Mathematics In The modern World Midterm Exam Reviewer
1.618034
(Golden Ratio) approximate value of Phi Φ
are of circles/are of the hexagon x 100%
(Packing Problem) hexagon packing formula
are of circles/are of the square x 100%
(Packing Problem) square packing formula
nothing
0 represents
Mathematics is about
1. Numbers 2. Operations 3. Functions 4. Thingification 5. Proof
Angle of rotation formula
360⁰/n n is the number of lines of symmetry of the object
sequence
A list of numbers that often form a pattern
interval notation
A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval. [ ]=included (used when the endpoints are included in the set ex. "≥" "≤" ) ( ) = excluded (used when the endpoint is not included ex. "between" "<" ">")
Fibonacci sequence
A sequence of numbers in which each number is the sum of the preceding two.
Unit Set
A set with only one element
Universal Conditional Statement
A statement that is both universal and conditional "for all, if then" Ex: For all animals, if a is a dog, then a is a mammal
Universal Existential Statement
A statement that is universal because its first part says that a certain property is true for all objects of a given type, and it is existential because its second part asserts the existence of something "for all, ther is"
Rotational (radial) symmetry
A type of symmetry a figure has if it can be rotated less than 360 degrees about its center and still look like the original.
The total number of family members correspond to a Fibonacci number
All of the following statements are correct about Fibonacci except:* The logarithmic spiral growth of the Nautilus shell is an example of Fibonacci. The total number of family members correspond to a Fibonacci number Fibonacci numbers are the root of the discovery of the secret behind sunflower seeds The numbers of petals of almost all flowers in the world correspond to the Fibonacci numbers.
Fibonacci Sequence
An infinite sequence of natural numbers and each value is obtained by adding the previous two.
closed interval
An interval that includes both of its ending points and all the points between these ending points is a closed interval. [ ]
irrational numbers
Any real number which cant be expressed as a fraction of two integers
Golden Ratio
Defines as the longer part divided by the smaller part is also equal to the whole length divided by the longer part.
2.71828
Euler's Constant
-Sneezeworts -Flower Petals -Pinecones
Examples of fibonacci in nature
November 23
Fibonacci day
-77
Find the 30th term of the arithmetic sequence, 10, 7, 4...
5,461,243
Find the exponential growth: P= 860,000 r=7 % t=8 years
Sₙ = fₙ₊₂ - 1
Formula for finding the sum of fibonacci numbers
symmetry
Fractal pattern, spiral pattern, and bilateral pattern. These are examples of __________ in nature.
son of bonacci
His nickname was Fibonacci which means:
Sunflower
It contains both radial and bilateral symmetry
Symmetry
It is conceivably the most basic pattern in nature.
Who created the Fibonacci Sequence?
Leonardo Pisano Bigollo (Leonardo Fibonacci)
Jacques Philippe Marie Binet
Mathematician who derived the binet's formula
All Set of Natural Numbers
N
A=Pe^rt
Population Growth formula for finding A
r = (A/P) / t
Population Growth formula for finding r (rate)
t = (A / P) / r
Population Growth formula for finding t (time)
pattern
Which is a repeated design and mathematically speaking, is series or sequence that repeats?
All set of Rational Numbers
Q
All set of Real Numbers
R
Golden Rectangle
The amazing grandeur of Fibonacci sequence was discovered in the structure of _______.
8144
The population of a certain town is 5000. If it increases 5% each years, what will be the approximate population at the end of 10 years?
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbers. (excluding zero)
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbers. excluding 0
35 years
The small town of West Fremont has a population of 50,000. If the growth rate of West Fremont is 2%, then how long will it take for the population of West Fremont to double?* 2/2 70 years
All set of Whole Numbers
W
Q
What is the next letter in the series; A, D, I, L?
60
What is the sum of Fib (10) + Fib (5)
10945
What is the sum of the first 20 Fibonacci numbers?
Geometric
What type of sequence deals with common ratio?
earthquakes
Which is NOT a manifestation of mathematics in nature?* honeycomb sand dunes ripples in the pond earthquakes tiger stripes
This enable the bees to store the maximum honey they can produce at a minimum amount of wax
Why honeycombs are hexagonal?
All set of Intigers
Z
All set of positive intigers
Z+
Universal Statement
a certain poperty is true for all elements in a set. universal qualifiers: "for all", "for each", "given any", "for every"
one-to-one function
a function where each element of the range is paired with exactly one element of the domain
relation
a set of ordered pairs
Null set
a set with no elements "∅" "{}"
Existential Universal Statement
a statement that is existential because its first part asserts that a certain object exists and is universal because its second part says that the object satisfies a certain property for all things of a certain kind
vertical line test
a visual way to determine if a curve is a graph of a function or not.
bilateral symmetry
arrangement of body parts so there are distinct left and right halves that mirror each other
open interval
does not include its endpoints, and is indicated with parentheses. ( )
indipendent variable
domain (x)
Fibonacci Recursive formula for n ≥ 2
fn = fn−1 + fn−2
symmetry
having the same shape, size, and position on both sides of a dividing line
tesselations
identical shapes fit together with no gaps
Conditional Statement
if one thing is true then some other things also has to be true "if-then"
packing problem
involve finding the optimum method of filling up a given space such as a cubic or spherical container
quadrant
one of four sections into which the coordinate plane is divided
dependent variable
range (y)
fractals
simple repeated shapes reduced in size when repeated
Cardinality
the number of elements in a set denoted by n(A)
The Golden Ratio
the ratio of successive Fibonacci numbers denoted by phi
Existential Statement
there is atleast one thing for which the property is true "there is"
functional notation
way to name a function that is defined by an equation; for an equation in x and y, the symbol f(x) replaces y and is read as "the value of f at x" or simple as "f" of "x"
Intigers
whole numbers and their opposites (including 0)