MODULE 1

• Patterns exist in different varieties of forms, from the petals of a flower to the arrangement of leaves, revealing a sequential pattern.
• Nature is bounded by different colors and shapes, from the rainbow mosaic of a butterfly’s wings to the undulating ripples of a desert dune.
• Patterns are molded with a strict regularity, as evidenced by the thousands of times over the cells of a honeycomb repeat their hexagonal symmetry.
• A pattern is something which helps us anticipate what we might see or expect to happen next, and may also help us know what may have come before or what we are seeing currently.
• There are four types of patterns: logic patterns, number patterns, geometric patterns and word patterns.
• Logic pattern is the ability to discover meaningful patterns in strange and unpredictable situations.
• Number pattern is a sequence of numbers that are formed in accordance with a definite rule.
• Geometric pattern is a pattern represented by geometrical figures such as polygons and isometric shapes.
• Word pattern are represented by jumbled words and analyze the hidden logic in it.
• A pattern has symmetry, and isometry of the plane that preserves the pattern is a way of transforming the plane that preserves geometrical properties such as length.
• There are four types of isometries according to Euclidian isometry of plane transformation: Translation, Reflection, Rotation, Dilation.
• Isometry is a way of transforming the plane that preserves geometrical properties such as length.
• Any orientable, compact (finite size) surface is determined by its number of holes (called the genus).
• Sometimes rigid transformation is added if there is a combination of three transformation that is translation, reflection and rotation.
• The four angles of the Golden Trees are 60°, 108°, 120° and 144°.
• Many natural systems can be modeled with fractal trees.
• A topological surface is orientable if you can determine the outside and inside.
• Topology investigates basic structure like number of holes or how many components.
• There are also four types of isometry or transformation according to Euclidian isometry; translation, reflection, rotation and dilation.
• The Sierpinski Gasket (right triangle version) can be obtained via the three maps which map the unit square to three smaller squares, and repeating those maps ad infinitum.
• For a given branching angle, there is a unique scaling ratio such that the corresponding symmetric binary tree is “self-contacting”.
• Transformation is a process which shifts points of the plane to possibly new locations on the plane.
• What happens to the perimeter as you do more iterations?
• A reflection (or a flip) can be thought of as getting a mirror image.
• An object is self-similar if it can be formed from smaller versions of itself (with no gaps or overlap).
• A rigid transformation is a combination of Reflection, translation and rotations that leave the dimensions of the object and its image unchanged.
• Seismologists use patterns to forecast earthquakes and landslides.
• Repeat the process indefinitely (this is called iterating)
• Translation or slide moves a shape in a given direction by sliding it up, down, sideways or diagonally.
• A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.