Fractals, Logic [MMW]

• Geometric pattern is a pattern that is represented by geometrical figures such as polygons and geometric shapes.
• Logic pattern is the ability to discover meaningful patterns in strange and unpredictable situations.
• Transformation is a process that shifts points of the plane to possibly new locations on the plane.
• Transformation includes translation or slide, reflection, rotation, and dilation.
• Translation or slide moves a shape in a given direction by sliding it up, down, sideways or diagonally.
• Reflection (or a flip) can be thought of as getting a mirror image.
• Rotation (or a turn) has a point about which the rotation is made and an angle that says how far to rotate.
• A dilation is a transformation which changes the size of an object.
• Fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.
• The Golden Ratio, also known as the Fibonacci Sequence, is one of the least understood of the rules of composition.
• The actual number used to describe the symbol is an irrational number that repeats infinitely, 1.618
• Mathematicians use Fibonacci’s sequence to describe certain shapes that appear in nature, known as logarithmic spirals, and Nautilus shells are just one example.
• Isometry is a way of transforming a plane that preserves geometrical properties
• Rigid Transformation is combination of translation, reflection, and rotation.
• Patterns originate from cells of honeycomb that repeat hexagonal symmetry
• Object is self-similar when it can be formed from smaller versions of itself
• Iterating is repeating process indefinitely
• Topology is the study of objects that could be stretch, bent, or distorted without tearing
• Golden Trees is composed of 4 angles, 60, 108, 120, 144
• Logic is a formal systematic study of the principles of valid inference and correct reasoning
• The invention of logic attributed to Aristotle.
• George Boole wrote Laws of Thoughts where logic was developed into abstract math
• Proposition is a declarative sentence that is either true or false, but not both simultaneously