Algebra articles, problems, and puzzles.

What Is Arithmetic?
What Is Algebra?
Arithmetic: Articles and Problems

  1. 17 rooks on an 8×8 chessboard
  2. 1962 IMO, Problem 2: an inequality with a twist
  3. 1=2 via Continued Fractions
  4. 3-Colors Tower of Hanoi [Java]
  5. 3 glass puzzle [JavaScript]
  6. 3-Term Arithmetic Progression
  7. A 2-Variable Optimization From a China Competition
  8. A 4-variable Inequality from the RMM
  9. 4x4 coloring problem
  10. 6th European Mathematical Cup (2017), Junior Problem 4
  11. A 49th Degree Challenge
  12. A Case for Determinants
  13. A Case of Divergence
  14. A Clique of Acquaintances
  15. A Curious Property of Numbers 3 and 5
  16. A Cyclic But Not Symmetric Inequality in Four Variables
  17. A Cyclic Inequality by Seyran Ibrahimov
  18. A Cyclic Inequality from Math Phenomenon
  19. A Cyclic Inequality in Three Variables
  20. A Cyclic Inequality in Three Variables II
  21. A Cyclic Inequality in Three Variables III
  22. A Cyclic Inequality in Three Variables IV
  23. A Cyclic Inequality in Three Variables V
  24. A Cyclic Inequality in Three Variables VI
  25. A Cyclic Inequality in Three Variables VII
  26. A Cyclic Inequality in Three Variables VIII
  27. A Cyclic Inequality in Three Variables IX
  28. A Cyclic Inequality in Three Variables X
  29. A Cyclic Inequality in Three Variables XI
  30. A Cyclic Inequality in Three Variables XII
  31. A Cyclic Inequality in Three Variables XIII
  32. A Cyclic Inequality in Three Variables XIV
  33. A Cyclic Inequality in Three Variables XV
  34. A Cyclic Inequality in Three Variables XVI
  35. A Cyclic Inequality in Three Variables XVII
  36. A Cyclic Inequality in Three Variables XVIII
  37. A Cyclic Inequality in Three Variables XIX
  38. An Estimate for the Roots of Quadratic Equation
  39. An Exercise in Complex Numbers: Problem 4217 from Crux
  40. An Inequality with Constraint XX
  41. A Cyclic Inequality in Three Variables XX
  42. A Cyclic Inequality in Three Variables XXI
  43. A Cyclic Inequality in Three Variables XXII
  44. A Cyclic Inequality in Three Variables XXIII
  45. A Cyclic Inequality in Three Variables XXIV
  46. A Cyclic Inequality in Three Variables XXV
  47. A Cyclic Inequality in Three Variables XXVI
  48. A Cyclic Inequality in Three Variables And One More
  49. >A Cyclic Inequality In Three Variables by Sorin Radulescu
  50. A Cyclic Inequality in Three Variables by Uche E. Okeke
  51. A Cyclic Inequality from India In Three Variables And More
  52. A Cyclic Inequality in Three Variables with Constraint
  53. A Cyclic Inequality in Three or More Variables
  54. A Cyclic Inequality of Degree Four
  55. A Cyclic Inequality With Constraint in Two Triples of Variables
  56. A Cycling Inequality with Integrals
  57. A Cycling Inequality with Integrals II
  58. A Cyclic Inequality with Many Sums
  59. A Cyclic Inequality with Powers 2 through 7
  60. A Cyclic Inequality in Three Variables with a Variable Hierarchy
  61. A Cyclic Inequality on [-1,1]
  62. A Diophantine Equation - Problem from 2000 Belarus MO
  63. A Diophantine Equation with Square Roots - Problem from the 2008 British MO
  64. A DIY Proof of the Irrationality of sqrt(2)
  65. A Fancy Sum from the APMO 2000, Problem 1
  66. A Few Variants of a Popular Inequality And a Generalization
  67. A Formula for sin(3x)
  68. A Functional Equation from 1968 IMO
  69. A Functional Equation from the 2012 IMO
  70. A Generalization of an Inequality from a Romanian Olympiad
  71. A Limit of a Sequence
  72. A Limit of Another Sequence
  73. A Limit of a Series of Determinants
  74. A Limit with Fractions, Roots, Powers and Series
  75. A Limit With Sums, Roots, And Binomial Coefficients
  76. A Little of Algebra for an Inequality, A Little of Calculus for a Generalization
  77. A Little More of Algebra for an Inequality, A Little Less of Calculus for a Generalization
  78. A Long Cyclic Inequality of Degree 4
  79. A Low Bound for 1/2 * 3/4 * 5/6 * ... * (2n-1)/2n
  80. A Mathematical Rabbit out of an Algebraic Hat
