The Nature of Mathematics

Why are honeycomb cells hexagonal? Why are planets spherical? Why are seashells spiral? Why are tigers' skin striped and cheetahs' spotted? Why are there wavy patterns on dessert sand dunes? 

Simple answer is --- because there is mathematics in nature.

Numbers, patterns, and mathematical rules keep the laws of nature working. Their shape, behavior, or existence are governed by some mathematical reason.

• Honeycomb cells are hexagonal because it's the best shape in order to cover more space but using the smallest amount of beeswax. (Read this or watch this to know more).

• Wave patterns in sand dunes are caused by aerodynamics between the dessert's surface and the atmosphere. (Here's a paper explaining the pattern using some equations.)

• Mathematical biologists model animal skin patterns using some advanced mathematics. One of which is called Turing's Model. Here is an article that explains it without much numbers involved.

So nature --- although it looks so complicated and random --- just appears to be governed by math.

Intended Learning Outcomes

• Identify patterns in nature and regularities in the world.

• Articulate the importance of mathematics in one's life.

• Argue about the nature of mathematics, what it is, how it is expressed, represented, and used.

• Express appreciation for mathematics as a human endeavor.

Lectures

• Lecture 1. Patterns and Numbers in Nature and the World

• Lecture 2. The Fibonacci Sequence

• Lecture 3. Mathematics for our World