Chapter-1-Mathematics-in-our-World-new

Introduction

• Title: Mathematics in the Modern World

• Institution: Cagayan State University

• Year: MCMLXXVIII

Quotes

• "Education is a natural process carried out by the child and is not acquired by listening to words but by experiences in the environment." - Maria Montessori

• "Look deep into nature, and then you will understand everything better." - Albert Einstein

Overview of Mathematics in Modern World

• Mathematics is defined as a system of knowing or understanding our surroundings.

• It offers insights into the thoughts and perceptions of renowned writers, philosophers, and psychologists.

• Studying their thoughts enhances our understanding of the world.

Key Concepts

Nature of Mathematics

• The rise of digital technology has increased data consumption and production.

• Accessibility to information is much faster compared to pre-internet times.

• Example: Research papers that used to take hours now only take minutes.

Patterns Recognition

• Humans are naturally inclined to recognize patterns, both consciously and subconsciously.

• Historical examples include the cycles of day and night, lunar phases, and seasonal changes.

• Patterns in nature and society can lead to survival and understanding of the world.

Mathematics in Nature and Human Endeavors

Patterns in Nature

• Patterns are evident in various forms such as the layout of tiles, design of skyscrapers, etc.

• Studying these patterns aids in identifying relationships and making generalizations.

Examples of Patterns in Nature

1. Snowflakes

   • Symmetry in snowflakes and how humidity and temperature affect their formation.

2. Honeycomb

   • Efficient hexagonal structure for honey storage, minimizing beeswax usage.

3. Flower Petals

   • Different flowers exhibit a unique number of petals related to the Fibonacci sequence.

4. Sunflower Seeds

   • Arranged spirals following Fibonacci numbers for optimal light access.

5. Snail Shells

   • Spiraled shells expanding proportionally as snails grow depict equiangular spirals.

Mathematical Sequences

Definition of a Sequence

• A sequence is an ordered list of numbers (terms) with potential repetitions.

• Sequences can be finite (with a definite number of terms) or infinite, like the Fibonacci sequence.

Analysis of Sequences

• Analyzing patterns helps in predicting future terms and relationships.

• Examples illustrate adding constants or observing changes in increment.

• Fibonacci Sequence: Derived from rabbit reproduction, visible in nature through various forms.

Applications of Mathematics

Predicting Natural Behavior

• Mathematics aids in predicting events like natural disasters through fractals.

• Benoit Mandelbrot’s work on fractals elucidates order in complex systems.

Mathematical Tools in Organizations

• Organizations utilize mathematical methods to analyze data for strategic adjustments.

• Histories of events help predict probabilities, such as in weather forecasting.

Control Through Mathematics

• Fractal Geometry finds applications across diverse fields: engineering, computer graphics, medicine, etc.

• Understanding patterns through mathematics allows for exerting control over nature's processes.

Indispensable Nature of Mathematics

• Applications:

  • Building structures.

  • Financial management.

  • Enhancing knowledge in various fields.

Reflections on Learning Mathematics

Short Response Questions

1. What new ideas about Mathematics did you learn?

2. How have your thoughts changed regarding Mathematics?

3. What is the most useful aspect of Mathematics for humankind?

Suggested Activities

• Explore patterns in nature; create photographic exhibits or portfolios.

• Prepare a video presentation on mathematical patterns.

References

• Essential Mathematics for the Modern World by Nocon and Nocon

• Nature’s Numbers by Ian Stewart

• Mathematical Excursions (Ch. 1) by R. Aufmann

• Video: https://vimeo.com/9953368