Patterns and Numbers in Nature and the World

Flashcards covering mathematical patterns in nature, types of symmetry, fractals, and the Fibonacci sequence as discussed in the lecture.

Ian Stewart

The author of the book "Nature by Numbers" who mentioned that we live in a universe of patterns.

Mathematics

Described as the cradle of all creations, it is a tool used to express, solve, and interpret puzzles observed in nature while making life orderly and systematic.

Symmetry

An exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

Reflection Symmetry

Also called mirror symmetry, line symmetry, or bilateral symmetry, it occurs when a line divides an object into two pieces that are mirror images of each other.

Rotational Symmetry

Also known as radial symmetry, this occurs when similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation.

Angle of Rotation for Starfish

Calculated by dividing $360$ by $5$ (since it has a $5$-fold symmetry), resulting in $72$. If rotated by $72$, the starfish achieves the same appearance as its original position.

Translational Symmetry

Exhibited by objects like a comb or brick which do not change size and shape even if moved to another location, provided the movement does not involve reflection or rotation.

Fractals

Never-ending patterns that are self-similar across different scales, where the image reappears over and over regardless of magnification.

Spirals

Curved patterns made by a series of circular shapes revolving around a central point.

Spots and Stripes

Patterns exhibited in the external appearances of various animals.

Flower Petals

Natural structures that have different numbers of petals, with $5$ petals being considered the most common.

Leonardo Pisano Bigollo

A famous Italian mathematician born in $1170$ and died in $1240$ who discovered the Fibonacci sequence and introduced the Arabic number system in Europe.

Fibonacci

A short term for the Latin "Filius Bonacci", which translates to "the son of Bonacci".

Fibonacci sequence

An infinite sequence of integers $0, 1, 1, 2, 3, 5, 8, 13 \text{...}$ where each subsequent number is found by getting the sum of the two preceding numbers.

Sequence

An ordered set of numbers, shapes, or any other mathematical objects arranged according to a rule.

Fibonacci Multiples Rules

In the sequence, every $3^{rd}$ term is a multiple of $2$, every $4^{th}$ term is a multiple of $3$, every $5^{th}$ term is a multiple of $5$, and every $6^{th}$ term is a multiple of $8$.