  81. A Memorable Fact
  82. A Middle School Problem from a Moscow Olympiad
  83. A New Proof That the Rationals Are Countable
  84. A Not Quite Cyclic Inequality
  85. A Not Quite Cyclic Inequality from Tibet
  86. A Not Symmetric Inequality [JavaScript]
  87. A Not So Simple Inequality in Three Variables
  88. A One-Line Proof of the Infinitude of Primes
  89. A Partly Cyclic Inequality in Four Variables
  90. A Problem for the 2015 New Year's Eve
  91. A Problem From a Mongolian Olympiad for Grade 11
  92. A Problem from Croatian TST
  93. A Problem from the Danubius Contest 2016
  94. A Problem from the Danubius-XI Contest
  95. A Problem From the Romanian Mathematical Competitions (2016)
  96. A Problem in Complex Numbers Sets 3 Aside
  97. A Problem in Division of Polynomials
  98. A Problem with a Magical Solution from Secrets in Inequalities
  99. A Proof by Game for a Sum of a Convergent Series
  100. A Property of Number 4
  101. A Property of Product of Special Matrices, Probably Folklore
  102. A Property of the fusc() Function
  103. A Refinement of Turkevich's Inequality
  104. A Representation of Rational Numbers
  105. A Quartic Equation
  106. A Series with k-Permutations
  107. A Simple Inequality with Many Variables
  108. A Simple Cyclic Inequality in Three Variables
  109. A Simple Inequality in Three Variables
  110. A simple integral
  111. A simple integral, III
  112. A Simple Integral of a Peculiar Function
  113. A Simplified Version of Leo Giugiuc's Inequality from the AMM
  114. A Sum by Dorin Marghidanu
  115. A Sum of a Double Series
  116. A System of Equations Begging for Generalization
  117. A System of Equations in Determinants
  118. A System of Two Equations Replete with Squares
  119. A Telescoping Series
  120. A Tricky Integral Inequality
  121. A Trigonometric Inequality from the RMM
  122. >A Trigonometric Observation in Right Triangle
  123. A Triple Integral Inequality
  124. A True Algebraic-Geometric Inequality
  125. A Warmup Inequality from Vasile Cirtoaje
  126. ab + bc + ca ≤ aa + bb + cc
  127. About numbers
  128. Absolute Value
  129. Absolute Value and 1998 integers
  130. Achieve the Equilibrium [Flash]
  131. Addition
  132. Addition and Subtraction Formulas for Sine and Cosine III
  133. Addition and Subtraction Formulas for Sine and Cosine IV
  134. Advancing a Millenium Problem [JavaScript]
  135. Affirmative Action Problem [Java]
  136. Algebraic-Geometric Inequality
  137. Algebraic Structure of Complex Numbers
  138. All Integers Are Equal to 1
  139. All Integers Are Even
  140. All Powers of 2 Are Equal to 1
  141. All Powers of x are Constant
  142. Almost every integer has the digit 3 in it
  143. Almost Integers - Gaussian Integers
  144. Amazing Mix of Triangular Numbers and Golden Ratio
  145. Ambassadors at a Round Table [Java]
  146. An Acyclic Inequality in Three Variables
  147. An Algebraic Lemma with Geometric Consequences [JavaScript]
  148. An Application of Quadratic Formula
  149. An Arctan Identity and its Consequence [JavaScript, GeoGebra]
  150. An Easy Cyclic Inequality And a Remark
  151. An Easy Inequality with Three Integrals
  152. An Elementary Inequality by Non-elementary Means
  153. An Elementary Proof for Euler's Series
  154. An Equation in Determinants
  155. An Equation in Factorials
  156. An Equation in Matrices
  157. An Equation in Radicals
  158. An Equation in Reciprocals
  159. An Equation in RxR from Romania
  160. An Equation in Squares [JavaScript]
  161. An Equation Involving Four Collinear Points
  162. An Exercise without Calculating Aids
  163. An Identity between the Roots of a Cubic Polynomial - Problem from the 2007 Irish MO
  164. An Identity From the 2010 China Mathematical Competition
  165. An Identity Involving the Integer Part - Problem from the 1981 Canadian MO
  166. An Incidental Sum of 24
  167. An Increasing Sequence from 2014 IMO
  168. An Inequality and Its Modifications
  169. An Inequality between AM, QM and GM
  170. An Inequality by Uncommon Induction
