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
