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