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Irrational number
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151	IRRATIONAL NUMBERS ARISING FROM CERTAIN DIFFERENTIAL EQUATIONS M. RAM MURTY AND V. KUMAR MURTY Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven’s proof to show that er is irrational for ev Add to Reading List Source URL: rinconmatematico.com Language: English - Date: 2005-04-23 05:41:16 Irrational number Integer sequences Mathematical analysis Transcendental number Euclidean algorithm Mathematics Pi Proof that π is irrational
152	Proceedings of the Edinburgh Mathematical Society[removed], 271–289 DOI:[removed]S0013091510001355 ON NUMBERS n DIVIDING THE nTH TERM OF A LINEAR RECURRENCE 1 Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2012-05-10 10:36:06 Modular arithmetic Arithmetic function Prime-counting function Exponentiation Fibonacci number Binomial coefficient Proof that π is irrational Mathematics Number theory Prime numbers
153	THE WADSWORTH MATHEMATICS SERIES S e r b Editors Raoul H.Bott, Harvard University David Eisenbud, Brandeis University Hugh L. Montgomery, University of Michigan Add to Reading List Source URL: www.plouffe.fr Language: English - Date: 2014-05-28 20:48:16 Field theory Transcendental numbers Modular arithmetic Number theory Algebraic integer Rational number Algebraic number Irrational number Algebraic number field Abstract algebra Mathematics Algebra
154 $Continued fractions / Convergent / Transcendental number / Equidistributed sequence / Irrational number / Rational number / Time complexity / Mathematics / Mathematical analysis / Diophantine approximation$	Acta Univ. Sapientiae, Informatica, 5, [removed]–34 Efficient computing of n-dimensional simultaneous Diophantine approximation problems Attila KOVÁCS Add to Reading List Source URL: www.acta.sapientia.ro Language: English - Date: 2013-06-22 03:17:08 Continued fractions Convergent Transcendental number Equidistributed sequence Irrational number Rational number Time complexity Mathematics Mathematical analysis Diophantine approximation
155	The Gift Exchange Problem David Applegate and N. J. A. Sloane(a) , AT&T Shannon Labs, 180 Park Ave., Florham Park, NJ[removed], USA. (a) Add to Reading List Source URL: neilsloane.com Language: English - Date: 2012-01-02 21:20:57 Number theory Orthogonal polynomials Bessel polynomials Summation Factorial Recurrence relation Combinatory logic Stirling number Proof that π is irrational Mathematics Integer sequences Combinatorics
156	8th Grade Mathematics ● Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the[removed]School Year. This document is designed to help North Carolina educators Add to Reading List Source URL: www.dpi.state.nc.us Language: English - Date: 2012-02-24 11:32:50 Elementary algebra Binary operations Numbers Real number Irrational number Square root Fraction Exponentiation Pi Mathematics Elementary arithmetic Elementary mathematics
157	2011 U OF I FRESHMAN MATH CONTEST Solutions 1. Let x = 0.[removed][removed]be the number whose decimal expansion consists of the sequence of natural numbers written next to each other. (a) Determine the 2011th digi Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-10-01 17:22:28 Combinatorics Number theory Mathematical series Complex analysis Binomial coefficient Factorial Pi Summation Proof that π is irrational Mathematics Mathematical analysis Integer sequences
158	Generic rigidity for circle diffeomorphisms with breaks Saša Kocić ∗ Department of Mathematics, The University of Mississippi Hume Hall 305, University, MS[removed]March 16, 2014 Add to Reading List Source URL: rene.ma.utexas.edu Language: English - Date: 2014-03-17 01:02:07 Mathematics Lie groups Functions and mappings Irrational rotation Rotation number Diffeomorphism Möbius transformation Circle map Geometry Dynamical systems Mathematical analysis
159	2014 UI UNDERGRADUATE MATH CONTEST Solutions 1. (a) Does there exist a multiple of 2013 whose decimal representation ends in the digits 2014? Explain! (b) Does there exist a power of 2 whose decimal representation ends i Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2014-02-15 21:13:47 Integer sequences Number theory Exponentials Binomial coefficient Factorial Summation Exponential function Proof that π is irrational Basel problem Mathematics Mathematical analysis Combinatorics
160	UIUC UNDERGRADUATE MATH CONTEST April 12, 2003 Solutions 1. Let Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2003-04-12 16:50:35 Integer sequences Number theory Factorial Proof that π is irrational Binomial coefficient Mathematics Mathematical analysis Combinatorics

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