1.2 Patterns and Numbers in Nature

Question 1

It is an arrangement which helps observers anticipate what they might see or what happens next. It
also shows what may have come before. It organizes information so that it becomes more useful.

Answer 1

Pattern

Question 2

It is a study of patterns and relationship, a way of thinking, an art, a language, and a tool. It is about patterns and relationships.

Answer 2

Mathematics according to e National Council of Teachers of Mathematics
(1991)

Question 3

It include symmetries,

fractals, spirals, meanders, waves, foams, tessellations, cracks, and stripes.

Answer 3

Natural Patterns

Question 4

It occurs when there is congruence
in dimensions, due proportions and arrangement. It can also be explained as the passage of time, a
spatial relationship and an aesthetic element found within abstract objects, theoretic models, language,
music and even knowledge itself.

Answer 4

Symmetry / Mathematical Symmetry

Question 5

The objects have a left side and a right side that are mirror images of each other. If a shape can be folded in half so that one half fits exactly on top of the other, then we say that the shapes are symmetric.

Answer 5

Reflection / Bilateral Symmetry / Mirror Symmetry

Question 6

The

fold is called a (???) because it divides the shape into two equal parts.

Answer 6

Line of Symmetry

Question 7

Bilateral-symmetric

objects have at least one (???). The lines of symmetry may be in any direction.

Answer 7

Line or Axis of Symmetry

Question 8

It is rotational symmetry around a fixed point known as the center. Images with more than
one lines of symmetry meeting at a common point exhibits this.

Answer 8

Radial Symmetry

Question 9

A pattern that repeat in no direction. It s consist of taking motif or an element and rotating and/or reflecting that element.

Answer 9

Rosette Pattern

Question 10

A rosette pattern is (cyclic, dihedral) if it

only admits rotational symmetries

Answer 10

Cyclic

Question 11

A rosette pattern is (cyclic, dihedral) if it admits both

rotational symmetries and bilateral or reflectional symmetries.

Answer 11

Dihedral

Question 12

A pattern that repeats in exactly one direction. It extends to the left and right in a way that the pattern can be mapped onto itself by a horizontal translation.

Answer 12

Frieze Pattern

Question 13

What are the seven types of Frieze Pattern?

Answer 13

1. Hop
2. Step
3. Sidle
4. Spinning hop
5. Spinning Sidle
6. Jump
7. Spinning Jump

Question 14

Type of Frieze Pattern:

The frieze pattern only admits a translational symmetry.

Answer 14

Hop

Question 15

Type of Frieze Pattern:

The frieze pattern only admits a translational and glide symmetries.

Answer 15

Step

Question 16

Type of Frieze Pattern:

The frieze pattern only admits translations and vertical reflections.

Answer 16

Sidle

Question 17

Type of Frieze Pattern:

The frieze pattern only admits translations and 180◦
rotations (half-turns).

Answer 17

Spinning Hop

Question 18

Type of Frieze Pattern:

The Frieze Pattern only admits translations, vertical reflections, rotations, and
glide reflections.

Answer 18

Spinning Sidle

Question 19

Type of Frieze Pattern:

The frieze pattern only admits translations, a horizontal reflection, and glide reflection.

Answer 19

Jump

Question 20

Type of Frieze Pattern:

The frieze pattern admits translations, vertical reflections, horizontal reflections,
rotations, and glide reflections.

Answer 20

Spinning Jump

Question 21

It is a pattern with translation symmetry in two directions. It is, therefore, essentially
an arrangement of friezes stacked upon one another to fill the entire plane.

Answer 21

Wallpaper Pattern

Question 22

According to him, in order for a plane figure to be considered a wallpaper pattern, it must
have at least the basic unit, one copy by translation, and a copy of these two by translation in the second
direction. There must be at least two rows, each one of at least two units long.

Answer 22

Nocon (2016)

Question 23

It is a repeating pattern of figures that covers a plane with no gaps or overlaps.
It is just like a wallpaper group in which patterns are created by repeating a shape to fill the plane.
A great example of it is the honeycomb.

Answer 23

Tessellation or Tiling