  171. An Inequality for Grade 8
  172. An Inequality from the 1967 IMO Shortlist
  173. An inequality from 1971 Canadian Mathematical Olympiad
  174. An Inequality from Marocco [JavaScript]
  175. An Inequality from Tibet
  176. An inequality in 2+2 variables from SSMA magazine
  177. Inequality in Convex Quadrilateral
  178. An Inequality in Determinants
  179. An Inequality in Four Weighted Variables
  180. An Inequality in Fractions with Absolute Values
  181. An Inequality in Integers [JavaScript]
  182. An Inequality in Integers II
  183. An Inequality in Parallelogram of Unit Area
  184. An Inequality in Reciprocals
  185. An Inequality in Reciprocals II An Inequality in Reciprocals III
  186. An Inequality in Three (Or Is It Two) Variables
  187. An Inequality in Triangle and In General
  188. An Inequality In Triangle and Without
  189. An Inequality In Triangle and Without II
  190. An Inequality in Two Or More Variables
  191. An Inequality in Two Or More Variables II
  192. An Inequality Involving Arithmetic And Geometric Means
  193. An Inequality Solved by Changing Appearances
  194. An Inequality with Angles and Integers
  195. An Inequality with Arbitrary Roots
  196. An Inequality with Areas, Norms, and Complex Numbers An Inequality with Central Binomials
  197. An Inequality with Complex Numbers of Unit Length
  198. An Inequality with Complex Numbers of Unit Length II
  199. An Inequality with Cubic Roots
  200. An Inequality with Cyclic Sums And Products
  201. An Inequality with Cyclic Sums on Both Sides
  202. An Inequality with Cyclic Sums on Both Sides II
  203. An Inequality with Cyclic Sums on Both Sides III
  204. An Inequality with Exponents
  205. An Inequality with Five Variables, Only Three Cyclic
  206. An Inequality with Fractions
  207. An Inequality with Integrals
  208. An Inequality with Integrals and Radicals
  209. An Inequality with Just Two Variable And an Integer
  210. An Inequality with Sines But Not in a Triangle
  211. An Inequality with One Tangent and Six Sines
  212. An Inequality with Powers And Logarithm
  213. An Inequality With Six Variables and Constraints
  214. An Inequality Where One Term Is More Equal Than Others
  215. An Inequality with a Parameter and a Constraint
  216. An Inequality with Absolute Values
  217. An Inequality with an Infinite Series
  218. An Inequality with Constraint
  219. An Inequality with Constraints II
  220. An Inequality with Constraint III
  221. An Inequality with Constraint IV
  222. An Inequality with Constraint V
  223. An Inequality with Constraint VI
  224. An Inequality with Constraint VII
  225. An Inequality with Constraint VIII [JavaScript]
  226. An Inequality with Constraint IX [JavaScript]
  227. An Inequality with Constraint X [JavaScript]
  228. An Inequality with Constraint XI [JavaScript]
  229. An Inequality with Constraint XII
  230. An Inequality with Constraint XIII
  231. An Inequality with Constraint XIV
  232. Inequalities with Constraint XV and XVI
  233. An Inequality with Constraint XVII
  234. An Inequality with Constraint XVIII
  235. An Inequality with Constraint XIX
  236. An Inequality with Constraint in Four Variables
  237. An Inequality with Constraint in Four Variables II
  238. An Inequality with Constraint in Four Variables III
  239. An Inequality with Constraint in Four Variables IV
  240. An Inequality with Constraint in Four Variables V
  241. An Inequality with Constraint in Four Variables VI
  242. An Inequality with Cot, Cos, and Sin
  243. An Inequality with Cycling Sums
  244. An Inequality with Determinants [JavaScript]
  245. An Inequality with Determinants II
  246. An Inequality with Determinants III
  247. An Inequality with Determinants IV
  248. An Inequality with Determinants V
  249. An Inequality with Determinants VI
  250. An Inequality with Determinants VII
  251. An Inequality with Exponents [JavaScript]
  252. An Inequality with a Generic Proof [JavaScript]
  253. An Inequality with Nested Radicals
  254. An Inequality via Young's Theorem
