Patterns and Numbers in Nature and Mathematics

Vocabulary flashcards covering types of patterns, key researchers in mathematical biology, and the Fibonacci sequence.

Pattern

A rule that repeats or evolves.

Discrete Patterns

Step-by-step patterns, such as sequences.

Spatial Patterns

Shapes repeating in space, with examples including tiling, fractals, and symmetry.

Dynamic Patterns

Patterns that change over time, such as population, growth, and waves.

Distance Decay

A geographic and social concept where things further apart tend to relate less, impacting maps, communication, and trade.

Benoit Mandelbrot

Conceptualized fractals—patterns in nature that repeat at different scales—and helped connect scaling patterns.

Carl Friedrich Gauss

Studied probability and normal distributions used to model real-world randomness.

Branching in Nature

A pattern observed in trees and blood vessels driven by efficiency to deliver resources with minimal cause.

D'Arcy Wentworth Thompson

Author who wrote the book "ON GROWTH IN FORM: Biology described with math ideas."

Lewis Fry Richardson

Researcher known for his study on the early mathematical modeling of diffusion in processes.

Fibonacci Sequence

A sequence starting with $[0, 1, 1, 2, 3, 5, 8, 13, 21, \frac{}{}]$ where each term is the sum of the previous two.

Fibonacci Sequence Formula

$$F(n) = F(n - 1) + F(n - 2)$$

Leonardo of Pisa (Fibonacci)

Mathematician who popularized the Fibonacci sequence in Europe.

Johannes Kepler

Studied the geometry of nature, leading to the later popularization of golden ratio ideas in relation to natural forms.

Ingrid Daubechies

Modern math biology researcher.