MMW Reviewer

• Polygon


  A solid two-dimensional shape with straight sides
• Types of polygons


  • Convex (internal angles less than 180 degrees)
  • Concave (no internal angles greater than 180 degrees)
  • Regular (all sides equal)
  • Irregular (sides not equal)
• Solid


  The geometry of a three-dimensional space, the kind of space we live in, with three dimensions: width, depth, and height
• Geometric Transformation


  A change of shape according to its size, orientation, or position following certain techniques in mathematics
• Object


  The original shape
• Image


  The new shape
• Symmetry results from geometric transformation
• Types of Geometric Transformation

  1. Translation (image moved or shifted without changing form)

  2. Rotation (image rotated given angular measure)

  3. Reflection (new image is a mirror of the original)

  4. Dilation (increase or decrease in size without changing shape)

  
• Pattern


  One aspect in geometry, usually found and utilized, can be simple or complex, and sometimes use the same object or color more than once

  
• Symmetry


  An integral part of nature and the arts of cultures worldwide, found in architecture, crafts, poetry, music, dance, chemistry, painting, physics, sculpture, biology, and mathematics
• Types of Symmetries/Patterns


  • Rosette Patterns (finite design with reflection and rotation)
  • Frieze Patterns (one-directional with reflection, rotation, translation, and glide reflection)
  • Wallpaper Patterns (two-directional with rotation, reflection, glide reflection)

  
• Pythagoras - Pythagoras Theorem
• Pythagorean Therorem - mathematcial formula which states that the square of the hypthenuse of a right triangle is equal to the sum of the squares on the other two sides.
• Johannes Kepler - Planetary Motion
• Johannes Kepler - A German mathematician and astronomer who discovered that the Earh and planets travel about the sun in elliptical orbits.
• Rene Descartes - Cartesian Plane
• Rene Descartes - Father of Modern Philosophy
• Rene Descartes - interested in certain knowledge and the relationship between the body and the mind. He bridged the gap between algebraa and geometry which resulted in the Cartesian coordinate system
• Blaise Pascal - Pascal's triangle
• Blaise Pascal - worked on conic sections and pojective geometry.
• Isaac Newton - the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. Work on optics and gravitation
• Gottfriend Leibniz - Calculus
• Gottfried Leibniz - German mathematician who developed the present-day notation for the differential and integral calculus.
• Friedrich Gauss - probability
• Friedrich Gauss - made important contribution to physics and astronomy and pioneered the application of mathematics to gravitation, electricity and magnetism
• Marie Curie - Radioactive
• Marie Curie - discovered polonium and radium, and won the Nobel Prize in 1903
• Albert Einstein - Theory or Relativity
• Albert Einsten - has a major impact on the development of atomic energy. Later in lide, focused on unified field theory.
• Fibonacci Sequence - named after Leonardo of Pisa, and Italian Mathematician
• Golden Rectangle - Leonardo of Pisa also known as Fibonacci discovered sequence of numbers that created an interesting pattern the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,...
• Golden Rectangle - can be broken down into squares the size of the next Fibonnaci number down and below. Spiral
• Golden Ratio - ratio of two consecutive Fibonacci numbers as the number of terms become large, approaches the golden ratio that os 1.61800339887
• Plane Crystallographic Pattern - also known as wallpaper patterns