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Irrational number
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161	U OF I UNDERGRADUATE MATH CONTEST MARCH 7, 2009 Solutions − denote the integer obtained by reversing the 1. Given a nonnegative integer n, let ← n Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2009-03-07 17:49:43 Combinatorics Exponentials Factorial Exponentiation Binomial coefficient Proof that π is irrational Mathematics Integer sequences Number theory
162	THE 3x + 1 CONJUGACY MAP Daniel J. Bernstein, Jeffrey C. Lagarias Add to Reading List Source URL: www.math.lsa.umich.edu Language: English - Date: 2007-11-29 15:05:50 Collatz conjecture Conjectures Conjugacy class Factorial Pythagorean trigonometric identity Proof that π is irrational Mathematics Number theory Combinatorics
163	Central Binomial Coe¢ cients Steven Finch March 28, 2007 Add to Reading List Source URL: www.people.fas.harvard.edu Language: English - Date: 2011-07-14 09:13:34 Combinatorics Irrational numbers Number theory Logarithms Natural logarithm of 2 Binomial coefficient Factorial Central binomial coefficient Summation Mathematics Mathematical analysis Integer sequences
164	U OF I UNDERGRADUATE MATH CONTEST MARCH 6, 2010 Solutions Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2010-03-09 10:38:49 Polynomial Summation Pi Proof that π is irrational Non-standard RAID levels Mathematics Mathematical analysis Number theory
165	UIUC UNDERGRADUATE MATH CONTEST April 17, 2004 Solutions 1. Suppose a, b and c are integers such that the equation ax2 + bx + c = 0 has a rational solution. Prove that at least one of the integers a, b and Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2004-04-17 15:48:09 Continuous function Fibonacci number Algebra Proof that π is irrational Characterizations of the exponential function Mathematics Mathematical analysis Function
166	REDUCTION FORMULAS OF THE COSINE OF INTEGER FRACTIONS OF π RICHARD J. MATHAR Add to Reading List Source URL: www.mpia-hd.mpg.de Language: English - Date: 2012-09-05 04:47:18 Geometry Trigonometric functions Sine Pi Valuation Irrational number Proof that π is irrational Prime number theorem Trigonometry Mathematical analysis Mathematics
167	9$3] BOOK REVIEWS Add to Reading List Source URL: www.ams.org Language: English* - Date: 2010-01-14 13:42:17 Mathematical logic Quadratic irrational Irrational number Quadratic residue Quadratic Nicolas Bourbaki Number Theorem Prime number Mathematics Logic Number theory
168 $Blind people / Leonhard Euler / Continued fraction / Fraction / Number / Pi / Transcendental number / E / Contributions of Leonhard Euler to mathematics / Mathematics / Mathematical analysis / Mathematical constants$	How Euler Did It by Ed Sandifer Who proved e is irrational? Add to Reading List Source URL: vanilla47.com Language: English - Date: 2013-11-23 10:25:22 Blind people Leonhard Euler Continued fraction Fraction Number Pi Transcendental number E Contributions of Leonhard Euler to mathematics Mathematics Mathematical analysis Mathematical constants
169	Inventing Numbers: How Mathematicians Filled the Inky Void - American Educator, Fall 2002 Add to Reading List Source URL: www.aft.org Language: English - Date: 2010-06-23 15:48:14 Field theory Binary operations Numbers Irrational number Number Real number Addition Richard Dedekind Fraction Mathematics Elementary mathematics Elementary arithmetic
170	Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010 Add to Reading List Source URL: www.mathunion.org Language: English - Date: 2013-04-24 07:33:09 Algebra Mathematical physics Fixed points Quantum field theory Renormalization group Rotation number Irrational rotation Renormalization Stable manifold Physics Dynamical systems Mathematics

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