MATH (MIDTERMS)
Arithmetic sequence
It is a sequence of numbers that follows a definite pattern. Look for common difference.
Rizaldi C. Nocon and Ederlina C. Nocon
Who illustrated the figure of Nature of mathematics?
1. Mathematics: pure and applied 2. Scientists : Natural and Social 3. Practically everyone
Who uses mathematics? (3)
Reflexive
"Is the father of" is not an example of what property of relation?
Transitive
"Is the mother of" is not an example of what property of relation?
Symmetric
"Is the sister of" is not an example on a set that contains a brother and sister of what property of relation?
(read the table page 45)
(read the table page 45)
(study the module)
(study the module)
Golden Rectangle
1. The amazing grandeur of Fibonacci sequence was also discovered in the structure of (blank). 2. This is made up of squares whose sizes, surprisingly is also behaving similar to the Fibonacci sequence.
1. Mechanical waves 2. Wind waves 3. Water waves
3 Different kinds of wave
1. Reflections 2. Rotations 3. Translations
3 Kinds of symmetry
1. Arithmetic sequence 2. Geometric sequence 3. Harmonic sequence 4. Fibonacci sequence
4 Different types of sequence
1. Patterns of Visuals 2. Patterns of Flow 3. Patterns of Movement 4. Patterns of Rhythm 5. Patterns of Texture 6. Geometric Patterns
6 Different Kinds of Pattern
IAN NICHOLAS STEWART
A British mathematician and was born on 24 September 1945 in England.
Sunflower
A type of flower that contains both radial and bilateral symmetry.
Fractals
A type of mathematical shape that are infinitely complex.
Closure
A binary operation on a set G, then, is simply a method (or formula) by which the members of an ordered pair from G combine to yield a new member of G. This condition is called (blank).
MATHEMATICS
A formal system of thought for recognizing, classifying, and exploiting patterns.
Mechanical waves
A kind of wave which propagate through a medium ---- air or water, making it oscillate as waves pass by.
Mathematics
A language we understand.
Patterns of Visual
A pattern that repeats forever, and every part of the fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image.
Ian Nicholas Stewart
A person who wrote "Whatever the reasons, mathematics is a useful way to think about nature. What does it want to tell us about the patterns we observe?..."
DR. CATHERINE P. VISTRO-YU
A professor of Mathematics Education, Ateneo de Manila University.
Transitive
A relation R on A is (blank) if given a R b and b R c then a R c.
Symmetric
A relation R on A is (blank) if given a R b then b R a.
Reflexive
A relation R on A is said to be (blank) if every element of A is related to itself. In notation, a R a for all a ∈ A.
Equivalence relation on A
A relation that is refexive, symmetric, and transitive is called (blank).
Closed
A set is (blank) under operation if the operation assigns to every ordered pair of elements from the set an element of the set.
Braces or Curly brackets { }
A set is denoted with (blank) and label or name the set by a capital letter such as A, B, C etc..
DR. CATHERINE P. VISTRO-YU
According to her, Mathematics, provides new questions to think about.
Difference of Sets
All elements which are in A but not in B.
Intersection of Sets
All elements which are in both A and B.
Union of Sets
All elements which are in either A or B (or both).
Compliment of Set
All elements which are not in A. (see example)
Cartesian Product
All possible ordered pairs where the elements of A are first and the elements of B are second.
telescope
Astronomers can use this tool to look at very distant galaxies.
1. precise (able to make very fine distinction) 2. concise (able to say things briefly); and 3. powerful (able to express complex thoughts with relative cases).
Characteristics of Mathematical Language
buttercup, columbine, and hibiscus
Classic five-petal flowers?
1. Helps us to take the complex processes 2. Facilitate not only to weather, but also to control the weather 3. Applied mathematics- used for solving problems in physics, - useful tool in biological sciences 4. Used by scientists and researchers in doing or performing researches
Essential Role of Mathematics
-"is equal to" (equality) _ "is a subset of" (set inclusion) _ "is less than or equal to" and "is greater than or equal to" (inequality) _ "divides" (divisibility).
