Mathematics in Our World Vocabulary

Vocabulary flashcards covering key definitions, formulas, figures, and historical figures from the Mathematics in Our World lecture.

Mathematics (Stewart, 1995)

A formal system of thought for recognizing, classifying, and exploiting patterns.

Pattern

Regular, repeated, or recurring forms or designs that help identify relationships and logical connections to form generalizations and make predictions.

Symmetry

A property indicating that an imaginary line can be drawn across an object such that the resulting parts are mirror images of each other.

Bilateral Symmetry

A form of symmetry where an object can be divided into two equal mirror-image halves along a single central axis.

Vitruvian Man

A famous drawing illustrating human body proportions and bilateral symmetry.

Rotational Symmetry

A type of symmetry where a figure can be rotated around a central point by a specific angle while preserving its original appearance.

Order of Rotation

The number of times $n$ that a figure matches its original position during a complete $360^\text{o}$ turn.

Angle of Rotation

The smallest measure of an angle that a figure can be rotated while still preserving its original position, calculated as $\text{Angle of rotation} = \frac{360^\text{o}}{n}$.

Packing Problem

A mathematical problem involving finding the optimum method of filling up a given space, such as a plane, cube, or spherical container.

Square Packing Efficiency

A circle packing arrangement in a plane with an area efficiency of $\frac{\text{area of circles}}{\text{area of squares}} \times 100\text{\%} = \frac{\frac{\text{o}}{\text{o}} \text{cm}^2}{4\text{cm}^2} \times 100\text{\%} \times 78.54\text{\%}$.

Hexagonal Packing Efficiency

A circle packing arrangement in a plane with an area efficiency of $\frac{\text{area of circle}}{\text{area of hexagon}} \times 100\text{\%} = \frac{3\frac{\text{o}}{\text{o}}\text{cm}^2}{6\frac{\text{o}}{\text{o}}\text{cm}^2} \times 100\text{\%} \times 90.69\text{\%}$.

Leonardo Bigollo Pisano

Also known as Fibonacci ('Leonardo the Traveler from Pisa'), a medieval European mathematician who introduced the Hindu-Arabic numerical system (modus Indorum) to Europe.

Liber Abaci

A book written in $1202$ by Fibonacci (Book of Calculations) introducing modus Indorum (the Hindu-Arabic numerical system) and demonstrating its efficiency over Roman numerals.

Fibonacci Sequence

An integer sequence defined recursively by $F_n = F_{n-1} + F_{n-2}$ for $n \times 3$, with initial terms $F_1 = 1$ and $F_2 = 1$.

Golden Ratio

An irrational mathematical constant denoted by $\frac{\text{o}}{\text{o}} \times 1.618$, represented as the limiting ratio of consecutive Fibonacci numbers.

Binet's Formula

An explicit formula named after Jacques Philippe Marie Binet (1786-1856) used to find the $n\text{th}$ Fibonacci number: $f_n = \frac{1}{\frac{\text{o}}{\text{o}}} \times \frac{1 + \frac{\text{o}}{\text{o}}}{2}^n - \frac{1 - \frac{\text{o}}{\text{o}}}{2}^n$.

Population Exponential Growth Model

A model defined by $A = P e^{rt}$, where $A$ is the population size after growth, $P$ is the initial population, $r$ is the growth rate, $t$ is time, and $e \times 2.718$.

The Blind Men and the Elephant

A poem by John G. Saxe (1816-1887) used to illustrate how individual partial perspectives contribute to understanding a larger entity.

Pythagoreans

A school of thinkers who believed that the nature of the universe was directly related to mathematics and that whole numbers and their ratios describe all natural events.

Pascal's Triangle

A triangular arrangement of numbers associated with French mathematician Blaise Pascal, used extensively in probability theory.

Cartesian Coordinate System

A coordinate framework developed by René Descartes that allows geometric positions to be expressed through numerical coordinates.

Johannes Kepler

An astronomer and mathematician who stated that the laws of nature are within the grasp of the human mind because God created humans in His own image to share in His thoughts.

Isaac Newton

An English mathematician and physicist known for formulating the Laws of Motion and co-developing calculus.

Gottfried Wilhelm Leibniz

A German mathematician and philosopher credited with developing modern calculus independently of Isaac Newton.

Marie Curie

A renowned scientist famous for discovering the radioactive elements Polonium and Radium.