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24 Cards in this Set

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  • Back
Rhind Papyrus

Who, what, and its significance?
-a document that recorded Egyptian mathematics
-named after Henry Rhind, who purchased it
-but no one created it, it's collection of work
-significance is that it's our main source for Egyptian mathematics
The Elements

Who, what, and its significance?
-Euclid created it
-consists of many geometric problems in 8 books
-significance was it provided a model of an axiomatic system with definitions, axioms, and theorems
On the Measurement of the Circle

Who, what, and its significance?
-Archimedes wrote it
-three propositions that showed the measurement of a circle or the area of a circle
-a closer estimate of pi
Arithmetica

Who, what, and its significance?
-Diophantus wrote it
-189 problems that used one variable and only got one positive solution
-syncopation of algebra
Commentary on the Nine Chapters on the Mathematical Art

Who, what, and its significance?
-Liu Hui wrote it
-Chinese mathematics
-it was the central to Chinese mathematical activity for over one hundred years
The Condensed Book on the Calculation of al-Jabr and al-Muqabala

Who, what, and its significance?
-Muhammad Al-Khwarizimi
-dealt with solutions of equations by using "the science of reunion and reduction"
-how to solve linear equations by adding and subtracting the same quantity on both sides of an equation and showed how to complete the square
Liber Abbaci

Who, what, and its significance?
-Fibonacci
-explained the virtues of Hindu-Arabic decimal system
-introduced the Hindu-Arabic numeration system to Europe
Ars Magna

Who, what, and its significance?
-Cardan wrote it
-text on algebraic equations and expanded Tartaglia's discoveries
-1st to take notice of negative roots
Geometry (Descartes)

Who, what, and its significance?
-Descartes wrote it
-Descartes' book that combined algebra and geometry
-created analytic geometry
Treatise on the Arithmetical Triangle

Who, what, and significance?
-Pascal wrote it
-an upward-sloping diagonal arrangement of the coefficients of the expansion of the binomial (x+y)^n-1
-created an easier way to compute Pascal's Triangle for (x+y)^n
The Principia

Who, what, and significance?
-written by Newton
-explained Nature and the Universe in a mathematical way
-showed the universe and nature in a more complex way
-most momentous scientific treatise ever printed
3 Stages of Algebraic Symbols
1) rhetorical-written in words
2) syncopated-shorthand and abbreviations (Diophantus)
3) symbolic-symbols are used to replace quantities
Ptolemaic and Copernican Models of the Universe
-Ptolemaic view was that the earth was at the center (geo)
-Copernican view was that the sun was at the center of the universe (hemo)
Kepler's Laws
1) the orbit of a planet is an ellipse with the sun at one focus
2) Law of Equal Area in Equal Time
-planet's orbit is fastest when closest to the sun
3) Period of Motion
-(P1)^2/(D1)^3=period/distance of 2nd planet
Descartes' Philosophy
-"I think I am, therefore, I am."
Newton's fluents, fluxions, and moments
-"fluents"- x and y, quantities that change with time
-"fluxions"- X, speed at which x changes
-"moments"- A, infinitely small period of time
Pythagorean Theorem
-in a right triangle, the sum of the squares of the length of the legs equals the square of the length of the hypotenuse
Fundamental Theorem of Arithmetic
-Every positive integer n>1 is either a prime or can be expressed as a product of primes
Fundamental Theorem of Algebra
-Every polynomial equation having complex coefficients and degree has at least one complex root
Fundamental Theorem of Calculus
-is what Newton proved
Euclid's Fifth Postulate
-If line C intersects two lines A and B, and the interior angles on one side are less than two right angles, then lines A and B will eventually intersect on that same side
Descartes
-created analytic geometry also known as Cartesian geometry
-wrote The Principia, La Geometrica, Discourse book
-found tangents to y^2 @ (a,a) and found positive roots and negative roots through sign changes
Newton
-Method of Fluxions
-wrote the Principia
-helped with the Fundamental Theorem of Calculus
-co-discoverer of Calculus with Leibniz
-contributed to Physics and Astronomy
-found a more complex universe
Leibniz
-similar to Newton
-co-discoverer of Calculus
-created Calculus