MathConnect

MathConnect turns equivalent infinitesimals into a fast connect-the-pairs puzzle for calculus practice.

Play the live game | View the source

Why This Exists

Equivalent infinitesimals are usually memorized as a list. MathConnect makes that list interactive: clear the board by connecting two formulas that behave the same as x -> 0, while following a Lianliankan-style path rule.

The result is a small browser game that helps learners recognize patterns like:

Family	Matching examples
x	sin x, tan x, arcsin x, arctan x, e^x - 1, ln(1+x)
2x	sin(2x), tan(2x), e^{2x} - 1, ln(1+2x)
x^2 / 2	1 - cos x
x^2	2(1 - cos x), sin^2 x

How To Play

1. Pick two tiles with equivalent behavior as x -> 0.
2. The tiles must connect through empty space with at most two turns.
3. Clear the full board and start another round.

Current Scope

• Level: equivalent infinitesimals for x -> 0
• Board: 6 by 10 on desktop, 8 by 6 on small screens
• Rendering: KaTeX-powered math tiles
• Stack: React, Vite, JavaScript, CSS
• Deployment: GitHub Pages

Roadmap

• Add timed and relaxed modes
• Add hint and shuffle controls
• Add more calculus levels: limits, derivatives, integrals, and Taylor expansions
• Track streaks, mistakes, and completion time
• Add a bilingual rules panel for classroom use

Local Development

npm install
npm run dev

Build for production:

npm run build

Run the lightweight game-logic check:

node testGame.js

License

MIT

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MathConnect 中文说明

MathConnect 将等价无穷小变成速配连连看游戏，用于微积分练习。

在线游玩 | 查看源码

为什么做这个

等价无穷小通常靠死记硬背。MathConnect 把那张表变成可交互的：在 x -> 0 时行为相同的两个公式之间连线消除，路径规则遵循连连看玩法。

游戏帮助学习者快速识别以下模式：

家族	配对示例
x	sin x, tan x, arcsin x, arctan x, e^x - 1, ln(1+x)
2x	sin(2x), tan(2x), e^{2x} - 1, ln(1+2x)
x² / 2	1 - cos x
x²	2(1 - cos x), sin² x

玩法

1. 点击两个在 x -> 0 时等价的方块。
2. 两个方块之间可通过空白区域相连，路径最多拐两次弯。
3. 清空全部方块即可进入下一局。

当前范围

• 关卡：x -> 0 等价无穷小
• 棋盘：桌面端 6×10，小屏 8×6
• 渲染：KaTeX 数学公式方块
• 技术栈：React, Vite, JavaScript, CSS
• 部署：GitHub Pages

路线图

• 增加限时模式和休闲模式
• 增加提示和洗牌功能
• 增加更多微积分关卡：极限、导数、积分、泰勒展开
• 记录连击、失误和完成时间
• 增加双语规则面板，便于课堂使用

本地开发

npm install
npm run dev

生产构建：

npm run build

运行轻量游戏逻辑测试：

node testGame.js

许可

MIT