Overview
This lecture introduces the nature of mathematics by exploring patterns, symmetry, sequences, and their occurrence in nature, concluding with mathematics’ role in real-world applications.
Patterns in Nature and the World
- Patterns are regular, repeated, or recurring forms or designs found in the environment.
- Examples include windows, tiles, spiderwebs, moon phases, and seasons.
- Patterns in numbers include perfect squares (e.g., 1, 4, 9, 16, 25, 36).
- Nature exhibits patterns such as flower petal counts and spiral structures in sunflowers and shells.
Mathematical Patterns and Sequences
- Sequences are ordered lists of numbers called terms, arranged by a specific rule.
- Example sequence: multiplying by 10 (1, 10, 100, 1000, 10000).
- Changing patterns can involve addition, subtraction, multiplication, or other rules.
- The Fibonacci sequence adds the two previous numbers to find the next (1, 1, 2, 3, 5, 8...).
Symmetry
- Symmetry means an object can be divided into parts that are mirror images.
- Bilateral symmetry divides an object into two equal mirror-image halves (e.g., the human body).
- Rotational symmetry exists when an object looks the same after rotation by a certain angle.
- The angle of rotation is calculated as 360° divided by the number of repeated parts.
Applications of Mathematics in Nature and Life
- Packing problems in nature (e.g., beehives) involve maximizing storage with minimal material.
- Mathematics can predict, control, and describe natural phenomena and relationships.
- Mathematics is essential and indispensable in science, engineering, and daily activities.
Key Terms & Definitions
- Pattern — A repeated or recurring form or design.
- Sequence — An ordered list of numbers arranged according to a rule.
- Symmetry — A property where two halves of an object are mirror images.
- Bilateral Symmetry — Symmetry across one line dividing an object into two equal parts.
- Rotational Symmetry — A shape looks the same after being rotated by a partial turn.
- Fibonacci Sequence — A sequence where each term is the sum of the two preceding terms.
- Packing Problem — The mathematical challenge of efficiently filling a space.
Action Items / Next Steps
- Review your module and complete the assessment focused on patterns.
- Observe and record patterns around you as practice for identifying mathematical patterns in nature.