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One of the two teachers of Pythagoras 

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Created Sandreckoner, "give me a lever and a place to stand, and I shall move the earth." 

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Made a 3dimensional method for doubling the cube 

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Founded the lycium, established systematic logic
Attempted to reaxiomize geometry. Wrote Foundations of Geometry. The last mathematician to have known all that existed related to math, in his time. 

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Questioned about first and secondorder differential equations whose solutions could not be found 

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Division algorithm Wrote the Elements There is no royal road to geometry 

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Finding primes, idea for longnitude and latitude lines 

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Developed proof that the square root of 2 is not rational. 

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Swindled by pirates, and squaring the loom. 

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A first female mathematician among European culture. 

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Proof that an angle of arbitrary measure cannot be trisected 

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Man with a strong connection to music, math, and religion 

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Everything is composed of water  "Know thyself" 

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Constructed a spiral using properties of right triangles and the square root of 17. 

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Made some errors in investigating the infinity. Paradox about a barber in town where people 

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A series of books that helped to see how to construct a geometry 

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The three types of numeration systems are 

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Place value, additive, multiplicative 


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Hypotheses of the base60 system? 

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1. Very divisible number 2. Finger counting 3. Lunar cycle 4. Cultures with a base 6 and base 10 system combined their systems 


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Achilles and the Turtle, Dichotomy 


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What culture used these systems?  Place value  Additive  Multiplicative 

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 Babylonian  Egyptians, Greeks  Chinese 


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The method of false position was developed by the ______.
The ______ used a vertical and positional system.
Euclid's algorithm? 

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 Ionic Greeks  Mayans  n = pq + r 


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Square with same area as a given shape
Numbers that are solutions to equations in algebra
Numbers that cannot be direct solutions of equations
Method of fitting figures with smaller shapes to approximate their area 

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 Quadrature  Algebraic  Transcendentals  Method of Exhaustion 


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Any symbol used for a numeric value is a ______ Any picture used for a numeric value is a ________ Schools of Pythagoras were? 

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 Logograms  Pictograms  Semicircle and Society schools 


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Problem of doubling the cube
What are the Platonic solids?
Tool used for finding prime numbers 

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 Delian problem  cube, tetrahedron, dodecahedron, and icosahedron  Sieve of Erasthostenes 


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First reference to the Golden Ratio. 

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Harmonic mean, Mathematical Collection, and quadrature of the circle 

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Showed that the square root of any nonsquare integer is an irrational number 

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Determined the methodology of the Babylonian number system, noticing that 60 had many divisors, and was an easily handled number. 

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Number assigned to each letter of the alphabet, 'sums' of different numbers make different words. 


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Another name for a number that cannot be expressed as a ratio of two integers. Had an application to geometry of line segments. 

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A number that can be represented by a series of dots comprising a geometric figure (such as a triangle). 

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Two integers such that the sums of all of their divisors add up to one another. 

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Number whose factors add up to that number. 

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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. 

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Deficient number Abundant number 


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The first tally stick, said to be 35000 years old 

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Another baboon fibula, said to be a tally stick, from the Upper Paleolithic era, and is about 20000 years old 

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A spiral constructed from contiguous right triangles. (the hypotenuse of the nth triangle is the base of the (n+1)st triangle.) 

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Machine made by Archimedes that could transfer water from a lowlying body of water into irrigation ditches. 

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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. 

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Highly symmetric, semiregular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices. 

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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. 

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Another papyrus containing early mathematical stuff from Egypt 

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A pillar of black basalt with three different languages, from which the hieroglyphic language was deciphered. 

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A tablet with the first results of Pythagorean Triples 

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Tablet found in 1936 that has several Babylonian uses of the Pyth. theorem. Includes problem of a isosceles triangle inscribed within a circle. 

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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. 

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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. 

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On the Sphere and Cylinder 


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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. 

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A 78page Mayan document with different aspects of their culture, including religion and astronomy. 

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Connection to the musical scale 

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Chief librarian at the Museum 

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There is a spiritual world independent of the material world 

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First to work with figurative numbers 

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Said existence could not be summed up as change 

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