5.-Problem-Solving-1 PDF PDF

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Warning: TT: undefined function: 32MATHEMATICSModern Worldin theJanina C. SerceniaCAS FacultyChapter I.The Nature of Mathematics Patterns and Numbers in Nature Fibonacci Sequence and the Golden RatioTypes of Pattern in Nature FRACTALS SPIRALS CHAOS SYMMETRY FRACTALSFractals are never-ending patterns...

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MATHEMATICS in the

Modern World

Janina C. Sercenia CAS Faculty

Chapter I.

The Nature of Mathematics • Patter ern ns an and d Num umb bers in Na Natu tu turre • Fib Fibon on onaacc ccii Seq Sequ uence an and d th the e Go Gold ld lden en Ra Rattio

A. Patter ns and Numbers in Nature • • • • • • •

What is Mathematics? Where is Mathematics? What is Mathematics for? What is Mathematics about? How is Mathematics done? Who uses Mathematics? Why is Mathematics Important to know/

Types of Patter n in Nature • • • •

FRACTALS SPIRALS CHAOS SYMMETRY

FRACTALS Fractals are never-ending patterns that are self-similar across different scales. It Involve symmetry of magnification (Dilation) - Its a shape that you could zoom in on a part of it in an infinite number of times and it would look the same.

FRACTALS

PROPERTIES • Self Similarity- appear the same under magnification. • Fractional Dimension • Formation of Iteration- form by a repeating process.

FRACTALS Applications

SPIRALS Spirals are curved patterns made by series of circular shapes revolving around central point.

SPIRALS

Applications/examples

CHAOS Chaos or chaotic pattern are simple patterns created from complicated underlying behavior. It used to described a kind of order which lacks predictability.

CHAOS

Applications/examples

SYMMETRY Symmetry is the exact correspondence of form and constituent configuration on the opposite sides of dividing line or plane or about a center or an axis. In Mathematics, an object are said to have symmetry when it remains unchanged after transformations such as rotation and scaling are applied to it.

SYMMETRY Different types of SYMMETRY A. Reflection Symmetry -Also called as mirror symmetry, line symmetry or bilateral symmetry. - It is made with a line going through an object which divides it into two pieces which are mirror images of each other.

Reflection Symmetr y

Applications/examples

SYMMETRY Different types of SYMMETRY B. Rotational Symmetry Also called as radial symmetry -It is exhibit by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation

Rotational Symmetr y Applications/examples

SYMMETRY Different types of SYMMETRY B. Translational Symmetry It is exhibit by objects which do not change its size and shape even if it moves to another location. (Note: the movement does not involve with reflection or rotation.)

Self Assessment Question: Identify whether the following is a Fractals, Spirals, chaos, or symmetry.

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Self Assessment Question: Identify whether the following is a Fractals, Spirals, chaos, or symmetry.

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Self Assessment Question: Identify whether the following is a Fractals, Spirals, chaos, or symmetry.

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Problem Set 1.A Identify whether the following is a Fractals, Spirals, chaos, or symmetry.

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