Mathematics Chapter 1: Nature and Patterns

Chapter 1: Nature of Mathematics

• Learning Outcomes:
  • Recognize the significance of mathematics in everyday life
  • Explain the value of mathematics in daily life
  • Identify patterns and regularities in the natural world
  • Understand and illustrate the Fibonacci sequence

Chapter 1.1: Patterns and Numbers in Nature and the World

• Patterns: Recurring and predictable arrangements of objects, events, or actions, perceived as meaningful or significant

In Mathematics: Fibonacci Sequence

• The Fibonacci sequence is (0, 1, 1, 2, 3, 5, 8, 13, 21, 34)
• This sequence is prevalent in nature (e.g., sunflowers, pinecones, Romanesco broccoli, seashells, galaxies)

In Art

• Repeated design
• Shapes
• Colors
• Tessellations

In Music

• Rhythm
• Melody
• Harmony of a piece
• Repeated chorus of a song

In Language

• Structure and grammar of a sentence
• Subject-Verb-Object (SVO) pattern
  • Subject: Who or what the sentence is about
  • Verb: What the subject is doing or the action
  • Object: Who or what receives the action

In Nature

• Shapes and structures of plants and animals

Real-Life Applications of Patterns

• Symmetry
  • Balanced and harmonious arrangement of identical or similar parts
  • Types of Symmetry:
    • Bilateral Symmetry: Mirror image of each other
    • Radial/Rotational Symmetry: Has a central point.
• Fractals: Never ending pattern (e.g., fern leaves, branching of trees)
• Spiral: Circling around a central point (e.g., sheep horn, seed head of a sunflower, Aloe polyphylla)
• Waves and Dunes: Alterations in space or matter transmitting energy (e.g., ocean waves, sand dunes)
• Tessellations: Tile patterns created by repetition (e.g., honeycomb, fish scales, scales of snake fruit)
• Cracks or Fractures: Linear slits releasing tension in materials (e.g., old pottery surface, dry mud)
• Stripes and Spots: Succession of bands (e.g., butterflies, zebras)
• World Population: Understanding trends and phenomena

Why Learn Mathematics?

• Mathematics is essential in daily life and advanced scientific research.
• Mathematics helps solve problems, organize activities (like playing games, art, spending money etc), and allows for technological innovation.

Examples

• Telling time involves numbers and other math skills
• Measuring distances uses rulers or tape measures
• Using money involves counting, saving, and spending money math skills.
• Weighing involves using scales.
• Adding or dividing is possible with calculators
• Construction uses math to determine sizes and measures needed
• Cooking uses math to measure ingredients.