1.2 Patterns and Numbers in Nature Flashcards
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.
Pattern
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.
Mathematics according to e National Council of Teachers of Mathematics
(1991)
It include symmetries,
fractals, spirals, meanders, waves, foams, tessellations, cracks, and stripes.
Natural Patterns
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.
Symmetry / Mathematical Symmetry
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.
Reflection / Bilateral Symmetry / Mirror Symmetry
The
fold is called a (???) because it divides the shape into two equal parts.
Line of Symmetry
Bilateral-symmetric
objects have at least one (???). The lines of symmetry may be in any direction.
Line or Axis of Symmetry
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.
Radial Symmetry
A pattern that repeat in no direction. It s consist of taking motif or an element and rotating and/or reflecting that element.
Rosette Pattern
A rosette pattern is (cyclic, dihedral) if it
only admits rotational symmetries
Cyclic
A rosette pattern is (cyclic, dihedral) if it admits both
rotational symmetries and bilateral or reflectional symmetries.
Dihedral
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.
Frieze Pattern
What are the seven types of Frieze Pattern?
- Hop
- Step
- Sidle
- Spinning hop
- Spinning Sidle
- Jump
- Spinning Jump
Type of Frieze Pattern:
The frieze pattern only admits a translational symmetry.
Hop
Type of Frieze Pattern:
The frieze pattern only admits a translational and glide symmetries.
Step
Type of Frieze Pattern:
The frieze pattern only admits translations and vertical reflections.
Sidle
Type of Frieze Pattern:
The frieze pattern only admits translations and 180◦
rotations (half-turns).
Spinning Hop
Type of Frieze Pattern:
The Frieze Pattern only admits translations, vertical reflections, rotations, and
glide reflections.
Spinning Sidle
Type of Frieze Pattern:
The frieze pattern only admits translations, a horizontal reflection, and glide reflection.
Jump
Type of Frieze Pattern:
The frieze pattern admits translations, vertical reflections, horizontal reflections,
rotations, and glide reflections.
Spinning Jump
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.
Wallpaper Pattern
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.
Nocon (2016)
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.
Tessellation or Tiling
