🤖 This instructional tool teaches how to compute oversized square canvases to fit rectangular resolutions inside circles, ideal for kaleidoscopic effects. We will extend these square canvases into cubes containing spheres containing kaleidoscopes in TV screens.

📘 How to Calculate the Kaleidoscope Square

This page is designed to help high school students and teachers understand how to mathematically determine the size of a square that:

1. Contains a circle
2. Which itself perfectly encloses a rectangle of a given resolution

Step-by-Step Explanation 🧠

1. Start with a Resolution

Choose a resolution like 3840×2160. This is your rectangle.

2. Use the Pythagorean Theorem

The diagonal of a rectangle is calculated using the Pythagorean theorem:

Diagonal = √(width² + height²)

Example:

width = 3840
height = 2160
Diagonal = √(3840² + 2160²) = √(14,745,600 + 4,665,600) = √19,411,200 ≈ 4405.45

3. Round Up to the Nearest Even Integer

To ensure a symmetrical layout for visual effects, we round the diagonal up to the nearest even number.

Rounded = 4406

4. Use the Rounded Value for a Square

This becomes the dimension of a square that fits the circle perfectly — which fits your original rectangle.

Final Square = 4406×4406

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