The Mathematics of Patterns and Symmetries

Question 1

A transformation changes the _____ , _____, or _________of a figure and creates a new figure.

Answer 1

size
shape
position

Question 2

either rigid or non-rigid; another word for a rigid transformation is “isometry”.

Answer 2

geometry transformation

Question 3

An isometry, such as a ____ , ______ ,
or _____ , does not change the size or shape of the figure.

Answer 3

rotation
translation
reflection

Question 4

not an isometry since it either shrinks or enlarges a figure

Answer 4

A dilation

Question 5

Types of Transformations

Answer 5

1. Translation
2. Reflection
3. Rotation
4. Dilation

Question 6

The initial object to be transformed is
called

Answer 6

pre-image

Question 7

the transformed object is called

Answer 7

image.

Question 8

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.

Answer 8

Translation

Question 9

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

Answer 9

Reflection

Question 10

It is a transformation that turns a figure about a fixed point called the center of rotation. Rotations can be done clockwise or counterclockwise.

Answer 10

Rotation

Question 11

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

Answer 11

Dilation

Question 12

can be combined to yield an effect shown
below.

Answer 12

Translation and reflection

Question 13

Naming of__________ is attributed to ______, an English mathematician who is active in finite theory, knot theory, number
theory, combinatorial game theory and coding theory.

Answer 13

Frieze Patterns
John Conway

Question 14

he died last April 11, 2020 due to COVID19.

Answer 14

John Conway

Question 15

patterns that repeat in a straight vertical or
horizontal line.

Answer 15

Frieze patterns

Question 16

are found in architecture, fabrics, and
wallpaper borders, just to name a few. There are seven types of frieze
patterns and we will discuss each type and how to identify them.

Answer 16

Frieze patterns

Question 17

7 Frieze Patterns

Answer 17

1. Hop (F1)
2. Step (F2)
3. Sidle (F3)
4. Spinning Hop (F4)
5. Spinning Sidle (F5)
6. Jump (F6)
7. Spinning Jump (F7)

Question 18

• A pattern which only involves translation.

Answer 18

1. Hop (F1)

Question 19

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

Answer 19

2. Step (F2)

Question 20

• The third consists of translation and vertical reflection symmetries.

Answer 20

3. Sidle (F3)

Question 21

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

Answer 21

4. Spinning Hop (F4)

Question 22

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

Answer 22

5. Spinning Sidle (F5)

Question 23

• It contains translation and horizontal reflection symmetries.

Answer 23

6. Jump (F6)

Question 24

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

Answer 24

7. Spinning Jump (F7)

Question 25

Symmetry comes from a Greek word _________ meaning _________ and is widely used in the study of geometry.

Answer 25

symmetria
‘to measure together’

Question 26

means that one shape becomes exactly
like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first.

Answer 26

symmetry

Question 27

Not all objects have symmetry;
if an object is not symmetrical, it is called _____

Answer 27

asymmetric

Question 28

widely used in fields of mathematics and
arts, it also appears in chemistry and biology.

Answer 28

Symmetry and pattern

Question 29

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

Answer 29

Bilateral symmetry

Question 30

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

Answer 30

Radial symmetry

Question 31

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

Answer 31

Tessellation

Question 32

The word tessellation comes from Latin word ______, which means a square tablet or die used in gambling.

Answer 32

tessera

Question 33

3 TYPES Tessellations

Answer 33

1. Regular Tessellation
2. Semi-Regular Tessellations
3. Demi-Regular Tessellations

Question 34

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

Answer 34

1. Regular Tessellation

Question 35

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

Answer 35

Archimedean Tessellations

Question 36

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

Answer 36

3. Demi-Regular Tessellations

Question 37

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

Answer 37

2. Semi-Regular Tessellations

Question 38

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

Answer 38

Fractals

Question 39

means repeating a process over and over. In mathematics, iteration means repeating a function over and over.

Answer 39

Iteration

Question 40

a special kind of iteration. With
recursion there is given starting information and a rule for how to use it to get new information.[

Answer 40

Recursion