MicroSims for Geometry

Interactive simulations to explore geometric concepts through hands-on manipulation and visual feedback.

• Angle Pairs

  

  Explore different angle pair relationships including vertical angles, linear pairs, corresponding angles, and alternate angles formed by parallel lines and transversals.

• Angle Type Explorer

  

  Discover angle classifications by manipulating a slider to create acute, right, obtuse, straight, and reflex angles with real-time visual feedback.

• Area Formulas for Quadrilaterals

  

  Compare area formulas for different quadrilaterals including squares, rectangles, parallelograms, rhombuses, and trapezoids.

• Barnsley's Fern

  

  Explore the Barnsley fern fractal created using an Iterated Function System. Adjust iterations, scale, leaf angle, and curl to create different fern variations.

• Cesaro Curve

  

  Explore the Cesaro curve (torn square) fractal. Starting from a divided square, watch how perpendicular displacement creates intricate lace-like patterns.

• Circle Area Calculator

  

  Calculate and visualize circle area by adjusting the radius. See how the area formula A = πr² produces the result in real-time.

• Circle Area Explorer

  

  Investigate the relationship between a circle's radius and its area through interactive manipulation and visual demonstration.

• Collinear and Coplanar Points

  

  Understand the concepts of collinear points (on the same line) and coplanar points (on the same plane) through interactive 3D visualization.

• Complementary and Supplementary Angles

  

  Explore angle relationships: complementary angles (sum to 90°) and supplementary angles (sum to 180°) with interactive sliders.

• Cosine Function

  

  Visualize the cosine function on the unit circle. See how the x-coordinate of a point on the circle relates to the cosine of the angle.

• Degrees vs Radians

  

  Convert between degree and radian angle measurements. Understand the relationship between these two common ways to measure angles.

• Distance Formula Explorer

  

  Calculate the distance between two points on a coordinate plane using the distance formula derived from the Pythagorean theorem.

• Graph Viewer

  

  Explore the geometry course learning graph showing 200 concepts and their dependencies. Navigate through foundational concepts to advanced topics.

• Koch Fractal

  

  Explore the Koch curve fractal. Watch how a simple line transforms into an increasingly complex pattern through recursive subdivision.

• Koch Snowflake

  

  Create the classic Koch snowflake by applying the Koch curve to each side of a triangle. Adjust recursion depth to see the fractal evolve.

• Levy C Curve

  

  Explore the Levy C curve (flowsnake), a space-filling fractal that uses 45-degree angles and eventually fills a 2D region.

• Line Relationships 3D

  

  Visualize relationships between lines in 3D space including parallel, intersecting, perpendicular, and skew lines.

• Make Lines Parallel

  

  Adjust line parameters to make two lines parallel. Understand what conditions must be met for lines to never intersect.

• Peano-Gosper Fractal

  

  Explore the Gosper curve (flowsnake), a space-filling fractal based on hexagonal geometry using L-system rules and turtle graphics.

• Point Line Explorer

  

  Investigate the relationship between points and lines. Explore concepts like distance from a point to a line and point position relative to lines.

• Point, Line, Plane

  

  Understand the fundamental building blocks of geometry: points (0D), lines (1D), and planes (2D) through interactive 3D visualization.

• Pythagorean Theorem

  

  Explore the Pythagorean theorem (a² + b² = c²) visually. See how squares on the sides of a right triangle relate to each other.

• Regular Polygon Explorer

  

  Investigate regular polygons from triangles to dodecagons. Explore interior angles, exterior angles, and the relationship between sides and angles.

• Regular Polygon Quiz

  

  Test your knowledge of regular polygons with an interactive quiz covering sides, interior angles, and exterior angles.

• Sierpinski Carpet

  

  Explore the Sierpinski carpet, a 2D fractal created by recursively removing the center of a 3×3 grid, leaving 8 squares each time.

• Sierpinski Triangles

  

  Create the Sierpinski triangle fractal by recursively removing the center triangle from each remaining triangle.

• Sine and Cosine Circle

  

  Visualize sine and cosine on the unit circle. See how a point's coordinates relate to trigonometric functions as it moves around the circle.

• Soccer Ball

  

  Explore the geometry of a soccer ball (truncated icosahedron) made of pentagons and hexagons using 3D WebGL visualization.

• Triangle Area Explorer

  

  Investigate triangle area using the formula A = ½bh. Manipulate the base and height to see how the area changes.

Using MicroSims in the Classroom

MicroSims (micro-simulations) are interactive visualizations that help students explore geometric concepts through hands-on manipulation and immediate visual feedback.

Learning Objectives

By using MicroSims, students will be able to:

• Visualize abstract geometric concepts through interactive manipulation
• Discover geometric relationships through exploration and experimentation
• Connect formal definitions to visual representations
• Develop intuition about geometric properties and relationships

Instructional Strategies

1. Guided Exploration: Demonstrate the MicroSim and guide initial exploration with questions
2. Discovery Learning: Allow students to discover relationships independently
3. Concept Reinforcement: Connect exploration to formal definitions and theorems

Best Practices

• Allow time for free exploration before structured tasks
• Encourage students to make and test predictions
• Use MicroSims to supplement, not replace, traditional instruction
• Connect virtual manipulations to real-world applications