Mathematics and Patterns

Definition of Patterns

• A pattern is an irregularity in the world recognized by humans.
• Patterns abstract ideas that repeat in a predictable manner.
• Example: Geometric patterns (e.g., wallpaper designs).

Types of Patterns

Mathematical Patterns

• Patterns can be numbers or sequences that are related in a certain way.
• Example: The sequence 2, 4, 6, 8 (increases by 2).

Natural Patterns

• Visible regularities in the world that can sometimes be modeled mathematically.
• Common natural patterns:
  • Symmetries
  • Fractals
  • Spirals
  • Fibonacci patterns
  • Tessellations

Examples of Natural Patterns

• Biological patterns:
  • Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21...
    • Each number is the sum of the two preceding numbers.
  • Symmetry: Found in living organisms and structures (e.g., human body, apple, snowflakes).
  • Fractals: Patterns that repeat on smaller and smaller scales (e.g., trees, rivers).
  • Tessellations: Patterns formed by repeated shapes (e.g., beehives, pineapples).
  • Spirals: Common in natural forms (e.g., shells, hurricanes).

Importance of Mathematics in Organizing Patterns

• Mathematics helps organize patterns and regularities in the world.
• Example: Arrangements that repeat can be observed in daily life (e.g., shapes, sounds, structures).
• Observing, questioning, and testing are key to understanding patterns.

Fibonacci Sequence and Golden Ratio

• The Fibonacci sequence is essential for measurements in art and nature.
• Golden Ratio: Example found in sunflowers (1.618033...) illustrates perfect seed arrangement for sunlight exposure.
• Mathematics is intertwined with nature and human creations (e.g., architecture).

Role of Mathematics in Society

• Symmetrical animals are often deemed more attractive, impacting mating choices.
• Mathematics connects global understanding and communication.
• Encourages innovation in culture and economy.
• Rethinking arithmetic provides students with a modern perspective on traditional topics.

Conclusion

• Mathematics is fundamental for understanding the world and solving real-world challenges.