Caltriangles: 2D Triangles

Caltriangles is a technical application designed to facilitate the study and resolution of triangles through precise computational methods. Oriented toward students of mathematics, physics, and engineering, the platform allows for an exhaustive analysis of geometric figures based on minimal input data.

Advanced Triangle Solving 🖥️

The application implements solving algorithms for all cases of congruence and similarity, providing immediate results for:

🔹Interactive Dynamic Graphics: Provides the ability to manipulate and adjust the triangle directly on-screen, ensuring a superior visual perspective and precise positioning of angles and sides.

🔹 Fundamental Cases: SSS, SAS, ASA, and AAS.

🔹 The Ambiguous Case (SSA): Rigorous identification of the existence of one, two, or no solutions, allowing the user to explore acute and obtuse variants independently.

Geometric Analysis and Notable Lines 📏

Beyond basic calculations of sides and angles, Caltriangles offers a complete characterization of the triangle:

✅ Automatic Classification: Precise classification based on sides (Equilateral, Isosceles, Scalene) and angles (Acute, Right, Obtuse).

✅ Centers and Radii Determination: Exact calculation of the Inradius (radius of the inscribed circle) and Circumradius (radius of the circumscribed circle).

✅ Calculation of Cevians and Notable Lines: Determination of the lengths of the three Altitudes (h), the three Medians (m), and the three Internal Bisectors (w).

Specialized Conversion Unit 🔄

To ensure versatility across different measurement systems, the tool integrates an angular unit conversion module:

🔸 Measurement Systems: Seamless transition between Sexagesimal Degrees and Radians.

🔸 Geometric Precision: Conversion of coordinates from Degrees, Minutes, and Seconds (DMS) to Decimal format.

Documentation and Technical Reports 📄

To support the learning process and academic documentation, the application allows exporting results into a professional PDF format. This report includes:

📊 Graphical Representation: A scaled diagram of the analyzed triangle.

📋 Data Matrix: A tabulated organization of angles, sides, areas, perimeters, and notable lines.

📥 Portability: Technical documentation ready for filing, printing, or academic submission.

Caltriangles combines mathematical rigor with an intuitive interface, making it an indispensable assistant for developing competencies in analytical geometry and trigonometry.