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24 Cards in this Set
- Front
- Back
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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 |
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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 |
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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 |
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Arithmetica
Who, what, and its significance? |
-Diophantus wrote it
-189 problems that used one variable and only got one positive solution -syncopation of algebra |
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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 |
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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 |
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Liber Abbaci
Who, what, and its significance? |
-Fibonacci
-explained the virtues of Hindu-Arabic decimal system -introduced the Hindu-Arabic numeration system to Europe |
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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 |
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Geometry (Descartes)
Who, what, and its significance? |
-Descartes wrote it
-Descartes' book that combined algebra and geometry -created analytic geometry |
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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 |
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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 |
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3 Stages of Algebraic Symbols
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1) rhetorical-written in words
2) syncopated-shorthand and abbreviations (Diophantus) 3) symbolic-symbols are used to replace quantities |
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Ptolemaic and Copernican Models of the Universe
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-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) |
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Kepler's Laws
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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 |
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Descartes' Philosophy
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-"I think I am, therefore, I am."
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Newton's fluents, fluxions, and moments
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-"fluents"- x and y, quantities that change with time
-"fluxions"- X, speed at which x changes -"moments"- A, infinitely small period of time |
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Pythagorean Theorem
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-in a right triangle, the sum of the squares of the length of the legs equals the square of the length of the hypotenuse
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Fundamental Theorem of Arithmetic
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-Every positive integer n>1 is either a prime or can be expressed as a product of primes
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Fundamental Theorem of Algebra
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-Every polynomial equation having complex coefficients and degree has at least one complex root
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Fundamental Theorem of Calculus
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-is what Newton proved
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Euclid's Fifth Postulate
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-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
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Descartes
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-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 |
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Newton
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-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 |
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Leibniz
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-similar to Newton
-co-discoverer of Calculus -created Calculus |