Example of Reflexive
Human Body, Animal Movement, Sunflower, Snowflakes, and Honeycombs/Beehive, and Starfish
Example of Symmetries in Nature
The beating of the heart and breathing
Example of patterns of rhythm?
(see it in the module)
FORMULA FOR COMPUTING FOR THE nth TERM IN THE FIBONACCI SEQUENCE?
Landscape Mathematics = Landscape Architecture + Mathematics + Engineering
Formula of Landscape Mathematics?
Ordered pair
Given elements a and b, the symbol (a, b) denotes the (blank) consisting of a and b together with the specification that "a" is the first element of the pair and "b" is the second element.
1. 618
Golden Ratio is approximately equal to?
1. With curiosity (Sherlock Holmes analogy) 2. With a penchant for seeking patterns and generalities (inquisitiveness) 3. With a desire to know the truth 4. With trial and error 5. Without fear of facing more questions and problems to solve
HOW IS MATHEMATICS DONE? (Vistru-Yu)
LEONARDO PISANO BIGOLLO
His nickname is Fibonacci, a Italian Mathematician and the most talented Western mathematician of the Middle Ages.
University of Warwick
IAN NICHOLAS STEWART institution?
1. Does God Play Dice? 2. The Science of Discworld.
Ian Nicholas Stewart was known for his book called?
Bilateral symmetry
It can be divided into two identical halves and its great example is our body.
Rotations
It captures symmetries when it still looks the same after some rotation (of less than one full turn).
Milky Way
It contains our Solar System. Also, a barred spiral galaxy with a band of bright stars emerging from the center running across the middle of it.
UNIVERSE
It describes the collection of all the things that exist in space.
Translations
It exists in patterns that we see in nature and in man-made objects. It also acquires symmetries when units are repeated and turn out to have identical figures, like the bees' honeycomb with hexagonal tiles.
Snowflake
It has six-fold radial symmetry.
Convention
It helps readers distinguish between different types of mathematical expression.
Binary operation on a set
It is a calculation that combines two elements of the set (called operands) to produce another element of the set.
Set
It is a collection of well-defined objects.
Mathematics
It is a formal system of thought that was gradually developed in the human mind and evolved in the human culture.
Geometric Patterns
It is a kind of pattern which consists of a series of shapes that are typically repeated.
Harmonic progression
It is a progression formed by taking the reciprocals of an arithmetic progression/ sequence
Texture
It is a quality of a certain object that we sense through touch. It exists as a literal surface that we can feel, see, and imagine.
Function
It is a relation in which every input is paired with exactly one output.
Geometric progression
It is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
FIBONACCI SEQUENCE
It is a series of numbers governed by some unusual arithmetic rule. It organized in a way a number can be obtained by adding the two previous numbers.
Unit Set
It is a set that contains only one element.
Infinite set
It is a set that elements in a given set has no end or not countable.
Empty set or Null set
It is a set that has no element.
Finite set
It is a set that the elements in a given set is countable.
Function
It is a special type of relation where every input has a unique output.
PATTERN
It is a structure, form, or design that is regular, consistent, or recurring.
Conditional
It is a type of statement is shown by "if , then" using →.
Mathematics
It is all about the unbelievable patterns of numbers formed by nature and of the universe.
Algebraic expression
It is an expression which is made up of variables and constants, along with algebraic operations.
Venn Diagram
It is an illustration of the relationships between and among sets, groups of objects that share something in common.
Landscape Mathematics
It is an interdisciplinary STEM field that combines knowledge in landscape architecture, mathematics, and engineering used to design, build, and perceive this world of numbers.
wave
It is any form of disturbance that carries energy as it moves.
Subset
It is called a proper subset.
Patterns of Rhythm
It is conceivably the most basic pattern in nature.
Roster or Tabular Method
It is done by listing or tabulating the elements of the set.
Rule or Set-builder Method
It is done by stating or describing the common characteristics of the elements of the set. We use the notation A = { x / x ... }
Mathematics
It is immensely useful, practical, and powerful.
Equal sign
It is one of the most popular mathematical verb.
Human Body
It is one of the pieces of evidence that there is symmetry in nature.
Mathematical sentence
It is the analogue of an English sentence; it is a correct arrangement of mathematical symbols that states a complete thought.
