与复数一起玩:为高年级小学生准备的真实生活之旅
Having Fun with Complex Numbers

原始链接: https://mathwonder.org/Having-Fun-with-Complex-Numbers/

陆秋江博士的《和复数一起玩》旨在让高年级小学生(8-12岁)更容易理解并*享受*高等数学概念。本书认为,将数字理解为表面上的点——比如触摸屏——比传统的数轴更直观,并将复数介绍为这些“表面数字”。 本书基于作者的原创研究,以宏观思维、现实生活例子和引人入胜的插图重新构想了复数理论。它摒弃了死记硬背,而是通过“帆船”冒险鼓励探索和建立自信。 学生们将掌握加法和乘法等基础数学技能,同时自然地发现新的概念。最终,本书旨在重燃好奇心,并证明数学可以是一场激动人心的冒险,而不是一项苦差事。

这个Hacker News讨论围绕一本新书展开,该书旨在通过一种新颖的方法,甚至向小学生教授复数。作者陆秋江博士“从头开始”重新构建了复数理论,不依赖于虚数单位的传统定义(i = sqrt(-1))。 评论者们争论这本书的原创性,一些人指出已经存在类似的几何方法——将'i'定义为π/2旋转。然而,另一些人强调作者独特的视角,将实数视为“伸展”,将虚数视为“旋转”,可能提供一种全新的直观理解。 几位用户推荐了相关资源:之前的Hacker News讨论、作者的视频,特别是Welch Labs的“虚数是真实的”系列,作为一种极佳的学习工具。还有人提到了Tristan Needham的“视觉复数”作为相关且备受推崇的资源。虽然一些人质疑作者关于一个500年未解难题的说法,但普遍的看法倾向于这本书如果能有效地通过视觉方式传达复杂概念,将是一种有价值的教育工具。
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原文

Having Fun with Complex Numbers

A Real-Life Journey for Upper Elementary Students
by Dr. Qiujiang Lu

Book description
Welcome to the amazing world of math—made just for kids like you!

Are you between 8 and 12 years old? Then get ready—this book is your gateway to unlocking the true power of math!

Regular numbers represent positions—called points—on a number line. Yet modern, widely used touchscreens suggest that selecting a point on a surface is more intuitive and fundamental than selecting one on a line. This shift makes the study of surface numbers more engaging and appealing, as it invites motion and interaction that bring math to life. Complex numbers, as it turns out, are precisely these surface numbers.

The author's research has redeveloped complex number theory from the ground up, making it accessible across broader educational levels—including elementary schools.

Inside, you’ll discover fresh, exciting ideas that turn tricky, mysterious topics into pure fun. If you’ve ever felt bored by textbooks or overwhelmed by endless numbers and tiny details, you’re not alone. That kind of math can drain your curiosity and make learning feel like a chore.

But this book is the total opposite—it’s a thrilling math adventure! Instead of sinking in a sea of numbers, you’ll hop aboard a sailing boat and chart your own course. With big-picture thinking, creative approaches, and motion illustrations that bring math moves to life, you’ll explore page by page, step by step.

Along the way, you’ll:

  • Dive into real-life examples and clever metaphors
  • Pick up awesome math tools
  • Discover new concepts naturally
  • Build confidence as you go

By the end of your journey, you’ll be amazed at what you’ve accomplished: mastering the number line, number grid, and the four key math moves—like adding and multiplying—that form the foundation for all your future math adventures!

So, are you ready to blast off? Flip the page, unlock the fun, and shout: “Math rocks!”

Author

Dr. Qiujiang Lu is an independent researcher and software developer in Silicon Valley whose work has re-created the imaginary unit in real life from first principles, which remained unknown for 500 years since the inception. His past research had involved discovering the mechanism of ice crystal growth habit change, an outstanding problem for more than 50 years in cloud physics that is closely related to the “thousands’ variations” in snowflakes. His interests are in physics, mathematics, software, and their multidisciplinary applications.

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