MMW Lesson 1

• A pattern is a repeated design or recurring sequence
• Patterns are the repeated or regular way in which something happens or is done
• Patterns can be any regularly repeated arrangement, especially a design made from repeated lines, shapes, or colors on a surface
• In nature, patterns are visible regularities of form found in the natural world
• is when different sides of something are alike
• Symmetry reflections may be mirror images with only two sides or symmetrical on several sides
• Types of symmetries in our surroundings:

  • Reflection / bilateral Symmetry:
  • Also called mirror symmetry or line symmetry
  • Made with a line going through an object dividing it into two mirror image pieces
  • Radial / Rotational Symmetry:
  • Exhibited by objects with similar parts regularly arranged around a central axis
  • Patterns look the same after a certain amount of rotation
  • Translational symmetry:
  • Something has undergone a movement, shift, or slide in a specified direction through a specified distance without rotation or reflection
• • Distances between points, angles, size, and shape do not change, only the location changes
• Fractals are 'never-ending' patterns that repeat indefinitely on an infinitely smaller scale

  • Fractals are objects where the same patterns occur at different scales and sizes
  • Infinitely complex patterns that are self-similar across different scales
• Spirals are common patterns in nature seen in living things

  • Logarithmic spiral is a special type of spiral that gets smaller as it goes
  • Hurricanes, galaxies, and some seashells display logarithmic spirals
• Meander is a series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or other water course
• Waves consist of oscillations or vibrations of a physical medium or a field around relatively fixed locations

  • Surface waves in water show water ripples
• Tessellation is the tiling of a plane using one or more geometric shapes called tiles, with no overlaps and no gaps
• Crack / Fracture is the separation of an object or material into two or more pieces under the action of stress
• Stripes are made by a series of bands or strips, often of the same width and color along the length
• Mathematics is important in daily life and helps with finances, cooking, shopping, computing test scores, and exercise
• Math helps with balancing budgets and subtracting balances for financial management
• Math skills help in adjusting recipes for different servings and calculating discounts while shopping
• Math is essential for calculating test scores and setting goals for exercise and health
• Mathematics is foundational in engineering, agriculture, political science, and geography
• Engineering relies on mathematics for surveying, designing, estimating, and construction
• Agriculture uses math for measurements, investments, production, labor costs, and more
• Political science analyzes voting patterns and factors influencing voting behavior using mathematics
• Geography requires mathematical descriptions of earth, its position, formation of days and nights, rainfall, etc.