transformasi dalam matematik
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1
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.
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