Pythagoras' Theorem - Animation Generation Collaboration 003 #MathsAnimationTMiP

Introduction

This tutorial will guide you through creating an animation that visually proves Pythagoras' theorem. The theorem is a fundamental principle in mathematics, stating that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This tutorial is relevant for educators, students, and anyone interested in visual mathematics and animation.

Step 1: Set Up Your Animation Environment

Before you start creating your animation, you need the right tools.

1. Download CindyJS

   • Visit CindyJS website.
   • Follow the installation instructions for your operating system.

2. Access Animation Package

   • Download the custom animation package from the GitHub repository: cindy_tools.
   • Ensure you have a working environment to run the animation scripts.

3. Explore Animation Code

   • Familiarize yourself with the provided code in the GitHub repository: tmip_animations.
   • Open the code files to understand the structure and how animations are implemented.

Step 2: Understand Pythagoras' Theorem

Before animating, ensure you have a solid grasp of the theorem.

• The Formula:

  • For a triangle with sides of lengths a and b, and hypotenuse c:
  • ( c^2 = a^2 + b^2 )

• Visual Representation:

  • Draw a right-angled triangle and label the sides.
  • Use squares on each side to visually represent the areas.

Step 3: Create Your Animation Script

Now, it’s time to write the code for your animation.

1. Set Up Basic Shapes:

   • Define the triangle and squares:

   var a = 3; // length of side a
   var b = 4; // length of side b
   var c = Math.sqrt(a * a + b * b); // hypotenuse
   
   // Create triangle
   var triangle = new Triangle([0, 0], [a, 0], [0, b]);
   

2. Animate the Squares:

   • Use loops to animate the area calculations:

   function animateSquares() {
       // Draw squares on each side
       drawSquare(a, 0);
       drawSquare(0, b);
       drawSquare(c, 0); // for hypotenuse
   }
   

3. Run the Animation:

   • Call the animation function within the main execution block:

   main() {
       animateSquares();
   }
   

Step 4: Test Your Animation

Run your animation in the CindyJS environment to see how it looks.

• Check for Errors:

  • Review your console for any errors in the code.
  • Make adjustments as needed to ensure smooth transitions and accurate representations.

• Refine Visuals:

  • Adjust colors, shapes, or sizes for clarity and visual appeal.
  • Consider adding labels or explanatory text for educational purposes.

Conclusion

In this tutorial, you learned how to create an animation that visually represents and proves Pythagoras' theorem using CindyJS. Key steps included setting up your environment, understanding the theorem, scripting the animation, and testing your work.

For next steps, consider expanding your animation with more complex examples of triangles or incorporating user interactions to enhance learning. Happy animating!