A robust desktop application designed to calculate the areas and volumes of geometric solids with absolute mathematical precision. Unlike standard calculators, this tool preserves symbolic constants such as
The Problem: Most geometry scripts and calculators convert irrational numbers into floating-point decimals, leading to a loss of precision and making the results difficult to use in formal proofs or academic exams.
The Solution: Leveraging the SymPy library, we processes formulas symbolically. Users can toggle between defining decimal values for constants or maintaining them as pure mathematical symbols. Additionally, the application features a reactive 3D visualization that scales instantly as dimensions are modified.
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Exact Symbolic Computation: Results maintain
$\pi$ and square roots without unwanted decimal approximations. -
Real-Time 3D Visualization: An integrated interface that renders the solid and scales the view instantly as inputs change.
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Multi-Base Support: Calculate pyramids and prisms with triangular, square, or hexagonal bases, automatically adjusting the apothem mathematics.
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Precision Geometry: Correct implementation of complex formulas, including the generatrix (slant height) for lateral area calculations in cones and pyramids.
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Reactive Interface: No "Calculate" buttons required. Results and the 3D plot update as you type.
| Component | Technology | Description |
|---|---|---|
| Language | Python 3.10+ | Core logic and integration |
| Interface (GUI) | PyQt6 | Framework for a native desktop experience |
| Mathematics | SymPy | Symbolic computation for exact precision |
| 3D Graphics | Matplotlib | Mesh and geometric surface rendering |
Ensure you have Python installed along with the required libraries:
pip install PyQt6 matplotlib sympy numpy- Clone the repository:
git clone https://github.com/cunhanina/Spatial-Geometry.git
cd Spatial-Geometry- Run the application:
python geometry.pyThe system is designed to be mathematically rigorous:
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Apothem Calculation: For regular polygons, the application derives the side length from the provided apothem (
$r$ ) to ensure the base area and perimeter are consistent with the 3D visualization. -
Slant Height (
$s$ ): In pyramids and cones, the lateral area is calculated via the Pythagorean theorem:$s = \sqrt{h^2 + r^2}$ , where$r$ is the base apothem. -
Symbolic Branching: If the user unchecks "Define constants," SymPy isolates the symbols throughout the entire calculation chain until the final output.
