MMW quiz 2 pt 1 Flashcards
is formed by adding the preceding numbers, beginning with 0 and 1 * Some book starts from 1 and 1.
Fibonacci Sequence
is an ordered list of numbers, called terms, that may have repeated values. The arrangement of these terms is set by a definite rule.
Sequence
Fibonacci means
Son of Bonacci
Published the Liber Abbaci, or Book of Calculation
Leonardo Pisano Bigollo (1170-1250)
an arithmetical text that concentrated primarily on financial computations and encouraged the use of Hindu- Arabic numerals
Book of Calculations / Liber Abbaci
A man had placed a pair of rabbits in a spot surrounded on all sides by a wall. How many pairs of rabbits will be created from that pair in a year if each pair is supposed to produce a new pair per month, with the second month being the most productive?
The Rabbit Production Problem
It is an irrational number. Geometrically, it can also be visualized as a rectangle perfectly formed by a square and another rectangle, which can be repeated infinitely inside each section.
Golden Ratio
Golden Ratio
1.618
It was discovered that the Fibonacci sequence’s mysterious and elusive properties have a deep association with
_____
the golden ratio
The golden ratio has an ________to the fibonacci sequence.
Asymptotic relationship
Fibonacci Sequence calcu formula
(1 ÷ √5)((((1 + √5) ÷ 2) ^ n) - (((1 - √5) ÷ 2) ^ n) )=
The the Golden ratio (or Golden Part, or Golden Proportion, or Divine Proportion) is generally denoted by the Greek letter ___________ which represents an irrational number 1.6180339887…
Phi (φ), in lower case,
It is said that Phi is the initial letters of ______ name adopted to designate the golden ratio.
Phidias
American mathematician, who proposed using the first letter of Phidias to represent the golden ratio in the 1900s
Mark Barr
the proportions of the length of the nose, the position of the eyes and the length of the chin all conform to some aspect of the Golden Ratio.
Mathematics and physical beauty
was a greek sculptor, painter, and architect. His statue of zeus at olympia was one of the seven wonders of the world.
Phidias or Pheidias
was an ancient Greek mathematician active as a geometer and logician. Considered the “father of geometry”, he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. Wikipedia
Euclid
was an ancient Greek philosopher born in Athens during the Classical period in Ancient Greece. In Athens, He founded the Academy, a philosophical school where he taught the philosophical doctrines that would later became known as Platonism
Plato
was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. Some of his famous works: The Last Supper, Mona Lisa, Veruvian Man, Lady with an Ermine, The Virgin and Child with St. Anne
Leonardo da Vinci
was an Italian sculptor, painter, architect, and poet of the High Renaissance. Born in the Republic of Florence, his work was inspired by models from classical antiquity and had a lasting influence on Western art. Some of his famous works: Sistine Chapel Ceiling, The Creatios of Adam, Doni Tondo
MIchelangelo Simoni
was an Italian painter and architect of the High Renaissance. His work is admired for its clarity of form, ease of composition, and visual achievement of the Neoplatonic ideal of human grandeur.
Raffaelo Sanzio da Urbino
was a Spanish surrealist artist renowned for hos technical skill, precise draftsmanship, and the striking and bizarre images in his work. Some of his famous works: The Sacrament of the Last Super, The Persistence of Memory
Salvador Dali
was an Italian painter of the Early Renaissance. His posthumous reputation suffered until the late 19th century, when he was rediscovered by the Pre-Raphaelites who stimulated a reappraisal of his work. Wikipedia Some of his famous works: The Birth of Venus, Primavera, Mars and Venus, Adoration of the Magi
Alessandro Filipepi
was a French post- Impressionist artist. He devised the painting techniques known as chromoluminarism and pointillism and used conté crayon for drawings on paper with a rough surface. Some of his famous works: The Circus, Bathers at Asnieres, A Sunday afternoon on the Island of La Grande Jatte 50 51
George Pierre Seurat
was a Dutch Golden Age painter, printmaker and draughtsman. An innovative and prolific master in three media, he is generally considered one of the greatest visual artists in the history of art and the most important in Dutch art history.
Rembrandt van Rijn
is a Gothic cathedral built in Paris between 1163 and 1250, which has a golden ratio in a number of its main architectural proportions
Notre Dame
used the golden ratio and was completed in 1648. The order and percentage of the arches on the main structure continues to decrease proportionately following the ratio.
Taj Mahal
In Paris, France,________________ also exhibits a golden ratio
the Cathedral of Our Lady of Chartes
the window design shows golden proportion.
united nations building
The tallest tower and freestanding structure in the world, __________________. The ratio of observation deck at 342 meters to the total height of 55,333 is 0.618 or Phi (Φ), the reciprocal of phi Q.
the CN Tower in Toronto,
Erected in 1889 _______________________ France, is an iron lattice. It was after the founder and builder of the tower, Alexandre Gustave Eiffel. The base is wider as it narrows down to the tip, following the golden ratio exactly.
the Eiffel Tower in Paris
THE APPLICATION OF MATHEMATICAL METHODS IN DIFFERENT FIELDS SUCH AS SCIENCE, ENGINEERING, BUSINESS, COMPUTER SCIENCE, AND INDUSTRY IS A COMBINATION OF MATHEMATICAL SCIENCE AND SPECIALIZED KNOWLEDGE.
Mathematics in Different Fields
Mathematics is applied specifically the differential and integral calculus to clarify the blurred image to clear image.
Another application of calculus is optimization (maximize or minimize) surface areas, volumes, profit and cost analysis, projectile motion, etc.
Forensic Science
Statistics, combinatorics, and graph theory are used by investigators to solve crimes.
Forensic Science
be numerical analysis in phenomena involving heat, electricity, and magnetism, relativistic mechanics, quantum mechanics, and other theoretical constructs.
Engineers
Modern computers are invented thru the help of mathematics. An important area of applications of mathematics is in the development of formal mathematical theories related to the development of computer science.
Computer science development includes, logic, relations and functions, set theory, counting techniques, graph theory, combinatorics, discrete probability, recursion and recurrence relations, number theory, computer-oriented numerical analysis, Operation Research techniques (Simulation, Monte Carlo Program, Evaluation Research Technique, Critical Path Method).
InfoTech
Just like Google, they use linear algebra to set itself apart from the other search engines by its ability to quantify “relevance” with the help of mathematics. On the other hand, Facebook uses graph theory to create inks between individuals.
Infotech
A combination of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering.
It is used in applications present in technologically advanced societies; examples include the security of ATM cards, computer passwords and electronic commerce.
Cryptography
use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to find patterns to shed light on past human behavior and in carbon dating artifacts.
Archeology
In economics, mathematics such as matrices, probability and statistics are used. The models may be stochastic or deterministic, linear or non-linear, static or dynamic, continuous or discrete, and all types of algebraic, differential, difference and integral equations arise for the solution of these models.
Social Science
Political analysts study past election results to see changes in voting patterns and the influence of various factors on voting behavior, on switching of votes among political parties and mathematical models for Conflict Resolution using Game Theory and Statistics.
Political Science
The rhythm that we find in all music notes is the result of innumerable permutations and combinations. Music theorists understand musical structure and communicate new ways of hearing music by applying set theory, abstract algebra, and number theory.
Music and Arts
It is said that the universe is written in language of mathematics, and its characters are triangles, circles, and other geometric figures.
Music and arts
In architecture, geometry, algebra, and trigonometry all play a crucial role. In order to plan their blueprints or original sketch designs, architects apply these math types. They also measure the likelihood of challenges that could be encountered by the construction team as they carry the design vision to life in three dimensions.
Why architectss should learn mathematics
