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)