Math in the Modern World

• It is an arrangement that helps observers what they might see or what happens next.

  Patterns
• It is a study of patterns and relationships. A way of thinking, an art, a language, and a tool.

  Mathematics
• It occurs when there is congruence in dimensions, due proportions and arrangement.


  Symmetry
• It is one of the most common kinds of symmetry that we see in the natural world.

  Mirror Symmetry
• It is an image with more than one lines of symmetry meeting at a common point.

  Radial Symmetry
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  A pattern that repeats in no direction.

  Rosette Patterns
• A pattern that repeats exactly in one direction

  Frieze Patterns
• A pattern that repeats in more than one direction.

  Wallpaper Patterns
• A rosette pattern that only admits rotational symmetries.

  Cyclic
• A frieze pattern that only admits a translational and glide symmetries.


  Step
• A frieze pattern that only admits translations and 180o rotations (half-turns).

  Spinning Hop
• It is a repeating pattern of figures that covers a plane with no gaps or overlaps.

  Tessellations
• It can be broken into squares the size of the next Fibonacci number down and below.

  Golden Rectangle
• It takes a golden rectangle, break it down into smaller squares based from Fibonacci sequence and divide each with an arc.

  Fibonacci Spiral
• It takes a golden rectangle, break it down into smaller squares based from Fibonacci sequence and divide each with an arc.

  Fibonacci Spiral
• A set of numbers in a specific order.


  Sequence
• A constant difference between successive terms.

  Common Difference
• It has the same ratios of consecutive terms.

  Geometric Sequence
• It shows the differences between successive terms of the sequence

  Difference Table
• A frieze pattern that only admits translations, a horizontal reflection, and glide reflection.


  Jump
• It is a declarative sentence that can be objectively identified as either true or false, but not both.


  Propositions
• It is false when p is true, and true when p is false

  Negation
• It is a proposition with only one subject and one predicate

  Single Propositions
• It is the proposition “p and q”, which is only true when both p and q are true.

  Conjunction
• It is the proposition of “p or q”, which is false on ly when both p and q are false.

  Disjunction
• It is the proposition of “p if and only if q”, which is true only if both p and q are true or both p and q are false.

  Biconditional Statement
• It is a ____ if its truth value remains true regardless of the truth values of its component propositions.

  Tautology
• It is a collection of well-defined and distinct objects, considered as an object in its own right.

  Sets
• These are sets with no elements.

  Empty Set
• A set with only one element.


  Singleton
• We say that A is a _ of B, if every element of A is an element of B.

  Subset
• Two finite sets A and B are said to be ___ if and only if n(A)=n(B).

  Equivalent
• It uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

  Venn Diagram
• The set of all objects of interest is called as the ____.

  Universal Set
• A compound proposition is a _____ if its truth value remains false regardless of the truth values of its component propositions.

  Contradiction