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MAT 101 > T5: Patterns and Symmetry > Flashcards

T5: Patterns and Symmetry Flashcards

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1
Q

a repeated arrangement of numbers, shapes, colors and so on

A

PATTERN

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2
Q

is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns

A

Geometric pattern

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3
Q

If the set of numbers are related to each other in a specific rule, then the rule or manner is called a __________

A

PATTERN

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4
Q

defined as one shape is exactly like the other shape when it is moved, rotated, or flipped

A
  • Symmetry
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4
Q

any non-empty plane set

A

motif

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5
Q

repetitions of a motif in the plane

A

pattern

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6
Q

is the rotation of a motif in a fixed angle about a fixed point

A

isometry

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7
Q

is either rigid or non-rigid

A

geometry transformation

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8
Q

is not an isometry since it either shrinks or enlarges a figure

A

dilation

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9
Q

The initial object to be transformed is called

A

pre-image

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10
Q

the transformed object is called

A

image

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11
Q

TYPES OF TRANSFORMATIONS

A
  1. Translation
  2. Reflection
  3. Rotation
  4. Dilation
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12
Q

It is a transformation in which the figure or object is mirror image of the other

A

REFLECTION

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13
Q

A mathematical term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way

A

TRANSLATION

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14
Q

It is a transformation that turns a figure about a fixed point called the center of rotation

A

ROTATION

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15
Q

is a transformation that changes the size of a figure. It can become larger or smaller, but the shape remains the same

A

DILATION

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16
Q

Translation and reflection can be combined to yield an effect

A

GLIDED REFLECTION

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17
Q

an English mathematician who is active in finite theory, knot theory, number theory, combinatorial game theory and coding theory

A

John Conway

18
Q

patterns that repeat in a straight vertical or horizontal line

A

FRIEZE PATTERNS

19
Q

A pattern which only involves translation

A

HOP

19
Q

DIFFERENT TYPES OF FRIEZE PATTERNS

A
  1. Hop
  2. Step
  3. Slide
  4. Spinning hop
  5. Spinning slide
  6. Jump
  7. Spinning jump
20
Q

it is a combination of translation and reflection shown by the following figure. Conway also called it glide reflection symmetry

A
  1. STEP
21
Q

The third consists of translation and vertical reflection symmetries

A

SLIDE

22
Q

It contains translation and rotation (by half turn or rotation at 180o angle) symmetries

A

SPINNING HOP

23
Q

It contains translation, glide, reflection and rotation (by a half-turn or rotation at 180o angle) symmetries

A

SPINNING SLIDE

24
Q

It contains translation and horizontal reflection symmetries

A

JUMP

25
Q

It contains all symmetries ( translation, horizontal and vertical reflection, and rotation)

A

SPINNING JUMP

26
Q

If translation symmetry is added in a second, independent direction

A

WALLPAPER GROUPS

27
Q

meaning ‘to measure together’

A

symmetria

28
Q

TWO KINDS OF SYMMETRY

A
  1. Bilateral symmetry
  2. Radial symmetry
29
Q

if an object is not symmetrical

A

asymmetric

30
Q

in which an object has two sides that are mirror images of each other

A

Bilateral symmetry

31
Q

this is where a center point and numerous lines of symmetry could be drawn

A

Radial symmetry

31
Q

A pattern covering a plane by fitting together replicas of the same basic shape

A

TESSELLATION

32
Q

a square tablet or die used in gambling

A

tessera

33
Q

DIFFERENT TYPES OF TESSELLATIONS

A
  1. Regular Tessellation
  2. Semi-Regular Tessellation
  3. Demi-Regular Tessellation
34
Q

A tessellation made up of congruent regular polygons which have the following properties:
o The tessellation must tile a floor (that goes on forever) with no overlaps or gaps.
o The tiles must be the same regular polygons.

A

REGULAR TESSELLATION

35
Q

Also known as Archimedean Tessellations are regular tessellations of two or more different polygons around a vertex which has the same arrangement of polygons

A

SEMI-REGULAR TESSELLATION

36
Q

Is an edge-to-edge tessellation, but the order or arrangement of polygons at each vertex is not the same.

A

DEMI-REGULAR TESSELLATION

37
Q

The function which iterates a figure to make it smaller and smaller or bigger and bigger using a scaling factor

A

FRACTALS

38
Q

means repeating a process over and over

A

ITERATION

39
Q

is a method for generating fractals involving a large number of calculations of a simple formula

A
  • The Iterative Function System (IFS)
40
Q

is a special kind of iteration

A
  • Recursion

MAT 101 (7 decks)

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