ch1: the nature of mathematics Flashcards
Mathematics is a valuable tool for?
Mathematics is a valuable tool for exploring nature and our surroundings.
The study of ____________________________________ is a natural extension of mathematics.
patterns in nature and the environment
Mathematics may be observed in almost every situation and is used to explain the?
Mathematics may be observed in almost every situation and is used to explain the most frequent phenomena
The history and usefulness of patterns and numbers can be traced back to the origins of?
MATHEMATICS
It is concerned with human-created thoughts and ideas that were transformed into products. They were
created to connect the meaning of a pattern to the perception of counting, sequence, and regularities.
There is a link between these two. When there is one, the other occurs.
There is a link between patterns and counting. When there is a pattern, counting occurs.
There is ________________ when there is counting. As a result, in nature, pattern corresponds to?
There is reasoning when there is counting. As a result, in nature, pattern corresponds to logic or logical arrangement.
A ____________ pattern has its own set of characteristics.
A specific pattern has its own set of characteristics.
most people believe that mathematics is the study of?
patterns
Mathematics, may be found everywhere.
(true or false)
true
Mathematics, like patterns in nature, may be found everywhere.
Patterns come in a singular form.
(true or false)
false
Patterns come in a variety of shapes and sizes.
Patterns, on the other hand, are more wider and more prevalent wherever and at any time
(true or false)
true
These type of patterns, such as 2, 4, 6, and 8, are recognizable to us since they are among the first patterns we learn when we are young.
Number patterns
These type of patterns, such as 2, 4, 6, and 8, are recognizable to us since they are among the first patterns we learn when we are young. We gain experience both within and outside of school as we progress. Patterns, on the other hand, are more wider and more prevalent wherever and at any time.
Patterns can be?
(enumerate)
Patterns can be:
- sequential,
- spatial,
- temporal, and even
- linguistic.
Patterns can be sequential, spatial, temporal, and even linguistic. All these phenomena create a repetition of names or events called?
regularity
the following are examples of what?
- Dates in the Calendar
- Days in a Calendar
- Months in a Year
- Regular Holidays
regularity
this is when same things happen in the same circumstances.
Regularity
this is a regularity in the world or man-made design.
Pattern
these are visible regularities found in the natural world.
Pattern in Nature or Natural Pattern
Pattern is a regularity in the world or a?
man-made design
Pattern in Nature or Natural Pattern are ____________ regularities found in the_________________.
Pattern in Nature or Natural Pattern are visible regularities found in the natural world.
Patterns are repeated design or?
recurring sequence.
It is also an ordered set of numbers, shapes or other mathematical objects that arranged according to a rule.
Patterns
Patterns is also an ordered set of ________________, ____________ or other ________________________ that arranged according to a ________.
Patterns is also an ordered set of numbers, shapes or other mathematical objects that arranged according to a rule.
One of the most intriguing things we see in nature is patterns.
(true or false)
true
We tend to think of patterns as sequences or designs that are somewhat disorganized and that are repeat object.
(true or false)
false
We tend to think of patterns as sequences or designs that are orderly and that are repeat object.
We recognize the spots on a giraffe as a pattern, because they are the same shape and size, regular, and orderly.
(true or false)
false
We recognize the spots on a giraffe as a pattern, but they are not regular nor are any of the spots the same size or shape.
Types of Patterns
(enumerate)
- Symmetry
- Spiral
- Meander
- Waves or Riffles
- Foams or Bubbles
- Tessellation
- Fractures or Cracks
- Stripes and Spots
- Fractals
it refers to a sense of harmonious and beautiful proportion and balance.
Symmetry
a curve which emanates from a point, moving farther away as it revolves around the point.
Spiral
one of a series of regular sinuous curves, bends, loops, turns, or winding in the channel of rivers, streams, or other water course.
Meander
a disturbance that transfer energy through matter or space, with little or no mass transport.
Waves or Riffles
a substance formed by trapping pockets of gas in a liquid or solid.
Foams or Bubbles
tilling of plane using one or more geometric shapes, called the tiles, with no overlaps and no gaps.
Tessellation
are patterns that are formed by repeated cubes or tiles.
Tessellation
separations of an object or material into two or more pieces under the action of stress.
Fractures or Cracks
series of bands or strips and spots, often of the same width and color along the length.
Stripes and Spots
a never-ending pattern. Infinitely complex pattern that are self-similar across different scales.
Fractals
Uses of Mathematics
(enumerate)
- Technology: navigation, prediction
- Engineering: construction, robotics
- Media: music, movie, election
- Medicine and Health: pharmacy, surgery
- Finance and Business: banking, gambling
Fibonacci was introduced in?
“Book of Counting”
begins with 0 and 1, adding the last two numbers: 0, 1, 2, 3 … (petals).
Fibonacci
The Golden ratio is also called?
- Golden Part, or
- Golden Proportion, or
- Divine Proportion
The Golden ratio is generally denoted by the?
Greek letter Phi (φ), in lower case,
The Golden ratio represents an?
represents an irrational number 1.6180339887…,
What was said about “Phi?”
It is said that Phi is the initial letters of Phidias’ name adopted to designate the golden ratio
set of all numbers in special orders
Sequence
number of(/in) a sequence
Terms
sum of terms
Series
has first and last terms
Finite Sequence
has first term but no last term
Infinite Sequence
this is when a term is obtained by adding d to the next term
Arithmetic sequence
