MATHEMATICAL IN EVERYDAY LIFE (NATRAH,NURUL ATIQAH,AMELIA)
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MATHEMATICAL INEVERYDAY LIFE
(NATRAH,NURUL ATIQAH,AMELIA)
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THE ROLE OF MATHEMATICS IN
MODERN TECHNOLOGIES(PARTICULAR ROBOTIC MOTION)
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ROBO
T
Any machine that is
capable of intelligently
controlling its motionthrough space
Designed to perform avariety of tasks by moving
parts, tools or specialized
devices.
Types
Mobile Stationary
free to move around remain in 1 place but have
arms that move
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ROBOTIC ARM
Hand
Base
Polar
Joints
Linear
Joint
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ROLE OF
MATHEMATICS IN
ROBOTIC MOTION
(ARM)
Coordinate system
Degree of freedom
Algebraic and
differential topology
Combinatoric
Optimization algorithm
Differential algebraic
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Algebraic and differential topology
had been used to understand configuration
spaces of many-particle or many-body systems
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Optimization algorithm
a robotic system design and many problems in
robot task planning can be formulated as
optimization problems, though they are typically
``hard'' in terms of complexity and lack of readily
recognizable or standard mathematical structures.
Success stories include graph-theoretic and
calculus of variation based approaches to
determining optimal paths, randomized algorithms
for finding solutions in complex spaces, optimal
feedback control policies for a range of robotic
tasks, and saddle-point policies for solving
differential games of pursuit and evasion.
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combinatoric
Relevant to discrete actuators which are
the smoothly actuated robotic arms and
other manipulators that can bereplaced by a cheaper network of
discrete actuators (devices that extend
or contract into only two positions).
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Differential algebraic
The used of differential algebraic inequalities inthe modeling of multibody systems in contact,
which in turn are central to robot manipulation.
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FRIEZES AND MOSAIC
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INTRODUCTION
´ MATH
- widely spread in several fields even in
architecture and art.- commonly use to describe the systematically
classification of friezes and mosaic.
´ FRIEZES & M
OSAIC
-used in decoration forseveral millennia by ancient worlds· like
Sumerian,Egyption,an Mayan civilization.
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EX AMPLE««
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FRIEZES
´ Oxford English Dictionary
-and of painted or sculptured decoration.
´ Mathematical point of view
(i) constant and finite width and infinitely long inthe perpendicular (horizontal) direction,
(ii) It is periodic, exist some minimal distance
where L > 0 such that the translation of thefrieze by distance L along the direction willleave the frieze unchanged
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FRIEZES
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REFLECTION BY HORIZONT AL
MIRROR
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REFLECTION BY VERTIC AL MIRROR
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MOSAIC
´ pattern that can be repeated to fill the plane.
´ periodic along two linearly independent
directions.´ linear independent directions
- remain the pattern unchanged under
translation.
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INVARI ANT (UNCHANGED) MOSAIC
´ Repeated pattern to fill the plane.
´ Periodic along two linearly independent
direction.-Vectors t1 and t2 along which may be translated
without change.
´ Can be classified by symmetry groups.
´ Any rotation must have one of the following
angles; , , , (60°,90°,120°,180°)
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THE POINT O AND TWO OF ITS
IMAGES A,B
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INVARI ANT MOSAIC
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APERIODIC TILING
´ Tiling plane with Penrose Tiles( PenroseRhombs).
´ no translational symmetry involves to tile the
plane. (arrange manually)
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APERIODIC PENROSE TILING
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ARCHIMEDE AN TILING
´ regular polygons.
´ each vertex is on the same type.
´ Both vertices must be coincident with similarpolygons and must appear in the same order.
´ 11 families in Archimedean tiling.
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ARCHIMEDE AN TILING
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ARCHIMEDE AN TILING
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ARCHIMEDE AN TILING
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INVESTIGATE THE BASES FOR CONTEMPOR ARY MATHEMATICS.
DISCUSS IN PARTICULAR BASE 2
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THE USAGE OF OTHER BASES IN RE AL
LIFE :´
Quinary (base-5
) ² language including Gumati,Nunggubuyu, Kuurn Kopan Noot andSaraveca.
1 - wanggany
2-marrma3 - lurrkun
4 - dambumiriw
5 - wanggany rulu
10 - marrma rulu15 - lurrkun rulu
20 - dambumiriw rulu
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Octal ( base 8 )
´
By Native AmericansThe Yuki language in California and the
Pamean languages in Mexico have octal
systems because the speakers count using
the spaces between their fingers rather than
the fingers themselves.
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Base 10
´ Decimal notation often refers to the base-10
positional notation such as the Hindu-Arabic
numeral system, however it can also be used
more generally to refer to non-positional
systems such as Roman or Chinese numerals
which are also based on powers of ten.
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BINARY ?
´ In mathematics and computer science, thebinary (base-two) numeral system is arepresentation for numbers that uses onlyzeroes and ones as digits.
´ Every communication that takes place insideyour computer uses this binary system becauseThe computer's CPU need only recognise twostates, on or off .
´ Usually arithmetic with base-two is easier thanbase-ten but the numbers are longer, making then harder to read.
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´ 2 to the power of 0 = 1 (2^0)
2 to the power of 1 = 2 (2^1)
2 to the power of 2 = 4 (2^2) or (2*2)
2 to the power of 3 = 8 (2^3) or (2*2*2)
2 to the power of 4 = 16 (2^4) or (etc.)
2 to the power of 5 = 32 (2^5)2 to the power of 6 = 64 (2^6)
2 to the power of 7 = 128 (2^7)
2 to the power of 8 = 256 (2^8)
«
2 to the power of x = (2^x)
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0 1 0 0 1 0 1 0 ?