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| was one of the first mathematicians who claimed, erroneously, that it is impossible to solve, by radicals, the general cubic equation in one variable. |
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| was the first mathematician who solved, by radicals, the depressed cubic equation. |
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| was the second mathematician who solved, by radicals the depressed cubic equation. He defeated Antonio Fior in a mathematical challenge. |
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| was the mathematician who found a method for depressing general cubic equations in one variable. |
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| was the mathematician who solved, by radicals, the general cubic equation in one variable. |
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| is Cardano's book that contains procedures to solve general cubic equations. |
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| was the first mathematician who used imaginary numbers as a vehicle to solve cubic equations. |
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| was the mathematician who solved, by radicals, the general quartic equation in one variable. |
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| was the mathematician who proved that the general quintic equation is unsolvable by radicals. |
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| was the first mathematician who attempted to prove the impossibility of solving the general fifth-degree equation in one variable. |
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| was the first mathematician who thought that the product of two segment magnitudes is a segment. |
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| was the mathematician who states, without proof, that the number of solutions of an algebraic equation in one variable is equal to its degree. |
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| was the first mathematician to prove that (1) any polynomial equation with real coefficients in one variable of degree n has at most n roots and (2) those roots are of the form a+bi, where a and b are real numbers. |
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| was the first mathematician to prove that (1) any polynomial equation with complex coefficients in one variable of degree n has at most n roots and (2) those roots are of the form a+bi, where a and b are real numbers. |
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| It took _____ years to completely solve the problem of solving polynomial equations in one variable of degree 3 or higher. |
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| was the first mathematician to attempt to prove that (1) any polynomial equation in one variable has n roots, and (2) those roots are complex numbers. |
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| _______, ________, and _________ were three mathematicians who assumed that any polynomial equation in one variable has n roots. |
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| is considered the master of double reduction ad absurdum |
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| is the author of the book "The Measurement of the Circle." |
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| is the author of the book "On the Sphere and the Cylinder." |
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| showed that the area of a circle is pir^2 (using a different notation). |
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| proved that the area of a circle is equal to the area of a right triangle in which one leg is equal to the radius and the other is equal to the circumference of the circle. |
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| showed that the area of the surface of a sohere is 4pir^2 (using different notation) |
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| showed that the area of a circle is directly proportional to the square of its diameter. |
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| is considered the master of the metod of exhaustion. |
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| began the study of symbolic algebra by considering the properties of the positive integers for addition and multiplication. |
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| was forced to create a non-commutative algebra to investigate a physical problem. |
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| represented a complex number by its associated ordered real number pair. |
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| was the creator of quaternions. |
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| investigated algebras involving ordered sets of n real numbers. |
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| was the mathematician who created matrix algebra when investigating some type of linear transformations. |
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| was the first historical example of a non-commutative algebra. |
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| Lie Algebras, Jordan Algebras |
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| _____ and ____ were the first historical examples of non-associative algebras. |
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| is the author of the book "An investigation of the Laws of Thought." |
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| was the mathematician who treated logic statements as objects in which we can perform logical operations in the same way that we can perform operations with numbers. |
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| was the mathematician who extended Boole's ideas by studying logical objects in their own right. |
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| was the first mathematician who represented graphically the relationship between dependent and independent variables. |
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| was one of the first mathematicians to use letters and equations to represent quantities and relations, respectively. |
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| _______ and ________ invented a coordinate system to graph the relationship between two unknown quantities. |
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| extended the coordinate system to negative coordinates. |
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| ________, ______, _____, and _____ are four of the early units of length based on the human body. |
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| For the Egyptians, a ____ was the length of a black granite royal rod. |
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| was the basic unit of length for the Babylonians. |
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| was the person that proposed to the French National Assembly a fundamental unit of length based on the length of a pendulum that beats at the rate of a full swing per second. |
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| International Bureau of Weights and Measures |
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| is the official bureau in charge of matters related to the metric system. |
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| The last definition of a meter was established in _________ |
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| is the distance traveled by light in a vacuum in 1/299,792,458 seconds. |
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| is 9,192,631,770 cycles of radiation associated with a particular charge of state of the Caesium-133 atom. |
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| is the mass of a litre of pure water. |
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| is the volume of a cubic decimeter. |
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| The Measurement of a Circle, On the Sphere and the Cylinder |
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| ______ and ____________ are the two books written by Archimedes related to measurement. |
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| is the Egyptian papyrus that contains a problem involving the area of a circle. |
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| was the mathematician who proved that 3 10/71 < pi < 3 10/70. |
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| Double Reduction to Absurdity |
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| The key idea to an argument involving _____________ is the elimination of two out of three possibilities. |
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| The Measurement of a Circle |
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| is the book written by Archimedes that contains his determination of circular area. |
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| On the Sphere and the Cylinder |
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| is the book written by Archimedes that includes volumes and surface areas of spheres and other 3-dimensional figures. |
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| Ptolomy, Viete, Van Ceulen |
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| ________, _______, and ________ are three scholars who found approximations to pi using Archimedean techniques. |
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| discovered that 1-1/3+1/5-1/7+1/9-1/11+... converges to pi/4. |
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| also known as the formula man, generated formulas that provide highly accurate approximations to pi. |
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| used the ENIAC to compute pi to 2035 decimal places in 1949. |
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| Some of the earliest units of length were based on the human body. |
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| Every polynomial with real coefficients can be expressed as a product of linear and quadratic factors. |
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| Egyptians knew an approximate "formula" for finding the area of a circle. |
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| There is evidence that the Babylonians had a general formula for solving cubic equations. |
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| Cardano was the first mathematician who found a procedure to solve depressed cubic equations in one variable. |
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| Cardano was the first mathematician who justified and published a procedure to solve depressed cubic equations in one variable. |
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| Ancient scholars up to Viete considered the product of two segment magnitudes an area. |
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| Every equation, in one variable, has as many distinct roots as its degree. |
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| Real numbers are complex numbers. |
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| Every polynomial of nth degree with real coefficients has precisely n distinct complex zeroes. |
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| Every polynomial of nth degree with complex coefficients has n complex zeroes. |
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| A polynomial equation in one variable of degree 5 or higher does not have a solution. |
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| All polynomial equations in one variable of degree 5 or higher are unsolvable by radicals. |
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| All general polynomial equations in one variable of degree 5 or higher are unsolvable algebraically. |
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| For Peacock, a-b(b>a) is not possible in arithmetic algebra but is possible in symbolic algebra. |
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| Multiplication of complex numbers is not commutative. |
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| Multiplication of quaternions is associative. |
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| Multiplication of quaternions is commutative. |
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| Multiplication of matrices is commutative. |
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| The fundamental theorem of algebra was one of the most important algebraic problems of the 18th century. |
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| Cardano used the same formula to find a root of a general cubic equation in one variable. |
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