Finite Mathematics – Geometry of Design & Patterns in Nature

Vocabulary flashcards covering core terms from the Finite Mathematics lecture on symmetry, geometric transformations, tessellations, patterns, and mathematical constants found in nature and art.

Finite Mathematics

A branch of mathematics focusing on practical applications of mathematical concepts in fields like business, economics, social sciences, and the arts; emphasizes problem-solving and critical thinking.

Geometry of Design

Content domain in Finite Mathematics that explores symmetries, transformations, tessellations, Frieze patterns, and mathematical patterns in nature and art.

Symmetry

A balanced and proportionate similarity between two halves of an object; one half is a mirror image of the other.

Symmetric Figure

An object whose halves are identical after a symmetry transformation.

Asymmetric Figure

An object that lacks symmetry; its halves are not identical.

Reflection Symmetry

A transformation in which a figure is flipped across a line of symmetry, producing mirror-image halves.

Line of Symmetry

The line across which a figure is reflected to create reflection symmetry.

Rotational Symmetry

A property where a figure looks the same after being rotated around a fixed point by a certain angle.

Center of Rotation

The fixed point about which a figure is rotated in rotational symmetry.

Angle of Rotation

The smallest positive angle through which a figure can be rotated to map onto itself.

Translation

A geometric transformation that slides every point of a figure the same distance in the same direction.

Dilation

A transformation that enlarges or reduces a figure by a scale factor relative to a fixed center.

Glide Reflection

A transformation combining a translation followed by a reflection across a line parallel to the translation.

Tessellation

A tiling of the plane using one or more polygons with no gaps or overlaps.

Escher-type Tessellation

An artistic tessellation inspired by M.C. Escher that often uses complex, interlocking shapes created through geometric transformations.

Frieze Pattern

An infinite strip pattern that repeats in one direction and can be generated by specific geometric transformations.

Golden Ratio (φ)

An irrational number, approximately 1.618, where a/b = (a+b)/a; often associated with aesthetics in nature and art.

Golden Rectangle

A rectangle whose side lengths are in the golden ratio.

Golden Spiral

A logarithmic spiral that grows outward by a factor of the golden ratio for every quarter-turn.

Golden Angle

An angle (≈137.5°) that divides a circle into two arcs whose lengths are in the golden ratio; observed in plant phyllotaxis.

Fibonacci Sequence

A sequence starting 0, 1, 1, 2, 3, 5, 8… where each term is the sum of the two preceding terms.

Fibonacci in Nature

Occurrences of Fibonacci numbers in biological settings, such as leaf arrangement, seed heads, and spiral shells.

Fractal

A self-similar geometric object that displays complexity at every scale; examples include snowflakes and coastlines.

Reflection Symmetry in Nature

Natural instances where organisms or structures exhibit mirror-image halves, e.g., butterfly wings or human faces.

Pattern Recognition

The cognitive skill of identifying regularities or structures; enhanced through studying symmetry and tessellations.