  255. An Inequality with Just Two Variable
  256. An Inequality with Just Two Variable II
  257. An Inequality with Just Two Variable III
  258. An Inequality with Just Two Variables IV
  259. An Inequality with Just Two Variables V
  260. An Inequality with Just Two Variables VI
  261. An Inequality with Just Two Variable VII
  262. An Inequality with Just Two Variable VIII
  263. An Inequality with Permutations, I [JavaScript]
  264. An Inequality with Permutations, II [JavaScript]
  265. An Inequality with Two Cyclic Sums
  266. An Inequality with Two Pairs of Triplets An Inequality with Two Triples of Variables
  267. An Inequality with Two Triples of Variables II
  268. Inequality with Two Variables? Think Again
  269. An Inequality with Two Variables from Awesome Math
  270. An Infinite Product from Recursion
  271. An Integral Estimate
  272. An Integral Identity with Two Functions
  273. An Integral from the RMM
  274. An Integral Inequality from the RMM
  275. An Old Inequality
  276. An Unsolvable Riccati Equation
  277. An Unusual Quadratic Equation
  278. Another Face and Proof of a Trigonometric Identity
  279. Another Inequality with Logarithms, But Not Really
  280. Another Integral Inequality from the RMM
  281. Another Problem from the 2016 Danubius Contest
  282. Another Property of Number 4
  283. Another simple integral
  284. An Unusual Problem by Leo Giugiuc
  285. Any Integer with Three 2s
  286. Application of Cauchy-Schwarz Inequality
  287. Applications of Schweitzer's Inequality
  288. Approximation Of Roots
  289. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  290. Areas on the Graphs of Power Functions
  291. Arithmetic-Geometric Means Inequality
  292. Arithmetic of Pie Sharing
  293. Ascending Bases and Exponents in Pascal's Triangle
  294. Assigning Numbers to Points in the Plane
  295. Associativity from 1977 IMO
  296. Averages, Arithmetic and Harmonic Means [Java]
  297. Averages in a sequence
  298. Ballot Lemma [Java]
  299. Banzhaf Power Index Calculator [Java]
  300. Barcode Encoding
  301. Barcode Magic [Java]
  302. Base Converter [JavaScript]
  303. Bergström's inequality
  304. Birth of an Inequality
  305. Bayes' Theorem
  306. Beatty Sequences
  307. Beauty and the Beast - in Trigonometry
  308. Bertrand's Postulate
  309. Bicubal Domino [JavaScript]
  310. Bilateral Diagrams [Java]
  311. Binet's Formula via Generating Functions
  312. Binet's Formula with Cosines
  313. Binomial Distribution [Java]
  314. Binomial Theorem
  315. Bisector of an imaginary angle may be real
  316. Brahmagupta-Fibonacci Identity [JavaScript]
  317. Byzantine Basketball
  318. Calculation of the Digits of pi by the Spigot Algorithm [Java]
  319. Calculus Proof of the Pythagorean Theorem
  320. Candido's Identity
  321. Cantor-Bernstein-Schroeder theorem
  322. Cantor's First Uncountability Proof
  323. Cardinal Numbers
  324. Cartesian Coordinate System [Java]
  325. Cassini's Identity
  326. Catalan Numbers in Pascal's Triangle
  327. Cavalieri's Principle [Java]
  328. Central and Inscribed Angles in Complex Numbers
  329. Chebyshev Inequality
  330. Chebyshev Holds a Key
  331. Check for Negative Roots
  332. Chess tournament with 1.5 Points Winners
  333. Chinese Remainder Theorem
  334. Clifford Algebras
  335. Clubs in a Vector Space
  336. Collatz Conjecture [Java]
  337. Coloring a Graph [Java]
  338. Coloring Squares, Adding up Numbers
  339. Combinatorial Proofs
  340. Combo Playground: Calculating the Number of Paths on a Square Grid
  341. Committee Chairs
  342. Comparing complex numbers
  343. Completing a Square and Quadratic Formula
  344. Completing the Square Where It Matters
  345. Complex Numbers: A Dynamic Tool [Java]
  346. Complex number to a complex power may be real
  347. Complicated Constraint - Simple Inequality
  348. Composition of Functions, an Exercise Constrained Inequality with Reciprocals
  349. Constrained Intermarriages [JavaScript]
  350. Constructible Numbers
  351. Construction of Pascal's Triangle [Java]
