Patterns in Nature and Symmetry

Patterns in Nature

• Patterns are diverse, from microscopic to gigantic, simple to complex, including colors and shapes.
• Patterns are not random; they are sequences or designs that repeat.
• Examples of patterns in nature include spots on a giraffe, symmetry in a sea star, and a snowflake's structure.

Symmetry

• Symmetry is when different sides are alike, such as mirror images.
• Symmetry can involve two sides (like the human body) or several sides (like an apple sliced in half) or all sides (like a cube).
• Living organisms often exhibit symmetry due to their need for balance within their environment.
• The purpose of symmetry in non-living things (like snowflakes or water splashes) is less understood.
• Snowflakes often display six-fold symmetry, though the reason is unclear.

Fractals & Spirals

• Fractals are patterns that repeat infinitely smaller as they are examined more closely.
• Fractals occur in many natural structures like trees, rivers, mountains, and more.
• Spirals are common in living things, such as the horns of a sheep or the shell of a nautilus.
• Some spirals, like logarithmic spirals, get smaller as they go.
• Logarithmic spirals appear in hurricanes, galaxies, and some seashells.

Fibonacci Patterns

• The Fibonacci sequence is a series where each number is the sum of the two preceding numbers (e.g., 1, 1, 2, 3, 5, 8...).
• Some plants exhibit Fibonacci patterns, like the branching of a tree.
• Honeybee colonies' family trees can also be modeled using Fibonacci numbers, with relationships linked to the parent count.
• The reason for Fibonacci patterns in nature is not well understood.

Tessellations

• Tessellations are patterns formed by repetitive shapes like cubes or tiles.
• Tessellations can occur in living and non-living things.

Technology

• Modern technology relies on basic research and often uses statistics, like GPS requiring an understanding of light speed.
• Various technologies, like weather prediction, internet, computers, and smartphones, use mathematical concepts and principles.

Engineering

• Math is crucial in engineering for design, development, maintenance of components and structures, testing real-life situations, and research.
• Engineering fields like construction, automotive, bridges, robotics, computer circuits, and rockets use math.

Media

• Mathematics is fundamental to media; shapes, proportions, and scale affect various aspects like camera lenses and advertisements.

Medicine and Health

• Medical devices use statistics, with consumer devices relying on math-based feedback and predictions.
• Examples include MRI and tomography, epidemiology, and population dynamics.

Finance and Business

• Business requires financial knowledge, including understanding supply chains, banking, gambling, insurance, loans, and mortgages.
• Mathematics plays a role in business aspects like fraud detection, pricing strategies, and risk management.