Mathematics in the Modern World

50 vocabulary flashcards covering Chapter I: Mathematics in Our World.

Mathematics

The study of the relationships among numbers, quantities, and shapes.

Arithmetic

The branch of mathematics that deals with numbers and their basic operations.

Algebra

A branch of mathematics in which arithmetic is extended to deal with unknown numbers or relationships using letters and other symbols.

Geometry

A branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

Trigonometry

A branch of mathematics dealing with the study of the relationship between the sides and angles of a right-angled triangle.

Statistics

The study of how to collect, organize, analyze, and interpret numerical information from data.

Calculus

The mathematics of change and motion.

Brahmagupta

The mathematician identified in the lecture notes associated with arithmetic.

Abu Jafar Muhammad Ib’n Al-Khwarizmi

The mathematician identified in the lecture notes associated with algebra.

Euclid

The mathematician identified in the lecture notes associated with geometry.

Hipparcus

The mathematician identified in the lecture notes associated with trigonometry.

Sir Ronald Aylmer Fisher

The statistician identified in the lecture notes associated with statistics.

Wilhelm Leibniz

The mathematician identified in the lecture notes associated with calculus.

Patterns in Nature

Visible regularities found in the natural world that persist in different contexts and can be modelled mathematically.

Numeric Patterns

One of two historical types of patterns studied by mathematicians, consisting of sequences of numbers.

Geometric Patterns

One of two historical types of patterns studied by mathematicians, consisting of sequences of geometric shapes or figures.

Spiral

A pattern formed by a circular curving line that goes around a central point while getting closer to or farther away from it.

Symmetry

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

Bilateral Symmetry

Also known as line symmetry, a form of symmetry where an object is mirrored across an axis.

Rotational Symmetry

The property a shape has when it looks the same after some rotation by a partial turn.

Angle of Rotation

The smallest angle that a figure can be rotated while preserving its original formation.

Angle of Rotation Formula

$\text{Angle of rotation} = \frac{360^\circ}{n}$, where $n$ is the order of rotation.

Mosaics

Something made up of different things that together form a pattern.

Stripes

A line or long narrow section differing in color or texture from adjoining parts.

Alan Turing

British mathematician who predicted the mechanism of morphogenesis and theorized that cellular chemical reactions and diffusion processes determine animal growth patterns like spots and stripes.

Tessellations

The tiling of a plane using one or more geometric shapes, called tiles, with no overlaps.

Radial Pattern

A pattern arranged with parts extending in straight lines outward from the center of a circle.

Joseph Plateau

19th-century Belgian physicist who examined soap films, leading him to formulate the concept of a minimal surface.

Minimal Surface

A concept formulated by Joseph Plateau in the 19th century after examining soap films.

Ernst Haeckel

19th-century German biologist and artist who painted hundreds of marine organisms to emphasize their symmetry.

D’Arcy Thompson

19th-century Scottish biologist who pioneered the study of growth patterns in plants and animals, showing that simple equations could explain spiral growth.

Aristid Lindenmayer

Hungarian biologist who, alongside Benoit Mandelbrot, showed how the mathematics of fractals could create plant growth patterns.

Benoit Mandelbrot

French-American mathematician who showed how fractal mathematics could create plant growth patterns.

W. Gary Smith

Landscape worker who adopted eight patterns in his work: scattered, fractured, mosaic, naturalistic drift, serpentine, spiral, radial, and dendritic.

Eight Landscape Patterns of W. Gary Smith

Scattered, fractured, mosaic, naturalistic drift, serpentine, spiral, radial, and dendritic.

Leonardo Pisano Bigollo

Italian mathematician (c. 1170–1250) nicknamed Fibonacci ('Son of Bonacci'), known for spreading Hindu-Arabic numerals across Europe and for the Fibonacci Sequence.

Hindu-Arabic Numerals

The digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ spread through Europe by Fibonacci to replace Roman numerals.

Fibonacci Sequence

A sequence of numbers defined by $0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \dots$

Fibonacci Day

An annual observance celebrated on Nov. 23.

nth Term Formula of Fibonacci Sequence

$F_n = \frac{\phi^n - (1 - \phi)^n}{\sqrt{5}}$, where $\phi \approx 1.618034$ and $n$ is the $n\text{th}$ term.

Golden Ratio

A constant represented by phi ($\phi$), approximately equal to $1.618034$, which is approached by the ratio of any two successive Fibonacci numbers.

Golden Spiral

A logarithmic spiral whose growth factor is phi ($\phi$), the golden ratio.

Fibonacci Flowers (3 Petals)

Flowers exhibiting 3 petals, such as the lily and iris.

Fibonacci Flowers (5 Petals)

Flowers exhibiting 5 petals, such as the wild rose, larkspur, buttercup, and columbine.

Fibonacci Flowers (13 Petals)

Flowers exhibiting 13 petals, such as ragwort, corn marigold, and cineraria.

Motion of a Pendulum

Harmonic motion where the period (time taken to swing back to original position) is related to length in a non-linear manner.

Free-Falling Object

An object falling under the sole influence of gravity, obeying the equations of uniformly accelerated vertical motion.

Action-Reaction Pair of Forces

Equal and opposite forces acting simultaneously on two interacting objects in an interaction.

Mathematics for Organization

The use of mathematical tools to organize data, conduct sound analysis, and guide decisions (e.g., store shopping habits, plotting animal migration routes).

Mathematics for Prediction

The use of mathematical models and probability to calculate event chances and forecast outcomes (e.g., weather forecasting).