Σ, f(x) swiss mathematician "e" natural logarithm

Father of Fractals

decoded the Nazi crypto-code protected by the infamous Enigma Machine

set theory, geometry, quantum mechanics - lead to were computers now

-Greatest Mathematician Ever - published “Arithmetical Investigations”

Greatest Scientist Ever -3 Laws of motion - first decompose white light into its components

independent work in Calculus

“We lived in a patterm-world cosmos”

visible regularities found in natural world

infinitely complex patterns that are self-similar across different scale

published by Pisabo-Bigollo encouraged to use of hindu arabic numerals

american mathematician who proposed using the firt letter of Phidias to represent the golden ration in the 1900s

"Timaeus" describes five possible regular solids that relate to the golden ratio

systematic means of communicating ideas the use of conventionalized signs, sounds, gestures, or marks having understood meaningfuls

study of numbers, number patterns and relationship, counting, measuring -also a way to communicate and analyze ideas -way of reasoning that is unique to human beings

-to communicate mathematical ideas among themselves

as a language has syntax to make the expression well-formed to make characters and symbols clear and valid ...,

the next term is found by multiplying by a constant called the common ratio

a fact, name, notation, or usage which generally agreed upon by Mathematicians

correct arrangements of mathematical symbols that states a complete thought

English:Phrases Mathematics:

expressed as a ratioof two whole numbers

mnemonic used to remember the order of operations in Mayh problems

a device, such as a formula or rhyme, used as an aid in remembering

“logic and imagination are required in Math"

AAA

number sequence we add a common difference to find for the mext term

able to make very fine distinctions

able to say things briefly

whose value is unknown to us which can take any value

an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

whose value is unknown to us which can take any value.

as it is a constant value used with the variable term and is well defined

value term which has a definite value

are made up of terms represented with the help of unknown variables, constants and coefficient

it is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign

well-formed according to rules that depend on the context. It is a correct arrangement of mathematical symbols used to represent a mathematical objects of interest. An expression does not state a complete thought; it does not make sense to ask if an expression is true or false

The most common expression are:

-the sum of a real number and imaginary number (a +bi) -denoted by (c)

The square root of -1.

The numbers which include both rational and irrational numbers.

These numbers include the non-terminating, non-repeating decimals such as pi and Phi (Golden Ratio)

number system

strict inequality, greater than

Any number that is a natural number or negative of the natural number or zero

able to express complex thoughts with relative ease.

statements that convey ideas or propositions are created by combining strings of symbols. For instance, the area of any plane figure may be represented by the symbol A

In the areas of mathematical genetics, mathematical ecology, mathematical neuro- physiology, development of computer software for unique biological and medical problems, mathematical theory of epidemics,...

company launches a significant project, an actuary may examine the project, evaluate the financial risk associated, forecast future financial results, and

dimension and magnitude of the earth, its situation and position in the universe, the formation of days and nights, lunar and solar eclipse, latitude and longitude, maximum and minimum rainfall, and so on are some of the numerous learning areas of geography that require the application of mathematics.

There are changes in soil fertility, forest distribution, and ecology that must be quantitatively calculated in order to exert desirable control over them.

help businesses by preparing their taxes and planning for future years. They deal with tax codes and forms, calculate interest using formulas, and spend a lot of time organizing paperwork.

anticipate the weather for farmers, pilots, holidaymakers, and people who rely on the sea. They read maps, work with computer models, and grasp physics' mathematical rules.

assess work costs and employ industry-specific math abilities. They work with slopes, areas, volumes, and distances and must have strong mathematical underpinnings.

study of numbers, shapes, and quantities

link to one another through the use of signs, symbols, and proof

derived from counting, describing objects, and measuring.

Series of bands or strips and spots, often of the same width and color along the length.

- has the smallest area possible, while meeting certain conditions -when bubbles are joined together, they change shapes to maximize their space-filling capabilities and minimize the energy required to contain the multiple volume of gases

a1

n

an = a1 + (n – 1) d

an = a1 (r) n-1

formed by adding the preceding numbers, beginning with 0 and 1

an ordered list of numbers, called terms, that may have repeated values.

The arrangement of these terms is a set by a definite rule.

"series of numbers in which the sum of the two previous numbers is each number

was first called the Divine Proportion which was explored by Luca Pacioli (Italian mathematician) entitled "De Devina Proportione" in 1509.

In the early 1500s, the golden ratio was first called the Divine Proportion which was explored by ______(italian mathematician)

it was possibly da Vinci who first named it the "Latin for Golden Section" which is “Section Aurea”.

(490 BC 430 BC) widely used the golden ratio in his works of sculpture. The exterior dimension of the in Athens, Greece embodies the golden ratio.

the first to give definition of the golden ratio as "a dividing line in the extreme and mean ratio" in his book the "Elements"

"The Creation of Adam" which can be seen on the ceiling of the Sistine Chapel. He also used the pentagram or golden star in his painting the “Holy Family.”

"The School of Athens,"

"crucifixions"

"Self-Portrait".

The Birth of Venus is one of the world's famous and appreciated work of art and it was painted between 1482 and 1485. The painting is in the Uffizi Gallery in Florence, Italy. "Birth of Venus"

French post-impressionist painter. It is said that his paintings the "Bathers at Asinnieres" (1884), the "Bridge of Courbevoie" (1887), and "A Sunday on La Grande Jatte" appear to have applied golden ratio to define the horizon, to place point of interest and to create balance

"The Sacrament of the Last Supper," Inspired by Leonardo da Vinci,

Gothic cathedral built in Paris between 1163 and 1250, which has a golden ratio in a number of its main architectural proportions.