  352. Constructive Existence of the de Bruijn Cycles
  353. Continued fractions
  354. cos/sin inequality
  355. cos(π/7)-cos(2π/7)+cos(3π/7) = 1/2
  356. Cospherical Points
  357. Countability of Rational Numbers
  358. Countability Principle
  359. Counting Chips On a Circle [Java]
  360. Counting Fat Sets
  361. Counting Squares in a Square [Java]
  362. Counting Triangles [Java]
  363. Counting Triangles II [Java]
  364. Covering a Chessboard with a Hole with L-Trominoes [Java]
  365. Covering A Chessboard With Domino
  366. Cubes Constrained
  367. Cubes in Pascal's Triangle
  368. Cubic Equation for the Sides of a Triangle
  369. Cubic Formula [JavaScript]
  370. Cubics and Bézout's Theorem
  371. Cubic Optimization with Linear Constraints
  372. Cubic Optimization with Partly Linear Constraints
  373. Curious Identities In Pythagorean Triangles
  374. Curious Identities Involving Integer Products

    Cute Exercise by Dorin Marghidanu

  375. Cyclic Inequality in Four Variables
  376. Cyclic Inequality in Four Variables By D. Sitaru
  377. Cyclic Inequality in Three Variables by Marian Cucoanes
  378. Cyclic Inequality In Three Variables from the 2018 Romanian Olympiad, Grade 9
  379. Cyclic Inequality In Three Variables From Vietnam by Rearrangement
  380. Cyclic Inequality with Arctangents
  381. Cyclic Inequality with Logarithms
  382. Cyclic Inequality with Square Roots
  383. Cyclic Inequality with Square Roots And Absolute Values
  384. Dan Sitaru's Amazing, Never Ending Inequality
  385. Dan Sitaru's Cyclic Inequality in Four Variables
  386. Dan Sitaru's Cyclic Inequality In One Variable
  387. Dan Sitaru's Cyclic Inequality In Many Variables
  388. Dan Sitaru's Cyclic Inequality In Three Variables
  389. Dan Sitaru's Cyclic Inequality in Three Variables II
  390. Dan Sitaru's Cyclic Inequality in Three Variables III
  391. Dan Sitaru's Cyclic Inequality in Three Variables IV
  392. Dan Sitaru's Cyclic Inequality in Three Variables V
  393. Dan Sitaru's Cyclic Inequality in Three Variables VI
  394. Dan Sitaru's Cyclic Inequality in Three Variables VII
  395. Dan Sitaru's Cyclic Inequality in Three Variables VIII
  396. Cyclic Inequality In Three Variables From Kvant
  397. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints
  398. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints IV
  399. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints V
  400. Dan Sitaru's Exercise with Pi and Ln
  401. Dan Sitaru's Inequality: From Three Variables to Many in Two Ways
  402. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints II
  403. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints III
  404. Dan Sitaru's Cyclic Inequality in Three Variables IX
  405. Dan Sitaru's Inequality by Induction
  406. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots
  407. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots II
  408. Dan Sitaru's Inequality with a Double Integral
  409. Dan Sitaru's Inequality with Roots and Powers
  410. Dan Sitaru's Inequality with Tangents
  411. Dan Sitaru's Inequality with Three Related Integrals and Derivatives
  412. Dan Sitaru's Integral Inequality with Powers of a Function
  413. Dan Sitaru's Sum of a Series
  414. Daniel Dan's Optimization in Three Variables
  415. Darij Grinberg's Inequality In Three Variables
  416. Deceptive Appearances
  417. Decimal Sums of Successive Integers
  418. Derivatives without Limits
  419. Descartes' Rule of Signs
  420. Determinant and Divisibility
  421. Determinant on a Circle
  422. Determinants in Pascal's Triangle
  423. Diagonal Argument
  424. Diophantine Equations
  425. Distance between the Orthocenter and Circumcenter
  426. Distance Between Strings [Java]
  427. Distance From a Point to a Straight Line [Java]
  428. Distance Inequality
  429. Distances to Three Points on a Circle
  430. Distinct Multisets with the Same Pairwise Sum
  431. Divergence of {cos(n)} [JavaScript]
  432. Divergence of the Harmonic Series (Details)
  433. Divide And Conquer in Cyclic Sums
  434. Dividing Loot Fairly
