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24 Cards in this Set
 Front
 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 alJabr and alMuqabala
Who, what, and its significance? 
Muhammad AlKhwarizimi
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 HinduArabic decimal system introduced the HinduArabic 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 upwardsloping diagonal arrangement of the coefficients of the expansion of the binomial (x+y)^n1 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) rhetoricalwritten in words
2) syncopatedshorthand and abbreviations (Diophantus) 3) symbolicsymbols 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 codiscoverer of Calculus with Leibniz contributed to Physics and Astronomy found a more complex universe 

Leibniz

similar to Newton
codiscoverer of Calculus created Calculus 