Rational values of the arccosine function
... For even n, a different method is suggested in that book, distinguishing between the cases√n = 2j and n not a power of 2. Thus, it is obtained that (1/π) arccos(1/ n) is rational if and only if n ∈ {1, 2, 4}. The relation (2) can be read in term of Chebyshev polynomials of the first kind. These poly ...
... For even n, a different method is suggested in that book, distinguishing between the cases√n = 2j and n not a power of 2. Thus, it is obtained that (1/π) arccos(1/ n) is rational if and only if n ∈ {1, 2, 4}. The relation (2) can be read in term of Chebyshev polynomials of the first kind. These poly ...
Let`s Do Algebra Tiles
... 7.NS.2a a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Inter ...
... 7.NS.2a a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Inter ...
Must All Good Things Come to an End?
... Diophantus of Alexandria Often known as the “Father of Algebra”. Best known for his Arithmetica, a work on the solution of algebraic equations and on the theory of numbers. However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived. The ...
... Diophantus of Alexandria Often known as the “Father of Algebra”. Best known for his Arithmetica, a work on the solution of algebraic equations and on the theory of numbers. However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived. The ...
Curriculum and Staffing
... For most students entering the Pre-Algebra math group, there are some major internal or affective obstacles. One of the most powerful things we can do during Math Jam is to change these students’ perception about themselves, mathematics and school. This is usually more effectively accomplished throu ...
... For most students entering the Pre-Algebra math group, there are some major internal or affective obstacles. One of the most powerful things we can do during Math Jam is to change these students’ perception about themselves, mathematics and school. This is usually more effectively accomplished throu ...
Solve Systems with Elimination
... Solving Systems of Equations • We will solved systems using graphing, substitution, and elimination. These notes go one step further and show how to use ELIMINATION with multiplication. • What happens when the coefficients are not the same? • We multiply the equations to make them the same! You’ll ...
... Solving Systems of Equations • We will solved systems using graphing, substitution, and elimination. These notes go one step further and show how to use ELIMINATION with multiplication. • What happens when the coefficients are not the same? • We multiply the equations to make them the same! You’ll ...
Theory Behind RSA
... Fermat’s Little Theorem Theorem: Let p be a prime and x be an integer such that x mod p 0. Then xp-1 1 (mod p). More generally, if x Zp, then xp x (mod p). Proof: Assume that 0 < x < p and x mod p 0, then ...
... Fermat’s Little Theorem Theorem: Let p be a prime and x be an integer such that x mod p 0. Then xp-1 1 (mod p). More generally, if x Zp, then xp x (mod p). Proof: Assume that 0 < x < p and x mod p 0, then ...
Algebra 1 Notes Equations and Inequalities A.REI.A.1 Understand
... BIG IDEA: Algebraic properties enable students to arrive at a solution of an equation in a logical step-by-step manner. Knowing the properties of equality can not only help you reduce complex equations to simpler ones, but also give you the tools to justify your solution. Solving linear equations an ...
... BIG IDEA: Algebraic properties enable students to arrive at a solution of an equation in a logical step-by-step manner. Knowing the properties of equality can not only help you reduce complex equations to simpler ones, but also give you the tools to justify your solution. Solving linear equations an ...
Full text
... The "angle" we have in mind is a gnomon, a planar region that has the general shape of a carpenterfs square. At the time of Pythagoras, a carpenterfs square was in fact called a gnomon. The term came from Babylonia, where it originally referred to the vertically placed bar that cast the shadow on a ...
... The "angle" we have in mind is a gnomon, a planar region that has the general shape of a carpenterfs square. At the time of Pythagoras, a carpenterfs square was in fact called a gnomon. The term came from Babylonia, where it originally referred to the vertically placed bar that cast the shadow on a ...
List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.Some reasons why a particular publication might be regarded as important:Topic creator – A publication that created a new topicBreakthrough – A publication that changed scientific knowledge significantlyInfluence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith.