transformasi dalam matematik

8/13/2019 transformasi dalam matematik

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TRANSFORMATIONS

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MAS IZWATU SOLEHAH BINTI MISWAN

MP 121310

NURUL AIN BINTI JOHARI MP 131040


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INTRODUCTION

TRANSFORMATION

REFLECTIONTRANSLATION

ENLARGEMENT

ROTATION

SIMILARITY

CONGRUENCE


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TRANSFORMATION

In mathematics, a transformation could be any functionmapping a set X on to another set or on to itself

In geometry, a transformation changes the position of ashape on a coordinate plane. It means that a shape ismoving from one place to another.


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TRANSLATIONTranslation moves a shape by sliding it up, down,sideways or diagonally, without turning it ormaking it bigger or smaller.


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Reflection in a line produces a mirror imagein which corresponding points on theoriginal shape and the mirror image are

always the same distance from the mirrorline.

REFLECTION


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Rotation turns a shape through a clockwiseor anti-clockwise angle about a fixedpoint known as the Centre of Rotation. All

lines in the shape rotate through the sameangle.

ROTATION


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Transformation that is invariant with respect todistance. That is, the distance between any twopoints in the pre-image must be the same as thedistance between the images. The shape and the

size must be exactly same. of the two points

CONGRUENCE


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Increasing the size of a shape by a scalefactor from a particular point, which iscalled the centre of enlargement.

ENLARGEMENT


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HISTORY OFTRANFORMATIONAL GEOMETRY

During the 17 th century, Ren Descartes (1596 1650 ), a Frenchmathematician and philosopher, introduce the use of theCartesian coordinate system. That is, every point of a curve isgiven two numbers that represent its location in a plane . Thisnew coordinate system helped to show that there was a link

between geometry and algebra , starting with a geometric shapeor curve and assigning an ordered pair to each point so algebraictechniques could be assigned to the figure.

Pierre de Fermat (1601 1665 ), a French jurist, proposed a system

of analytical geometry similar to the one noted byDescartes. Fermats system used a more direct approach and ismore similar to the system currently used. Fermat and Descartesare both credited with independently developing the ideas ofanalytical geometry .


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Felix Klein (1849 1925), a German geometer, showed theimportance of groups in geometry. This new idea allowedKlein to unify geometry. Kleins address in Erlanger,

Germany proposed that the study of geometry should bedefined as the study of transformations that leave objectsinvariant (unchanged). His 1872 Erlanger Program, classifyinggeometries by their underlying symmetry groups, was ahugely influential synthesis of much of the mathematics of theday.

Felix KleinRene Descarte Pierre de Fermat


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NATURAL PHENOMENA

Reflection


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Reflection


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Reflect ion


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affective, and psychomotor

Rotation


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Transla t ion


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Enlargement


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POTENTIAL

ArtEngineeringArchitecture

MedicalAdvertisingAstronomy and MeteorologyBusiness

Education


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ART

Tesselation -A tessellation is the tiling of a planeusing one or more geometric shapes, called tiles,with no overlaps and no gaps.

Tessellations were used in Ancient Rome and inIslamic art such as in the decorative tiling of theAlhambra palace.


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Work by Maurit Cornellis Escher

Decorative at AlHambra


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ENGINEERING

EYE ON MALAYSIA


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ARCHITECTURE


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MEDICAL

DENTAL MIRRORWHEEL CHAIR


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ASTRONOMY AND METEOROLOGY

THEODOLITE ANEMOMETER


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ADVERTISING /COMMERCIAL


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MUSIC

SOUND MACHINES


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BUSINESS (FOOD , TEXTILE )


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EDUCATION

MICROSCOPE BRAILLE


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NO LIMITATION


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ANALISIS BUKU TEKS

BUKU TEKS: MATHEMATICS FORM 5First Published 2006

Maxporia Sendirian Berhad


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Ciri-ciri Buku teks di Malaysia:

1. Berdasarkan kurikulum Matematik.2. Sejarah perkembangan dan penemuan mengikut

pelbagai tamadun.3. Mempunyai bahan rangsangan tertentu.4. Pelbagai bentuk latihan.5. Nota ringkas.

6. Aktiviti pengukuhan.(Noraini Idris, 2001)


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BUKU TEKS: MATHEMATICS FORM 5

CHAPTER 3:TRANSFORMATION III


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KEKUATAN:1. Mengaitkan konsep lain seperti tesellation , molecular

structure dan konsep simetri yang mempunyaihubungan dengan konsep transformation.


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KEKUATAN:

2. Memberikan contohpenyelesaian masalahberdasarkan konsep Polya.


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KELEMAHAN:

1. Tiadasejarah

penemuan.


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KELEMAHAN:

2. Penyelesaian Masalah mudah dan ringkas. Kurangelemen KBAT.


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KELEMAHAN:

3. Tiada bahan rangsangan yang menarik.4. Rajah kurang jelas dan kurang mengaitkan dengankehidupan harian.


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CADANGAN PENAMBAHBAIKAN:

1. Memasukkansejarah penemuanberkaitan tajuk.

2. Mempelbagaikanlagi aktiviti denganmemasukkan aktivitimenggunakankalkulator grafik,origami dan aktivitisimulasi.

3. Elemen KBAT dalamsoalan soalan latihandan pengukuhan.

Date post:	04-Jun-2018
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transformasi dalam matematik

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