Midterm M1-3 Flashcards
(42 cards)
The ___________________. Mathematics covers designs that assist
us with understanding our general surroundings. As a study of dynamic
articles, Mathematics depends on rationale as opposed to on
perception as its standard of truth, logic, and even observation as
methods for finding truth
Nature of Mathematics
- Study of numbers and Arithmetic Operations
- Science which involves logical reasoning, drawing conclusions
from assumed premises and strategic reasoning based on
accepted rules, Laws, or probabilities - Is a language
- It is an art which studies patterns
What is Mathematics?
—-is an arrangement which helps the observers
anticipate what they
Might see or what happen next.
—-it also shows what may have come before
—-it organizes information for it to be useful.
—–used to analyze and solve problems
—–
Pattern are studied because they are everywhere; people just
learn to notice them.
Pattern
- indicates
that you can draw an
imaginary line across an
object and resulting parts
are mirror images of each
other.
The figure is symmetric about the axis if you divide the
figure vertically the left and right portion are exactly the
same.
This is known as line or bilateral symmetry , this is evident
in most animals , including human.
1.Symmetry
This tree was described by Leonardo Da
Vinci and according to him, if all
branches of the tree are put together, its
thickness will equal to that of the trunk
Another version stated that when a
branch splits, when put together the thickness equals to the parent
branch.
Fractal-like patterns occur widely in nature, some examples are the
clouds, river networks, fault lines, mountains, coastlines, animal
coloration, snow flake and many more. Can you think of some?
The Growth patterns of certain trees resemble Lindenmayer system
fractals
2.Trees, fractal
Spirals are common in plants and in some animals.Plants spirals can
be seen in the arrangement of leaves on a stem, and in the
arrangement of the plant parts as in composite flower heads , and the
seeds heads like the sunflower or fruit structure of pineapple .
- Spirals
- Chaos, flow, meanders
___________________ is the study of how simple patterns can be generated from
complicated underlying behavior. Chaos theory helps us to understand
patterns in nature.
Chaos
The flow pattern is the way in which fluids move through a reactor.
Density gradients, caused by temperature or composition variations,
tend to control the overall flow pattern of the fluid. . The flow pattern is
the way in which fluids move through a reactor.
(The motions of air water organize the skies ,the earth and the oceans)
Flows
___________________ is one of a series of regular sinuous curves, bends, loops,
turns, or windings in the channel of a river, stream, or other
watercourse. It is produced by a stream or river swinging from side to
side as it flows across its floodplain or shifts its channel within a valley
Meanders
: Waves, dunes Wind waves are sea surface waves that
create the characteristic chaotic pattern of any large body of water,
though their statistical behavior can be predicted with wind wave models.
As waves in water or wind pass over sand, they create patterns of ripples
- Waves
A soap bubble forms a sphere, a surface with minimal area. Two bubbles
together form a more complex shape: the outer surfaces of both bubbles
are spherical; these surfaces are joined by a third spherical surface as the
smaller bubble bulges slightly into the larger one.
A foam is a mass of bubbles; foams of different materials occur in
nature.
- Bubbles, foams
Tessellations are patterns formed by repeating tiles all over a flat
surface. There are 17 wallpaper groups of tillings. While common in art
and design, exactly repeating tillings are less easy to find in living
things.
ARRAYS: Honeycomb
Snake fruit
TILLINGS
- Tessellations
Cracks are linear openings that form in materials to relieve stress.
When an elastic material stretches or shrinks uniformly, it eventually
reaches its breaking strength and then fails suddenly in all directions,
creating cracks with 120 degree joints, so three cracks meet at a
node.
Drying inelastic mud with 90° cracks
Cracking Wood
- Cracks
A long narrow band distinguished, as by color or texture, from the
surrounding materi al or surface.
- A textile pattern of parallel bands or lines on a contrasting
background.
-A fabric having such a pattern..
-Leopards and ladybirds are spotted; angelfish and zebras are striped.
These patterns have
an evolutionary explanation: they have
functions which increase the chances that the offspring of the patterned
animal will survive to reproduce. One function of animal patterns is
camouflage;] for instance, a leopard that is harder to see catches more
prey.
- Spots, stripes
A pattern is a series or sequence that repeats. Math patterns are
sequences that repeat based on a rule, and a rule is a set way to
calculate or solve a problem. In mathematics, we can form patterns by
doing one or more mathematical operations repeatedly.
Number Pattern:
A sequence is an enumerated collection of objects in which repetitions
are allowed and order does matter. Like a set, it contains members
(also called elements, or terms).
SEQUENCE:
-Is a sequence in which the difference between each consecutive
term is constant can be defined by an explicit formula;
an = a1 + ( n – 1 ) d
where: an = nth term, a1 = 1st term ,n = term position ,d =
common difference
Arithmetic Sequence
Is a progression formed by taking the reciprocal of an
arithmetic progression , formed by taking the reciprocals of an
arithmetic sequence.
Harmonic Sequence (Harmonic Progression)
Mathematics is useful in the development of social, intellectual,
moral, spiritual and cultural
AT THE PERSONAL LEVEL:
Changes in the social structure, like modern facilities, mode of
transportation, means of communication, science and technology is
possible because of mathematics.
Social
Mathematics helps the brain active. Almost all courses in
tertiary level offers includes at least one mathematics subject in their
curriculum, Problem solving helps in the development of mental
abilities.
Intellectual
Mathematics helps the students to be prepare for technical and
other vocation like engineering, architecture, accountancy, banking,
business, agriculture, tailoring, carpentry, surveying, baking and others.
Vocational
Mathematics can contribute to the student’s character and
moral development. It helps in character and moral development.
Moral
Student enjoy in solving math problem especially when she/he
gets the correct answer to his problem with that every student feels
satisfied , confident and self-reliant .
Spiritual
