Different Kinds of Pattern PDF

Different Kinds of Pattern  Patterns of Visuals   Visual patterns are often unpredictable, never quite repeatable,  and often contain fractals. These patterns are can be seen from the  seeds and pinecones to the branches and leaves. They are also visible  in self-similar replication of trees, fern...

Different Kinds of Pattern  Patterns of Visuals   Visual patterns are often unpredictable, never quite repeatable,  and often contain fractals. These patterns are can be seen from the  seeds and pinecones to the branches and leaves. They are also visible  in self-similar replication of trees, ferns, and plants throughout nature.  Patterns of Flow  The flow of liquids provides an inexhaustible supply of nature's  patterns. Patterns of flow are usually found in the water, stone, and  even in the growth of trees. There is also a flow pattern present in  meandering rivers with the repetition of undulating lines. Different Kinds of Pattern  Patterns of Movement  In the human walk, the feet strike the ground in a regular  rhythm: the left-right-left-right-left rhythm. When a horse, a four legged creature walks, there is more of a complex but equally rhythmic  pattern. This prevalence of pattern in locomotion extends to the  scuttling of insects, the flights of birds, the pulsations of jellyfish, and  also the wave-like movements of fish, worms, and snakes. Different Kinds of Pattern  Patterns of Rhythm  Rhythm is conceivably the most basic pattern in nature. Our  hearts and lungs follow a regular repeated pattern of sounds or  movement whose timing is adapted to our body's needs. Many of  nature's rhythms are similar to a heartbeat, while others are like  breathing. The beating of the heart, as well as breathing, have a default  pattern.  Different Kinds of Pattern  Patterns of Texture  A texture is a quality of a certain object that we sense through  touch. It exists as a literal surface that we can feel, see, and imagine.  Textures are of many kinds. It can be bristly, and rough, but it can also  be smooth, cold, and hard.  Geometric Patterns  A geometric pattern is a kind of pattern which consists of a series  of shapes that are typically repeated. These are regularities in the  natural world that are repeated in a predictable manner. Geometrical  patterns are usually visible on cacti and succulents. Patterns Found in Nature  Waves and Dunes  Patterns Found in Nature  Spots and Stripes Patterns Found  in Nature  Spiral Symmetries  Reflection symmetry  sometimes called line   symmetry or mirror symmetry,  captures symmetries when the left  half of a pattern is the same as the  right half.  Symmetries  Rotations  also known as rotational   symmetry, captures symmetries  when it still looks the same after  some rotation (of less than one full  turn). The degree of rotational  symmetry of an object is   recognized by the number of  distinct orientations in which it  looks the same for each rotation.  Symmetries  Translations  This is another type of   symmetry. Translational symmetry  exists in patterns that we see in  nature and in man-made objects.  Translations acquire symmetries  when units are repeated and turn  out having identical figures, like the  bees' honeycomb with hexagonal  tiles.  Sequence  Sequence refers to an ordered list of numbers called terms, that may  have repeated values. The arrangement of these terms is set by a  definite rule.   There are different types of sequence and the most common are the  arithmetic sequence, geometric sequence, harmonic sequence, and  Fibonacci sequence.  Sequences  **Arithmetic Sequence ** Arithmetic sequence. It is a sequence of numbers that follows a  definite pattern. To determine if the series of numbers follow an  arithmetic sequence, check the difference between two consecutive  terms. If common difference is observed, then definitely arithmetic  sequence governed the pattern. Sequences  **Geometric Sequence ** It is a sequence in which every term (except the first term) is  multiplied by a constant number to get its next term. i.e., To get the  next term in the geometric sequence, we have to multiply with a fixed  term (known as the common ratio), and to find the preceding term in  the sequence, we just have to divide the term by the same common  ratio. Sequences  **Harmonic Sequence ** In the sequence, the reciprocal of the terms behaved in a manner like  arithmetic sequence. Sequences  **Fibonacci Sequence ** The Fibonacci numbers are a series of numbers that often occur in  nature. This number sequence was developed in the middle ages, and  it was named after Leonardo Pisano Bigollo, a famous Italian  mathematician who also happened to discover Fibonacci. Fibonacci is  the short term for the latin filius bonacci, which means "the son of  Bonacci".​ **[Characteristics of Mathematical Language]** 1. Precise   [2. Concise]   3\. Powerful **[Characteristics of Mathematical Language]** 1. Precise   [2. Concise]   3\. Powerful **[Vocabulary Vs. Sentences] ** Every language has its vocabulary, and its rules for  combining these words into complete thoughts.  **Importance of Mathematical Language ** Comprehension  Development of Mathematics Proficiency Better Communication **[Vocabulary Vs. Sentences] ** Every language has its vocabulary, and its rules for  combining these words into complete thoughts.  **Importance of Mathematical Language ** Comprehension  Development of Mathematics Proficiency Better Communication **[Natural and Mathematical Language] ** Nouns in Mathematics could be fixed things such as  numbers, or expressions with numbers  Verbs could be equal sign "=", or inequalities "\" Pronouns could be variables **[Natural and Mathematical Language] ** Nouns in Mathematics could be fixed things such as  numbers, or expressions with numbers  Verbs could be equal sign "=", or inequalities "\" Pronouns could be variables **[Expressions and Sentences] ** A **Mathematical Sentence** expresses a complete  mathematical thought about the relation of a  [mathematical object to another mathematical]  object.   6(x + 4) 3x + 4 = y  [(6 - k)/ 12 x + 2x = 3x]  11m + 7 x -- 1 = 0 **[Expressions and Sentences] ** A **Mathematical Sentence** expresses a complete  mathematical thought about the relation of a  [mathematical object to another mathematical]  object.   6(x + 4) 3x + 4 = y  [(6 - k)/ 12 x + 2x = 3x]  11m + 7 x -- 1 = 0 **Conventions in mathematics, some commonly used symbols, its meaning and  example**   **[Basic Operations and Relational Symbols]** **[Basic Operations and Relational Symbols]** **[\ ]** **[Sets of Numbers]** **[Translating Words into Symbols] ** 1\. The sum of a and b   2\. The product of x and y  [3. The sum of x and the difference of y and z] 4. The product of x and the sum of y and z 5. Six less than twice a number is forty five. 6. A number minus seven yields ten.  7. A total of six and some number  [8. Twelve added to a number]  9\. Eight times a number is forty-eight. **[Translating Symbols into Words]** 1. x (y + z)  2\. xy + xz  3\. (x + z) + (y - z) **[Four Basic]  [Concepts] ** Sets, Functions, Relations,  and Binary Operations **[Sets and Subsets] ** Use of the word "set" as a formal mathematical term  was introduced in 1879 by Georg Cantor. For most  [mathematical purposes we can think of a set]  intuitively, as Cantor did, simply as a collection of  elements.  ***A set is a collection of well-defined objects.*** **[Sets] ** Examples:  [A set of counting numbers from 1 to 10.]  A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A= {x/x ⋲ N~1~, x\