Using AI and HTML Animation to Solve a Geometry Problem: An Interactive Learning Approach

As a parent, helping your child with math homework can sometimes feel challenging, especially when dealing with complex problems in subjects like geometry.

My son, who is currently in 7th grade, recently came across a geometry problem that required finding when two rotating rays become perpendicular to each other.

At first, I wasn’t sure how to approach the problem myself, but I decided to turn to ChatGPT for some guidance.

ChatGPT helped me solve the math problem.

While solving the problem on paper was one thing, I realized that my son would benefit from seeing the rays rotate in real-time. I wanted to make the solution more engaging by visually demonstrating how the rays rotate and when they become perpendicular.

However, I encountered a challenge. I didn’t have much experience with animations in HTML or JavaScript, and I wasn’t sure where to start. So, I turned to ChatGPT once again to help me animate the solution.

This turned out to be a fantastic way to make the learning process more engaging and interactive. Here’s how we went from a challenging math problem to a visual solution!

Problem Overview

The problem involved two rays, OC→\overrightarrow{OC} and OD→\overrightarrow{OD}, rotating counterclockwise from two different directions.

They move at different speeds, and the task was to determine when they would become perpendicular to each other. Specifically, we needed to figure out at what time t the angle ∠COD=90.

The Challenge of Visualization

After the math was solved, I knew that my son would benefit from visualizing the rotating rays to better understand the concept.

However, I wasn’t sure how to animate the problem effectively. This is when I encountered my own challenge. I didn’t have much experience with animations in HTML or JavaScript, and I wasn’t sure how to get started.

That’s when I decided to ask ChatGPT for help. ChatGPT guided me step by step on how to create a simple animation that would show the rays rotating over time and allow us to see when they become perpendicular.

Using its guidance, I was able to build an interactive animation that made the problem much clearer.

Visualizing the Solution with HTML and JavaScript

Here’s the complete solution in code that allowed us to visualize the rotating rays.

The animation shows how the rays OC→\overrightarrow{OC} and OD→\overrightarrow{OD} rotate over time, and it highlights when they become perpendicular:

How the Animation Works

1. Canvas Setup: The canvas element is used to draw the rays, and the center represents the origin of both rays.
2. Angle Calculation: As the animation progresses, the angles of the rays OC→\overrightarrow{OC} and OD→\overrightarrow{OD} are updated based on the time tt, and the rays are drawn from the center of the canvas.
3. Perpendicular Check: The animation checks if the absolute difference between the angles of the rays equals 90∘90^\circ (or 270∘270^\circ), indicating that the rays are perpendicular.

Here is the video for this animation.

Here’s a basic conceptual chart:

Conclusion

While solving the problem itself was straightforward with ChatGPT’s help, it was the animation that truly brought the concept to life. By following ChatGPT’s instructions, I was able to visualize the rotation of the rays, which made it much easier for my son to understand how the two rays moved and when they became perpendicular.

This made the learning process not only easier for my son but also much more fun and interactive.

If you ever face a similar challenge, whether it’s math-related or technical, using AI tools like ChatGPT can be an invaluable resource to help you understand and solve problems creatively and efficiently.