Maths
-Geometric shapes that curve inward, like a star or an arrowhead,
Concave
If they also have the same measure as each other, they are said to be
Congruent
-complex patterns that are self-similar across different scales -used in modelling natural structures and occurrences like mountain formation and erosion, crystal structures and a lot more
Fractal
- based on geometric shapes, often combined and altered to form beautifully intricate patterns.
Geometric design
can be defined as figure or area closed by a boundary which is created by combining the specific number of curves, points, and lines.
Geometric shapes
-Combines translation and reflection. - It must be determined by the line ofsymmetry and the translation vector. - Note that the line ofsymmetry and the translation vector must be parallel. - The order by which the reflection and translation are performed does not matter.
Glide Reflection
-series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or other water course -snake-like river
Meander
which will change the size but not the shape of the pre-image
Non-Rigid Transformation
a pattern that uses numbers
Numeric Pattern
these designs involve translation but only in one direction that is usually horizontal.
One-Directional designs/ Border Designs/ Frieze Patterns
made by a series of bands or strips, often of the same width and color along the length, just like the stripes of a zebra, or stripe patterns found in plants
Stripes
- agreement in dimensions, due proportion and arrangement - it refers to a harmonious and beautiful proportion and balance, just like butterfly wings. - the uterus is an example of symmetry, according to a gynecologist at the University Hospital in Leuven in Belgium. -Medical doctors can tell whether a uterus looks normal and healthy based on its relative dimensions.
Symmetry
-also known as tiling -a pattern of shapes that fit perfectly together, and have no overlaps nor gaps.
Tessellation
method of describing set in words.
The Verbal Description Method
-shape that has three dimensions -length, with, and height
Three-dimensional,
-involve taking a pre-image and transforming it in some way to produce a similar or identical image
Transformations
-Moving a pre-image in space without changing its size, shape, or form. - It is performed by identifying the length and direction (called translation vector). The pre-image is then translated according to the vector.
Translation
shape that has two dimensions - length and width.
Two-dimensional
-these are designs on a flat surface.
Wall Paper Designs
-disturbance that transfers energy through matter or space, with little or no associated mass transport.
Wave
Geometric shapes that curve outward, like a square or hexagon, are
convex
-set with no elements or has no members
empty set, or null set
-contains elements that can be counted and terminates at certain natural number
finite set
deals with the characteristics of various objects, or with order.
logic patterns
-visible regularity or consistency in the world or in a man-made design. Patterns and numbers are correlative.
pattern
Geometric shapes that have the same shape as each other are said to be
similar
-set with only one element
singleton or a singleton set.
-also a type of transformation or movement which leaves the shape of a given figure unchanged.
symmetry
by listing each element of the set inside the braces {} Example: A = {1, 2, 3, 4} B = {p, h, i, l, n, e, s
List Notation/Roster Method
-substance formed by trapping pockets of gas in a liquid or solid
Foams
-It is expanding or narrowing a pre-image without changing its shape or location. - The shape becomes bigger or smaller. It's just like zooming in or out the image.
Dilation or Resizing
-sets that contain exactly the same elements.
Equal sets
sets that contain the same number of elements.
Equivalent sets
-simplest designs - usually occur in glasswareornaments and pottery designs, on familiar artifact -generated by the repetition of parts around a central point axis. There are only two classes of symmetries of finite designs, those that contain only rotation, and those that contain both rotation and reflection.
Finite Designs
-working under the pseudonym Fibonacci, came up with the sequence when calculating the ideal expansion of pairs ofrabbits over the course of one year.
Leonardo Pisano Bigollo,
-Flipping a pre-image across a line without changing its size or shape. - It is performed by moving a pre-image into a new position such that the resulting image is a mirror image with respect to a line called line of symmetry (horizontal line, vertical line, and arbitrary slant line of symmetry)
Reflection
does not change the shape or size of the pre-image.
Rigid Transformation or Isometries
-It is rotating a pre-image about a fixed point without changing its size, shape. - It is performed by identifying the center of rotation, as well as the amount of rotation (angular measure).
Rotation
-method that lists the rules that determine whether an object is an element of the set rather than the actual elements
Set Builder Notation
-curve which emanates from a point, moving farther away as it revolves around the point
Spiral