Question: Create a clean, high-resolution educational infographic about the **Pythagorean Theorem**, closely matching the provided reference image.
**Layout:** Landscape 4:3 educational poster, white background. At the very top center, place a large bold black italic title: **“Pythagorean Theorem”**. Place a small NASA-style circular logo on the top-left and a small blue scientific/space-themed circular logo on the top-right.
**Left side:** Add a black educational explanation in a bold, clear sans-serif font:
“For any right triangle
with sides $a$ and $b$ and
hypotenuse $h$, the square
of the hypotenuse is
equal to the sum of the
squares of the
other two sides.”
Below the explanation, display the formula prominently:
**$h^2 = a^2 + b^2$**
with **$h^2$** and **$a^2$** in red and **$b^2$** in blue.
**Right side diagram:** Show a simple right triangle with three squares constructed externally on its three sides.
* A **red square** attached to the vertical leg, labeled **“Area = $a^2$”** in white.
* A **blue square** attached to the horizontal leg, labeled **“Area = $b^2$”** in white.
* A **large light-gray square**, rotated according to the triangle's hypotenuse, attached to the hypotenuse and labeled **“Area = $h^2$”** in black.
* Clearly label the triangle's vertical side **“$a$”** in red, horizontal side **“$b$”** in blue, and hypotenuse **“$h$”** in black.
* Add the text **“$h=\text{hypotenuse}$”** above the diagram.
Use clean geometric lines, accurate mathematical proportions, sharp edges, strong contrast, and a professional NASA educational-poster aesthetic. Keep the composition uncluttered and very close to the reference. Make all mathematical symbols and labels correctly spelled and positioned. **No extra objects, no decorative background, no modern redesign, no 3D effects, no unnecessary shadows.**
**Style:** vintage educational science poster, crisp textbook infographic, simple flat geometric shapes, high-resolution, realistic print texture kept minimal, accurate typography, white background, red/blue/gray color scheme.
1. **Problem Statement:**
We want to create an educational infographic illustrating the Pythagorean Theorem, which states that for a right triangle with legs $a$, $b$ and hypotenuse $h$, the relationship is:
$$h^2 = a^2 + b^2$$
2. **Formula and Explanation:**
The Pythagorean Theorem formula is:
$$h^2 = a^2 + b^2$$
This means the area of the square built on the hypotenuse ($h^2$) equals the sum of the areas of the squares built on the other two sides ($a^2$ and $b^2$).
3. **Diagram Construction:**
- Draw a right triangle with vertical side labeled $a$ in red, horizontal side labeled $b$ in blue, and hypotenuse labeled $h$ in black.
- Construct three squares externally on each side:
- A red square on side $a$ labeled "Area = $a^2$" in white.
- A blue square on side $b$ labeled "Area = $b^2$" in white.
- A large light-gray square on the hypotenuse $h$, rotated to align with $h$, labeled "Area = $h^2$" in black.
- Add the text "$h=\text{hypotenuse}$" above the diagram.
4. **Styling and Layout:**
- Use a white background with a landscape 4:3 ratio.
- Place a large bold black italic title "Pythagorean Theorem" centered at the top.
- Place a small NASA-style circular logo top-left and a small blue scientific/space-themed circular logo top-right.
- On the left side, place the educational explanation in bold black sans-serif font.
- Use red for $h^2$ and $a^2$, blue for $b^2$, and light gray for the hypotenuse square.
- Keep the design clean, geometric, with sharp edges and strong contrast.
5. **Final Result:**
The infographic clearly communicates the Pythagorean Theorem visually and textually, with accurate labels and color coding, suitable for educational use.