上做饭，可是晚上八点到十点是“峰时段”，电费要比白天贵很多。
Grandma Wang handed him the electricity notice. Little Colin studied it carefully and found that Grandma Wang's electricity bill was indeed much higher than last month. He examined it closely and discovered the problem was with the timing of electricity usage—Grandma Wang was used to cooking dinner at night, but eight to ten at night was "peak hours," and electricity cost much more than during the day.
“王奶奶，我帮您算了一下，”小黄峥认真地说，“如果您把做饭的时间改到下午五点到七点，那段时间是'谷时段'，电费可以省下一大半呢！一个月下来，能省二十多块钱呢！”
"Grandma Wang, I calculated it for you," little Colin said seriously, "if you change your cooking time to between five and seven in the afternoon, that's 'off-peak hours,' and you could save more than half on electricity! That adds up to over twenty yuan a month!"
王奶奶惊讶地看着他：“真的吗？那太好了！小峥啊，你可真是个聪明的孩子！”
Grandma Wang looked at him in amazement, "Really? That's wonderful! Xiao Zheng, you're such a smart child!"
小黄峥不好意思地挠挠头：“其实这个不难，就是加减乘除而已。王奶奶，您下次要是还有看不懂的，就来找我，我帮您算！”
Little Colin bashfully scratched his head, "Actually, this isn't difficult at all, it's just addition, subtraction, multiplication, and division. Grandma Wang, if you have anything else you don't understand next time, just come find me, I'll help you figure it out!"
从那以后，小黄峥就多了一个“职务”——帮王奶奶算账。他还会帮王奶奶比较超市里不同品牌大米的价格，计算哪个更划算；帮王奶奶算每个月的生活费支出，看看有没有可以省钱的地方。
From then on, little Colin took on an extra "role"—helping Grandma Wang with her accounts. He would also help her compare prices of different rice brands at the supermarket to figure out which was the best deal; help her calculate monthly living expenses to see where she could save money.
“王奶奶，您看，这种大米每斤3块5，那种每斤3块8，但是这种一袋有10斤，那种只有8斤。我帮您算了一下，实际上第一种更便宜……”
"Grandma Wang, look, this type of rice is 3.5 yuan per jin, that type is 3.8 yuan per jin, but this one comes in 10-jin bags while that one only has 8 jin. I calculated it, and actually the first one is cheaper..."
王奶奶每次听完小黄峥的分析，都会笑着从口袋里掏出一颗糖塞给他：“小峥啊，你真是个好孩子！长大了肯定有出息！”
Every time Grandma Wang finished listening to little Colin's analysis, she would smile and pull a candy from her pocket to give him: "Xiao Zheng, you're such a good child! You'll definitely make something of yourself when you grow up!"
小黄峥接过糖，心里美滋滋的。他发现，帮助别人解决问题，是一件特别开心的事情。
Little Colin took the candy, feeling happy inside. He discovered that helping others solve problems was something especially joyful.
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班级里的智多星
The Brainiac in Class
黄峥上小学三年级的时候，班上发生了一件事。
When Colin was in third grade of elementary school, something happened in his class.
这一天的数学课上，老师出了一道难题：“同学们，有一根绳子，长度是100米。如果每天剪掉它的一半，要多少天才能把绳子剪到小于1米？”
This day's math class, the teacher presented a difficult problem: "Children, imagine there's a rope that's 100 meters long. If you cut it in half every day, how many days will it take until the rope is shorter than 1 meter?"
班上的同学都皱起了眉头，这道题看起来好复杂啊！每天剪一半，那要算多少次？
All the classmates frowned. This problem looked so complicated! Cutting it in half every day—how many times would they have to calculate?
小黄峥没有急着动笔，他在心里默默算着：
Little Colin didn't rush to start writing. He calculated silently in his mind:
第一天：100 ÷ 2 = 50米 第二天：50 ÷ 2 = 25米 第三天：25 ÷ 2 = 12.5米 第四天：12.5 ÷ 2 = 6.25米 第五天：6.25 ÷ 2 = 3.125米 第六天：3.125 ÷ 2 = 1.5625米 第七天：1.5625 ÷ 2 = 0.78125米
Day 1: 100 ÷ 2 = 50 meters Day 2: 50 ÷ 2 = 25 meters Day 3: 25 ÷ 2 = 12.5 meters Day 4: 12.5 ÷ 2 = 6.25 meters Day 5: 6.25 ÷ 2 = 3.125 meters Day 6: 3.125 ÷ 2 = 1.5625 meters Day 7: 1.5625 ÷ 2 = 0