# Shared Flashcard Set

## Details

History of Mathematics- Midterm
Material for the first half of the class, includes proofs
63
Mathematics
10/25/2012

Term
 Wrote the Rhind Papyrus
Definition
 Ahmose (or Ahmes)
Term
 One of the two teachers of Pythagoras
Definition
 Anaximander
Term
 Created Sandreckoner, "give me a lever and a place to stand, and I shall move the earth."
Definition
 Archimedes
Term
 Made a 3-dimensional method for doubling the cube
Definition
 Archytas
Term
 Founded the lycium, established systematic logicAttempted to re-axiomize geometry. Wrote Foundations of Geometry. The last mathematician to have known all that existed related to math, in his time.
Definition
 AristotleDavid Hilbert
Term
 Questioned about first and second-order differential equations whose solutions could not be found
Definition
 Diophantus
Term
 -Division algorithm-Wrote the Elements-There is no royal road to geometry
Definition
 Euclid
Term
 Finding primes, idea for longnitude and latitude lines
Definition
 Eratosthenes
Term
 How to square a circle!
Definition
 Ferdinand Lindemann
Term
 Developed proof that the square root of 2 is not rational.
Definition
 Hippasus
Term
 Swindled by pirates, and squaring the loom.
Definition
 Hippocrates of Chios
Term
 A first female mathematician among European culture.
Definition
 Hypatia
Term
 Proof that an angle of arbitrary measure cannot be trisected
Definition
 Pierre Wantzel
Term
 Man with a strong connection to music, math, and religion
Definition
 Pythagoras
Term
 -Everything is composed of water- "Know thyself"
Definition
 Thales
Term
 Constructed a spiral using properties of right triangles and the square root of 17.
Definition
 Theodorus
Term
Definition
 Zeno
Term
 A series of books that helped to see how to construct a geometry
Definition
 Elements
Term
 The three types of numeration systems are
Definition
Term
 Hypotheses of the base-60 system?
Definition
 1. Very divisible number2. Finger counting3. Lunar cycle4. Cultures with a base 6 and base 10 system combined their systems
Term
Definition
 Achilles and the Turtle, Dichotomy
Term
 What culture used these systems?- Place value- Additive- Multiplicative
Definition
 - Babylonian- Egyptians, Greeks- Chinese
Term
 The method of false position was developed by the ______.The ______ used a vertical and positional system.Euclid's algorithm?
Definition
 - Ionic Greeks- Mayans- n = pq + r
Term
 Square with same area as a given shapeNumbers that are solutions to equations in algebraNumbers that cannot be direct solutions of equationsMethod of fitting figures with smaller shapes to approximate their area
Definition
 - Quadrature- Algebraic- Transcendentals- Method of Exhaustion
Term
 Any symbol used for a numeric value is a ______Any picture used for a numeric value is a ________Schools of Pythagoras were?
Definition
 - Logograms- Pictograms- Semicircle and Society schools
Term
 Problem of doubling the cubeWhat are the Platonic solids?Tool used for finding prime numbers
Definition
 - Delian problem- cube, tetrahedron, dodecahedron, and icosahedron- Sieve of Erasthostenes
Term
 First reference to the Golden Ratio.
Definition
 Eudoxus
Term
 Harmonic mean, Mathematical Collection, and quadrature of the circle
Definition
 Pappus of Alexandria
Term
 Showed that the square root of any nonsquare integer is an irrational number
Definition
 Thaetetus
Term
 Determined the methodology of the Babylonian number system, noticing that 60 had many divisors, and was an easily handled number.
Definition
 Theon of Alexandria
Term
 Gematria
Definition
 Number assigned to each letter of the alphabet, 'sums' of different numbers make different words.
Term
 Another name for a number that cannot be expressed as a ratio of two integers.Had an application to geometry of line segments.
Definition
 Incommensurable
Term
 A number that can be represented by a series of dots comprising a geometric figure (such as a triangle).
Definition
 Figurative numbers
Term
 Two integers such that the sums of all of their divisors add up to one another.
Definition
 Amicable numbers
Term
 Number whose factors add up to that number.
Definition
 Perfect number
Term
Definition
 Social Number
Term
 Number for which the sum of all its divisors is less than the number.Number for which the sum of its divisors is greater than the number.
Definition
 Deficient numberAbundant number
Term
 The first tally stick, said to be 35000 years old
Definition
 Lebombo bone
Term
 Another baboon fibula, said to be a tally stick, from the Upper Paleolithic era, and is about 20000 years old
Definition
 Ishango bone
Term
 A spiral constructed from contiguous right triangles. (the hypotenuse of the nth triangle is the base of the (n+1)st triangle.)
Definition
 The Spiral of Theodorus
Term
 Machine made by Archimedes that could transfer water from a low-lying body of water into irrigation ditches.
Definition
 Water screw
Term
 Theorems for the surface area of a solid of revolution is equal to the arc length s and the distance traveled by the geometric centroid, d.A = sd.
Definition
 Pappus Centroid Theorem
Term
 Highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices.
Definition
 Archimedean solids
Term
 Way of solving a standard equation with one unknown; involved making a guess, and then refining until the correct value that makes the equation true is found.
Definition
 Method of False Position
Term
 Another papyrus containing early mathematical stuff from Egypt
Definition
 Moscow Papyrus
Term
 A pillar of black basalt with three different languages, from which the hieroglyphic language was deciphered.
Definition
 Rosetta Stone
Term
 A tablet with the first results of Pythagorean Triples
Definition
 Plimpton 322
Term
 Tablet found in 1936 that has several Babylonian uses of the Pyth. theorem. Includes problem of a isosceles triangle inscribed within a circle.
Definition
 The Susa Tablet
Term
 An axiomic work by Aristotle that looks at what can be asserted about anything that exists just because of its existence and not because of any special qualities it has.
Definition
 Metaphysics
Term
 Document published by Archimedes that talks about surface areas of a sphere and the contained ball; a relationship between the radius of the sphere and the height of another solid.
Definition
 On the Sphere and Cylinder
Term
 An ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations.
Definition
 Arithmetica
Term
 A 78-page Mayan document with different aspects of their culture, including religion and astronomy.
Definition
 Dresden Codex
Term
 Connection to the musical scale
Definition
 Pythagoras
Term
 "Everything is number."
Definition
 PYTHAGORAS
Term
 Chief librarian at the Museum
Definition
 Eratosthenes
Term
 There is a spiritual world independent of the material world
Definition
 Plato
Term
 'Beta'
Definition
 Eratosthenes
Term
 Method of Exhaustion
Definition
 Eudoxus
Term
 Mule, laziness, sponges
Definition
 Thales
Term
Definition
 Plato
Term
 First to work with figurative numbers
Definition
 Pythagoras
Term
 Said existence could not be summed up as change
Definition
 Zeno
Term
 Squared the lune
Definition
 Hippocrates
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