Expression
It is the mathematical analogue of an English noun; it is a correct arrangement of mathematical symbols used to represent a mathematical object of interest.
Universal Set
It is the set of all elements under discussion
Equal Set
It is two or more sets consisting of exactly the same elements
Equivalent set
It is two or more sets consisting of the same number of elements
Symmetry
It is used to classify and organize information about patterns by classifying the motion or deformation of both pattern structures and processes.
Sequence
It refers to an ordered list of numbers called terms, that may have repeated values.
Relation
It shows a relationship between two values.
Reflection symmetry
It sometimes called line symmetry or mirror symmetry, captures symmetries when the left half of a pattern is the same as the right half.
Patterns of Movement
It talks about the left-right-left-right-left rhythm.
1. Use mathematics in their daily tasks and activities. 2. Important tool in the field of sciences, humanities, literature, medicine, and even in music and arts. 3. Helps us cook delicious meals by exacting our ability to measure 4. Helps us to shop wisely, read maps, use the computer, remodel a home
Mathematics is everywhere (4)
1. Everyone uses mathematics, whoever they are, wherever they are, and whenever they need to. 2. From mathematicians to scientists, from professionals to ordinary people, they all use mathematics. 3. For mathematics puts order amidst disorder. 4. It helps us become better persons . 5. It helps make the world a better place to live in.
Mathematics is for everyone according to Vistru Yu. (5)
National Aeronautics and Space Administration
NASA?
Cartesian Product
Notation: A × B
Difference of Sets
Notation: A − B
Intersection of Sets
Notation: A ∩ B
Union of Sets
Notation: A ∪ B
Compliment of Set
Notation: A' (or A^C )
OCEAN WAVES
The MUSIC OF NATURE
Terms
The elements in the sequence.
2^n
The formula for finding the total number of subsets of a given set.
Georg Cantor
The founder of Set Theory.
Nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes.
The great secret uncovered by mathematics?
A and B
The proper way of reading A ∧ B.
Golden Ratio
The ratios of successive Fibonacci numbers approach the number (phi)
Range or co-domain of the function
The set of all resulting value of y is called (blank).
Operands
The two elements in a operation is called (blank).
Domain of the function
The values of x is called (blank).
Patterns of Visual
These patterns are can be seen from the seeds and pinecones to the branches and leaves.
Water waves
They are created by energy passing through water causing it to move in a circular motion.
wind waves
They are surface waves that create the chaotic patterns of the sea.
Patterns of Flow
They are usually found in the water, stone, and even in the growth of trees. It presents in meandering rivers with the repetition of undulating lines.
Starfish
They have a radial fivefold symmetry.
Language
This is a system of communication consisting of sounds, words and grammar, or the system of communication used by people in a particular country or type of work.
Language
This is one of the most important thing among the people because it has an important role in communication.
Wallpaper symmetry
This kind of symmetry is created when a pattern is repeated until it covers a plane and its great example is honeycomb.
Patterns of Movement
This prevalence of pattern in locomotion extends to the scuttling of insects, the flights of birds, the pulsations of jellyfish, and also the wave-like movements of fish, worms, and snakes.
1. numbers and counting (operations) 2. numeric and geometric patterns 3. patterns of movement
Three common notions associated with mathematics?
Disjoint Sets
Two sets which are mutually exclusive or not having common element/s.
Joint Sets
Two sets who have common elements.
geometric sequence
We need to look for the common ratio.
study of pattern, art, language, set of problem-solving tools, and process of thinking.
What are five NATURE OF MATHEMATICS?
1. To organize patterns and regularities as well as irregularities. 2. To be able to predict. 3. To help us control weather, epidemics. 4. To provide tool for calculations. 5. To provide new questions to think about.
What mathematics is for? (5)
IAN NICHOLAS STEWART
Who wrote this statement "Mathematics is a formal system of thought that was gradually developed in the human mind and evolved in the human culture."?
Cardinal Number
are numbers that used to measure the number of elements in a given set. It is just similar in counting the total number of element in a set.
Whirlpool Galaxy
spiral galaxy
Applied mathematics
used for solving problems in physics,