Geometry of Design Flashcards

Vocabulary flashcards covering symmetries, geometric transformations, tessellations, and frieze patterns from the Geometry of Design lecture notes.

Symmetry

A balanced arrangement of parts where one part matches another.

Line of Symmetry

An imaginary line that divides a figure into two identical mirror-image parts.

Reflection Symmetry

A property of a figure that can be divided into two mirror-image halves.

Rotational Symmetry

A property of a figure that looks the same after being rotated less than $360^{\circ}$.

Center of Rotation

The fixed point around which a figure rotates.

Angle of Rotation

The smallest angle through which a figure rotates and matches its original position.

Translation

A transformation that moves every point of a figure the same distance in the same direction, preserving shape and size (isometry).

Reflection

A transformation that maps each point to its mirror image across a fixed line called the line of reflection (axis).

Rotation

A transformation that turns every point of a figure through an angle about a fixed point called the center of rotation.

Dilation

A transformation that enlarges or reduces a figure by a scale factor $k$ from a center of dilation; it is NOT an isometry.

Glide reflection

The composition of a translation (glide) along a line followed by a reflection over that same line; it is the only isometry that cannot be reduced to a single simpler transformation.

Tessellation (or tiling)

An arrangement of one or more shapes that completely covers a plane with NO gaps and NO overlaps.

Monohedral

A tessellation that uses only one shape.

Polyhedral

A tessellation that uses multiple shapes.

Maurits Cornelis Escher (1898–1972)

A Dutch graphic artist known for transforming simple geometric shapes into recognizable figures like birds, fish, and lizards.

Metamorphosis

An Escher technique where shapes gradually transform from one motif into another.

Frieze Pattern (or border pattern)

An infinite strip design that repeats a motif along a single axis, extending infinitely in both directions while remaining bounded vertically.

Hop

A frieze pattern transformation involving translation only.

Jump

A frieze pattern transformation involving Translation + Horizontal Reflection.

Sidle

A frieze pattern transformation involving Translation + Vertical Reflections.

Spinning Hop

A frieze pattern transformation involving Translation + $180^{\circ}$ Rotation.

Step

A frieze pattern transformation involving Translation + Glide Reflection.

Spinning Sidle

A frieze pattern transformation involving Translation + Vertical Reflection + $180^{\circ}$ Rotation.

Spinning Jump

A frieze pattern transformation involving all 4 transformations.