Interactive Polygon Explorer

A hands-on geometry learning tool for exploring polygon properties and angle measurements. Create polygons with 3-20 sides, drag vertices to form convex and concave shapes, and observe how angle measurements change in real-time.

This interactive polygon explorer features draggable polygon vertices with real-time angle calculations, interior, exterior, and conjugate angle measurements, and visual feedback for self-intersecting polygons. You can create cyclic polygons with vertices locked to a circumcircle, customize polygon sides, radius, and rotation, and use grid snapping with measurement tools for precise construction.

The tool provides educational angle visualization with color-coded arcs, making it perfect for students, teachers, and anyone learning geometry concepts including polygon interior angle sums, exterior angles, and the relationship between convex and concave polygon properties. It supports exploration of regular and irregular polygons with immediate visual feedback.

How to Use

The controls are organized into two main sections: the Variables tab contains the core polygon construction and measurement tools, while the Style tab controls colors and visual appearance.

Building Your Polygon

Start by adjusting the Radius to set the size of your polygon. Use the Sides control to choose how many sides your polygon will have, from triangles up to 20-sided polygons. The Rotate Angle lets you rotate the entire polygon to any orientation you prefer.

Toggle the circumcircle button to show or hide the circle that passes through all vertices of a regular polygon. When you want to constrain your polygon to remain on this circle while dragging vertices, activate the cyclic polygon constraint - this magnetic circle feature keeps vertices locked to the circumference.

Angle Measurements

The Interior angle display lets you choose how to visualize the interior angles of your polygon. You can show just the arc, the numerical value, or hide them entirely.

For Exterior angles, you have several options: clockwise exterior angles (the traditional geometric definition) or conjugate angles (the supplementary angles). Each can be displayed as arcs only or with both arcs and numerical values.

Control the precision of your angle measurements with Angle Accuracy, which lets you round to the nearest whole number or show one or two decimal places.

Measurement Tools

Two powerful measurement tools are available: toggle the protractor for measuring angles anywhere on the canvas, and the ruler for measuring distances between points.

Use the Snap to feature to make precise constructions by snapping dragged vertices and tools to grid positions - choose from full squares, half squares, quarter squares, or no snapping at all.

Customizing Appearance

Click the Style tab to access visual customization options.

Polygon Colors

Customize your polygon’s appearance with Polygon Fill to set the interior color, Polygon Stroke for the border color, and Circle Fill for the circumcircle color when it’s visible.

Background and Grid

Choose your working surface with the Paper selector - options include square grid lines, isometric (triangular) grid lines, square dots, triangular dots, or a plain background.

Customize the colors of your workspace using Paper Color for the background and Line/Dot Color for the grid pattern.