MATH 1

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Last updated 11:29 AM on 9/10/26
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50 Terms

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Phyllotaxis
The arrangement of plant leaves in a beautiful geometric pattern around the stem
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Symmetry

A figure or design is symmetric if there is an isometry that maps the figure onto itself

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Geometry

is the fundamental science of forms and their order

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Transformation
A function which changes the position, orientation, and possibly the size of a geometric shape
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Prime

a transformed shape is labelled with the same letters with this symbol attached

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Translation
Each point of a figure is moved the same distance in the same direction
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Vector of translation
A translation is determined by this
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Translational symmetry
A figure has this if it looks the same after being moved a certain distance in a straight line
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Reflection
A figure is reflected about a line called the line of reflection or reflection axis
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Line of reflection
A reflection is determined by this
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Reflection symmetry
A figure that has two sides that are mirror images of each other
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Line of symmetry
An imaginary line that divides a shape or object into two identical matching halves
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Rotation
A figure is rotated about a fixed point through a given angle
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Center of rotation
A rotation is determined by this and an angle of rotation
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Angle of rotation

A rotation is determined by a center and this. Smallest angle the object can be rotated to coincide with itself

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Rotational symmetry

A pattern has this if it is mapped by a rotation of angle 360° divided by n onto itself

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Order of rotation
The number n in n-fold rotational symmetry
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Order 1 rotational symmetry
It actually means the figure has no rotational symmetry
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Order of symmetry

number of times a figure maps onto itself as it rotates from 0 to 360

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Dilation
A figure is resized by a scale factor about a point
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Scale factor
A dilation is determined by this and a point of dilation
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Point of dilation
A dilation is determined by a scale factor and this
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Isometry
A transformation that preserves distance
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Glide reflection
A product of a reflection and a translation whose direction is parallel with the line of reflection
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Parallel vector
A glide reflection is determined by a line of reflection and this
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Symmetric pattern
A figure or design that has an isometry which maps the figure onto itself
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Symmetry group
The set of all isometries that map the figure onto itself
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Rosette patterns
Finite symmetric patterns whose symmetry group contains no translation
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Cyclic

The symmetry group consists of rotations only such that the highest order of rotation is n
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Dihedral

The symmetry group consists of rotations and reflections where the highest order of rotation is n
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Frieze pattern
A basic motif repeats itself indefinitely in one direction
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Frieze symmetry group
It necessarily contains translations in one direction
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HOP
The symmetry group contains translations only
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STEP
The symmetry group contains translations and glide reflections only
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SIDLE
The symmetry group contains translations and vertical reflections only
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JUMP
The symmetry group contains translations, a horizontal reflection, and glide reflection
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SPINNING HOP
The symmetry group contains translations and rotations of 180°
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SPINNING SIDLE
The symmetry group contains translations, vertical reflections, rotations, and glide reflections
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SPINNING JUMP
The symmetry group contains translations, vertical reflections, horizontal reflections, rotations, and glide reflections
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Wallpaper pattern
A pattern covers the plane and can be mapped onto itself by translations in more than one direction
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There are blank number of wallpaper patterns

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p1
The symmetry group contains translations only
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p2
The symmetry group contains rotations of 180° and translations
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p3
The symmetry group contains rotations of 120° and translations
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p4
The symmetry group contains rotations of order 90° and translations
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pm
The symmetry group contains translations and reflections parallel to one axis of translation and perpendicular to the other axis of translation
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Tessellation
A repeating pattern of closed shapes that covers a surface with no gaps and no overlaps
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Tesserae
The root word from which the word tessellation comes and which means tile
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M.C. Escher
The most famous tessellation artist
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Regular polygon
Escher knew that only a regular polygon like a square, triangle, or hexagon could be tessellated