Symmetry and Asymmetry
Whether something looks the same (symmetry) or different (asymmetry) when split in half

Mirror Images

What: Shapes that are identical when reflected
Why: Foundation for geometric understanding
How does it help: Develops spatial awareness and pattern recognition

Geometric patterns form the foundation of many mathematical principles and can be observed in various forms:


  • Regular polygons and their properties
  • Tessellations and surface coverings
  • Symmetry in natural and man-made objects
  • Fractal patterns and self-similarity
Geometric Pattern Example

Pattern Recognition

What: Finding regular arrangements in shapes and designs
Why: Essential for advanced math concepts
How does it help: Strengthens visual reasoning and logical thinking

There are several types of symmetry in mathematics:


  • Reflection symmetry (flip)
  • Rotational symmetry (turn)
  • Translational symmetry (slide)
  • Point symmetry
Symmetry Examples

Shape Symmetry

What: Understanding when shapes are balanced around a line or point
Why: Important in art, nature, and design
How does it help: Builds geometric intuition and spatial reasoning

Tessellations can be created using:


  • Regular polygons
  • Irregular shapes
  • Transformed shapes
  • Combined patterns
Tessellation Examples

Asymmetrical Art

What: Analyzing unbalanced designs
Why: Develops understanding of (im)balance and design
How does it help: Enhances creative thinking and spatial comprehension

Famous examples of fractals include:


  • The Mandelbrot Set
  • Koch Snowflake
  • Sierpinski Triangle
  • Dragon Curve
Fractal Examples

Related Resources

Math is Fun Geogebra Toy Theater