Mathematics in the Modern World MMW Lesson 1 PDF

Mathematics in the Modern World Polytechnic University of the Philippines Neil Mari D. Alcantara Bachelor of Science in Psychology - 1st Semester Lesson 1: Mathematics in our World Objects...

Mathematics in the Modern World Polytechnic University of the Philippines Neil Mari D. Alcantara Bachelor of Science in Psychology - 1st Semester Lesson 1: Mathematics in our World Objects are mirror images of each other. Mathematics Bilateral-symmetric Study of numbers objects have at It is a set of problem-solving tools least one line or A language axis of symmetry. A process of thinking Study of patterns Mathematics is a branch of science, which deals with numbers and their operations. It involves calculation, computation, solving of problems, etc. Mathematics helps us to organize ○ Radial/Rotational and systematize our ideas about Symmetry patterns. Is when an object is rotated in whatever Patterns and Numbers in Nature degree, it is still the A Pattern is an arrangement which helps same or looks the observers anticipate what they might see same. or what happens next. It can be found both in natural and According to the National Council of human made Teachers of Mathematics (1991), objects. Mathematics is a study of patterns and relationships, a way of thinking, an art, a language, and a tool. Patterns Symmetry - occurs when there is congruence in dimensions, due proportions and arrangement. ○ Reflection or Bilateral Symmetry It is the simplest kind of symmetry Classifications of Symmetric Patterns One of the most Rosette Patterns common kinds of ○ Those that repeat in no symmetry that we direction see in the natural ○ Patterns with rotation world symmetry and/or reflection Also called as symmetry “mirror symmetry”  Mathematics in the Modern World Polytechnic University of the Philippines Neil Mari D. Alcantara Bachelor of Science in Psychology - 1st Semester Sidle - The frieze ○ Types of Rosette Pattern pattern only admits Cyclic - Only translations and rotational symmetry vertical reflections. Spinning Hop - The frieze pattern only admits translations and Dihedral - Both 180° rotations rotational symmetry (half-turns) and reflectional symmetry Spinning Siddle - The frieze pattern only admits translations, vertical reflections, rotations, and glide Frieze Patterns reflections. ○ Those that repeat in exactly one direction ○ It is a pattern in which a Jump - The frieze basic motif repeats itself pattern only admits over and over in one translations, a direction horizontal reflection, ○ It extends to the left and and glide reflection right in a way that the pattern can be mapped onto itself by a horizontal Spinning Jump - translation. The frieze pattern ○ Review on Geometric admits translations, Transformations vertical reflections, Hop - The frieze horizontal pattern only admits reflections, a translational rotations, and glide symmetry reflections. Step - The frieze Wallpaper Patterns pattern only admits ○ Those that repeat in more a translational and than one direction glide symmetries  Mathematics in the Modern World Polytechnic University of the Philippines Neil Mari D. Alcantara Bachelor of Science in Psychology - 1st Semester ○ It is a pattern with translation symmetry in two directions ○ Any particular wallpaper pattern is made up of a combination of the following symmetries; reflection, rotation, and glide reflection. ○ In order for a plane figure to be considered a wallpaper pattern, it just has at least the basic unit, one copy of these two by translation in the second direction. There must be at least two rows, each one of at least two units long. ○ Kind of Wallpaper Pattern Tessellation or Tiling - is a repeating pattern of figures that covers a plane with no gaps or overlaps. It is just like a wallpaper group in which patterns are created by repeating a shape to fill the plane.