Mathematics in the Modern World - Vocabulary Flashcards

A set of vocabulary flashcards covering key concepts from the notes on mathematics, patterns, symmetry, and natural patterns.

Mathematics

A language that uses symbols and notations to describe numerical, geometric, and graphical relationships; a human activity that observes, represents, and investigates patterns and relationships in physical and social phenomena and among mathematical objects.

Pattern

A regular, repeated, or recurring arrangement or design that reveals relationships and helps form generalizations.

Radial symmetry

Symmetry obtained by rotating an object by a fixed angle (360° divided by the number of folds) to reproduce the same figure.

Bilateral symmetry

Symmetry achieved by drawing an imaginary line that divides an object into two equal mirrored halves.

Snowflake (Natural Chaotic Symmetry)

A natural example of symmetry with delicate, intricate patterns that are symmetric and aesthetically harmonious.

Honeycomb

A hexagonal lattice structure (bees’ wax) that efficiently fills space; hexagons optimize packing and space usage.

Tiger stripes and spots

Notable natural patterns used for camouflage: stripes in some animals (e.g., tigers, zebras) and spots in others (e.g., leopards, hyenas).

Constellations

Groups of stars named as patterns in the sky; examples include Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.

Four seasons

The annual cycle of weather patterns; a recurring natural pattern in nature.

Pi (π)

The mathematical constant representing the ratio of a circle’s circumference to its diameter; approximately 3.14.

Pythagorean theorem

In a right triangle, a^2 + b^2 = c^2, relating the lengths of the sides.

Difference of squares

Factoring identity: a^2 − b^2 = (a + b)(a − b).

Square of a binomial

Expansion: (a + b)^2 = a^2 + 2ab + b^2.

Power rule for multiplication (exponents)

(ab)^n = a^n b^n, the rule for raising a product to a power.

Pattern types

Regular, Repeated, Recurring forms or designs; identifying these helps reveal relationships and form generalizations.

Natural phenomena patterns

Patterns in nature such as waves, sand dunes, rock formations, stalagmites/stalactites, and the formation of typhoons.