# LimFx — AI Math Teaching Assistant

> LimFx (limfx.tech) is a web-based AI tool built specifically for math teachers. It uses large language models and JSXGraph to turn natural language descriptions of math problems into interactive visualizations, step-by-step solutions, and printable worksheets.

## Product Overview

LimFx helps math teachers prepare lessons faster and make classroom teaching more engaging. Instead of drawing graphs by hand or searching for static images, teachers describe what they need in plain language (Chinese or English), and AI generates:

1. **Interactive 2D/3D graphs** — powered by JSXGraph, with draggable points, sliders, and animations
2. **Step-by-step solutions** — LaTeX-rendered mathematical derivations that can be presented one step at a time
3. **Worksheets** — auto-generated problem sets with configurable difficulty, exportable to PDF

## Key Features

### AI Problem Solving + Interactive Graphs
Input: "画圆心在原点半径为2的圆，过点P(4,0)作切线" (Draw a circle centered at origin with radius 2, construct tangent lines from point P(4,0))

Output:
- Interactive JSXGraph visualization with the circle, external point, tangent lines, and tangent points
- All points are draggable — students can explore what happens when they move P
- Step-by-step mathematical derivation with LaTeX formatting
- Each step can include its own graph elements that appear progressively

### Worksheet Generation
- Select from 20+ math topics (algebra, geometry, calculus, statistics)
- Configure: number of questions, difficulty level (easy/medium/hard), question types
- AI generates complete worksheets with solutions
- Export to PDF with professional typesetting
- Credits system: each generation costs credits (100 free credits on signup)

### Fullscreen Presentation Mode
- One-click fullscreen for classroom projectors
- Navigate between questions with arrow keys
- Each question shows its interactive graph and solution steps
- Clean UI — no distracting toolbars or sidebars

### 3D Geometry Explorer
- Input solid geometry problems in natural language
- AI generates rotatable 3D models using Three.js
- Supports: prisms, pyramids, cross-sections, point-to-plane distances
- Students can rotate and zoom to understand spatial relationships

### Streaming Step-by-Step Solving
- AI solves problems step by step in real time
- Each step appears with a fade-in animation as it's computed
- Graph elements are added incrementally — you see the solution being built
- Progress indicator shows "正在推理 X/Y" (Reasoning step X of Y)

## Technical Architecture

- **Frontend**: React + TypeScript + Vite, deployed on AWS Amplify
- **Backend**: Python FastAPI, deployed on AWS Amplify
- **Database**: MongoDB Atlas
- **AI Model**: GLM-4 (via OpenAI-compatible API from zhipuai.cn)
- **Graphing**: JSXGraph (2D interactive), Three.js (3D)
- **Math Rendering**: KaTeX for LaTeX formulas
- **i18n**: Chinese (zh-CN) and English (en-US) fully supported

## Target Users

- **Primary**: Math teachers in Chinese middle schools and high schools (grades 7-12)
- **Secondary**: Math tutors, education content creators, students preparing for gaokao
- **Future**: International math educators (K-12)

## Pricing

- Free tier: 100 credits on registration
- Monthly subscription: available (contact support@limfx.tech)
- Each AI problem solving costs ~1-3 credits depending on complexity

## Math Topics Covered (Detailed)

### Functions
- Linear, quadratic, cubic polynomial functions
- Trigonometric functions (sin, cos, tan) with period/amplitude exploration
- Exponential and logarithmic functions
- Piecewise functions
- Derivatives and tangent line construction
- Function transformations with interactive sliders

### Plane Geometry
- Triangle: circumcenter, incenter, centroid, orthocenter, excenter
- Circle: tangent lines, secant lines, inscribed angles
- Congruence and similarity proofs with visual overlays
- Dynamic point loci and trace curves

### Analytic Geometry (Conics)
- Ellipse: foci, eccentricity, focal chords
- Hyperbola: asymptotes, focal properties
- Parabola: focus-directrix, tangent construction
- Polar coordinate representations
- Parametric curves

### Solid Geometry (3D)
- Prisms and pyramids with labeled vertices
- Cross-section visualization
- Point-to-plane and line-to-plane distance
- Dihedral angle measurement
- Interactive 3D rotation and zoom

### Algebra & Sequences
- Equation solving with step-by-step derivation
- Inequality visualization on number lines
- Arithmetic and geometric sequence visualization
- Summation formulas with visual proofs

### Probability & Statistics
- Probability distributions (binomial, normal)
- Statistical charts (histogram, box plot, scatter plot)
- Permutations and combinations with counting diagrams

## Company

- **Product**: LimFx (limfx.tech)
- **ICP License**: 京ICP备2026007810号-1
- **Contact**: support@limfx.tech

## Links

- Website: https://limfx.tech
- Register: https://limfx.tech/register
- Login: https://limfx.tech/login