History of Mathematics- Final Exam

Eudoxus is developing new methods of proof inducing a precursor to integral calculus

360 BCE

One extension of Pythagorean Theorem

Distance between two objects, on the Cartesian coordinate place

Who are two people that used game theory before its invention in 1944 by John Neumann?

Emile Borel, Waldegrave, and Hernan Cortez (burned the boats)

Calculates the circumference of the world

Eratosthenes

What is considered the greatest contribution of the ancient Egyptians to geometry? Significance?

Estimate of pi, 3.16, the closest to the real answer for over a millenium. Helped with geometry, architecture, and more. Perfect circles and keep tracks of days and years

Tacitly assumed the existence of points and lines, continuity and the infinite extent of a line

Euclid

Look at Pythagorean Theorem proof

Exam 1, Question 7

Dodecahedron

Face- pentagon #- 12

Icosahedron

Face- triangle #- 20

Tetrahedron

Face- triangle #- 4

Octahedron

Face- triangle #- 8

Develops the basis of trigonometry and maps around 850 stars

Hipparchus

Who first discovered the idea of irrational numbers and how?

Hippasus of Metopontum, a Pythagorean, trying to find the hypotenuse of a 1,1,rt2 triangle/ find rt2 and he got thrown overboard

Young Fibonacci get into math?

His dad was a merchant so he read many books brought to the port

An archivist, mathematician, and engineer working at the Library of Alexandria

Hypatia

Why was there no probability theory in the West before Pascal and Fermat?

No good numbers to use or place values

Liber Abaci (Fibonacci)

displayed Fibonacci sequence, Hindu-Arabic numeral system, used examples in nature and showed geometric correlation

Cube

face- square #- 6

Oldest evidence of geometry in China

300 BCE

Egyptians use unit fractions

1,000 BCE

First mathematical artifacts found in China

1,000 BCE

Olmec civilization in Mexico develops use of numbers

1,200 BCE

Mesopotamians produce tables of Pythagorean triples, use quadratic equations

1,600 BCE

Rhind papyrus of mathematical problems in Egypt

1,650 BCE

A Eulerian path, a path that visits each edge only once, is only possible in one of two scenarios

1. Exactly 2 nodes of odd degree 2. When all nodes are even degree

Earliest known use of zero as a decimal digit is introduced by Indian mathematicians

300 CE

The Christian Church is divided into the Western Catholic and Eastern Orthodox churches

1054 CE

The Crusades waged by the Christians of Europe against the Islamic Empire

1100-1300 CE

Founding of the University of Oxford

1117 CE

Genghis Khan is elected as the emperor of the Mongols, establishing the Mongol Empire

1200 CE

The Magna Carta is sealed by John of England

1215 CE

The Black Death begins in Central Asia and eventually makes its way to Europe

1340 CE

Jain mathematicians write a manuscript containing many mathematical results including work on number theory, operations with fractions, and permutations and combinations

150 BCE

The Nine Chapters on the Mathematical Art is completed

150 BCE

The Rosetta Stone is inscribed in a block of basalt

196 BCE

Stonehenge

2,500 BCE

Beginning of the construction of the Great Wall of China

200 CE

Egyptians develop hieroglyphic numerals

3,000 BCE

Mesopotamians divide the circle into 360 degrees

3,000 BCE

Euclid writes his Elements

300 BCE

Eudoxus develops techniques establishing him as one of the greatest of classical Greek mathematician

300 BCE

Traditional "fall" of Rome

476 CE

Birth of Buddha

500 BCE

Birth of Confucius

500 BCE

The Hagia Sophia cathedral is consecrated

537 CE

Muhammad is born in Mecca

570 CE

The eruption of Vesuvius

79 CE

India, first mention of a symbol for zero

900 BCE

Writes the first known proofs by mathematical induction

Al-Karaji

Writes Al-Jabr, which introduces systematic algebraic techniques

Al-Khwarizimi

This book is a great synthesis of the mathematical astronomy of the Greek World

Almagest

Invents a device that raises water from a lower level to a higher one

Archimedes

Concludes that the Earth is in orbit around the sun

Aristarchus

In the 18th and 19th centuries, who were the main three pioneers of statistics

Bayes, Gauss, LeGendre

Which mathematicians play the most important role in complex numbers?

Bombelli, Carneaux, and Euler

Writes the first known work in which zero is clearly explained. It also gives rules for working with positive and negative numbers

Brahmagupta

What is the difference between the definite integral crossing the x axis and the area of the curve crossing the x axis?

Can't treat as area, but as a sum of sections; using anti-derivative as opposed to sections; subtract negative area

Technical advisor to the commission tasked with revising the calendar

Clavius

What catalyzed the advancement of statistics in not only criminal justice, but also all other fields?

Computers

Who published the first work on probability theory?

De Ratiociniis In Ludo Aleae by Christiaan Hnygens

First steps toward algebraic notation

Diophantus

Writes that a continuous line is composted of an infinite number of indivisible points separated by an infinite number of minuscule empty spaces

Galileo

Briefly describe one way statistics is used in criminal justice today

Geographic profiling, resource allocation for policing

Al-Samawal's defintion of algebra

Handling unknown variables using arithmetic tools in the same way arithmeticians would handle knowns

Why didn't Archimedes not leave any writing or commentary about his inventions?

He was more interested in his higher math having his name than his inventions, and not everyone could read so pictures would be more helpful

This book is a brilliant original work on indeterminate analysis

Liber quadratorum

What kinds of problems in the ancient times were statistics developed to solve?

Mean, median, mode How long a ladder should be

His attempts at proving the parallel postulate show the possibility of non-Euclidean geometries

Omar Khayyam

What was the letter used for Euler's number before e?

Originally labeled as constant b

Wrote a manuscript containing the first use of Fibonacci numbers and Pascal's triangle

Pingala

What are game trees used for in games such as Tic Tac Toe

Represents all possibilities of the outcomes

Wrote a mathematical manual including the Chinese Remainder Theorem

Sun Zi

What else was going on when Riemann was alive?

Washing machines invented, tai ping, mexican independence, civil war

Significance of Hagia Sophia cathedral

architectural masterpiece that used complex mathematical formulas, was a Catholic cathedral, Eastern orthodox cathedral and mosque

Importance of Euclid's Elements

basis on axioms, laid the foundation for modern calculus and algebra, helped spark mathematicians later

Achievements of Nicole Oremse?

rectangular coordinate system before Descartes, pushed it to 3-d and was the first to prove the Harmonic series was divergent

Significance of Timbuktu Mathematical Manuscripts

shows there were still advancing in mathematics and sciences in Sub-Saharan africa when when hiding from European colonizers

Method of False Assumption

the guess and check method, assume an answer then use proportions to get the correct answer

Significance of House of Wisdom in Baghdad

translated mathematical works into different languages, facilitating the spread of knowledge

Syncopated algebra

use of words and variables/numbers