Title: Mathematics in the Modern World
Institution: Cagayan State University
Year: MCMLXXVIII
"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
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.
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.
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.
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.
Snowflakes
Symmetry in snowflakes and how humidity and temperature affect their formation.
Honeycomb
Efficient hexagonal structure for honey storage, minimizing beeswax usage.
Flower Petals
Different flowers exhibit a unique number of petals related to the Fibonacci sequence.
Sunflower Seeds
Arranged spirals following Fibonacci numbers for optimal light access.
Snail Shells
Spiraled shells expanding proportionally as snails grow depict equiangular spirals.
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.
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.
Mathematics aids in predicting events like natural disasters through fractals.
Benoit Mandelbrot’s work on fractals elucidates order in complex systems.
Organizations utilize mathematical methods to analyze data for strategic adjustments.
Histories of events help predict probabilities, such as in weather forecasting.
Fractal Geometry finds applications across diverse fields: engineering, computer graphics, medicine, etc.
Understanding patterns through mathematics allows for exerting control over nature's processes.
Applications:
Building structures.
Financial management.
Enhancing knowledge in various fields.
What new ideas about Mathematics did you learn?
How have your thoughts changed regarding Mathematics?
What is the most useful aspect of Mathematics for humankind?
Explore patterns in nature; create photographic exhibits or portfolios.
Prepare a video presentation on mathematical patterns.
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