Triangle Inequality Explorer

Inequality Explorer is an interactive digital sandbox where students physically build and manipulate triangles to prove the Triangle Inequality Theorem. By adding colourful unit blocks to form two sides and dragging them on a hinge, 11th graders instantly see how the third side reacts in real time. It takes a foundational geometric rule and turns it into a satisfying, tactile proof that is perfect for visualizing boundaries.

This app seamlessly blends hands-on mathematical modeling with dynamic technology, letting students construct geometric proofs through interactive play.

STEAM learning

• Mathematics: Triangle Inequality Theorem — Students construct sides block-by-block and manipulate angles to visually prove that the sum of two side lengths must always exceed the third. The live equation updates instantly, grounding abstract rules in concrete geometry.
• Technology: Dynamic Modeling — The app's real-time physics and auto-scaling third side give students immediate feedback as they drag the hinge. This creates a responsive sandbox that encourages rapid testing without setup time.
• Logic: Boundary Testing — Students are playfully challenged to flatten the shape and break the inequality, transforming the greater-than sign into an equals sign. This boundary-testing cements their understanding of geometric limits and degenerate triangles.