  435. Divisibility and Modulo Arithmetic at IMO 2007
  436. Divisibility by Powers of 2
  437. Dollars in Pockets
  438. Doodling on April 1st
  439. Dorin Marghidanu's Believe It Or Not
  440. Dorin Marghidanu's Calculus Lemma
  441. Dorin Marghidanu's Cyclic Inequality in Three Variables
  442. Dorin Marghidanu's Cyclic Inequality in Three Variables II
  443. Dorin Marghidanu's Cyclic Inequality in Three Variables III
  444. Dorin Marghidanu's Cyclic Inequality with Constraint
  445. Dorin Marghidanu's Inequality in Complex Plane
  446. Dorin Marghidanu's Inequality in Integer Variables
  447. Dorin Marghidanu's Inequality in Many Variables
  448. Dorin Marghidanu's Inequality in Many Variables Plus Two More
  449. Dorin Marghidanu's Inequality with Constraint
  450. Dorin Marghidanu's Inequality with Generalization
  451. Dorin Marghidanu's Inequality with Radicals
  452. Dorin Marghidanu's Light Elegance in Four Variables
  453. Dorin Marghidanu's Permuted Inequality
  454. Dorin Marghidanu's Spanish Problem Dorin Marghidanu's Sums and Products
  455. Dorin Marghidanu's Tribute to Descartes
  456. Dorin Marghidanu's Two-Sided Inequality
  457. Dot Patterns and Sierpinski Gasket [Java]
  458. Dots and fractions [Java]
  459. Double and Half Angle Formulas
  460. Double Sums by Dorin Marghidanu
  461. Ducci Sequences [Java]
  462. e in the Pascal Triangle
  463. EAN-13 Encoding [Java]
  464. Eigenvectors by Inspection
  465. Elves and Gnomes [JavaScript]
  466. Entry 1.414... in Ramanujan's Notebooks
  467. Equation in Permutations
  468. Equation in Radicals as a System of Equations
  469. Equations of the Staight Line [Java]
  470. Equivalence Relations
  471. Escape of the Clones
  472. Euclid's Algorithm
  473. Euclid's Algorithm: An Interactive Illustration [Java]
  474. Euler Cycles in Digraph
  475. Euler's formula for e
  476. Euler's Function and Congruence Theorem
  477. Evolution of Algebraic Symbolism
  478. Exercise with Square Spiral [GeoGebra]
  479. Existence of the de Bruijn Cycles via Graphs
  480. Exponential Inequalities for Means
  481. Extension of Euclid's Algorithm
  482. Extrema of x^3+y^3+z^3-xyz on the unit sphere
  483. Factorial Products
  484. Factorials and division
  485. Fair Division: Method of Sealed Bids II [Java]
  486. Falsity implies anything
  487. Farey Series
  488. Fermat's Like Equation
  489. Fermat's Little Theorem
  490. Fermat's Only Published Proof
  491. Fibonacci Idendtities with Matrices
  492. Fibonacci's Quickies
  493. Fibonacci Tilings
  494. Filling a Grid with Good Neighbors [Java]
  495. Filling an Array with 0s and 1s - and Counting [Java]
  496. Filling Pool with Fluids
  497. Find Minimum without Calculus
  498. Find the Maximum and Minimum of a Function
  499. Finding Hamilton Paths and Circuits [Java]
  500. Finite Sums of Terms 2^(n-i) i²
  501. First 1008 Digits
  502. First Geometric Interpretation of Complex Numbers [Java]
  503. Five Methods of Apportionment [Java]
  504. Five Lattice Points [Java]
  505. Five Squares in Complex Numbers [GeoGebra]
  506. Fixed Point of a Family of Parabolas
  507. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  508. Flipping Items Simultaneously [Java]
  509. Flipping Items Simultaneously II [Java]
  510. Flipping Items Simultaneously III [Java]
  511. Flipping pancakes [Java]
  512. Floor Function
  513. Formal Systems - an Example
  514. Formula for Primes
  515. Four Hinged Squares: using complex numbers
  516. Four Integrals in One Inequality
  517. Four Numbers, Six Differences, GCD of the Products
  518. Four Pegs That Form a Square
  519. Four Voting Methods [Java]
  520. From The Sum of Angles To The Sum of Sines
  521. Function
  522. Function in the Plane That Vanishes
  523. Functional Inequality from Vietnam
  524. Fundamental Theorem of Algebra
  525. Futurama Theorem and Puzzle [Java]
  526. Gasoline Stations on a Circular Trek
  527. Gauss and Euler Integrals
  528. Gauss' Lemma
  529. Gauss' theorem on constructibility of regular polygons
  530. GCD of Fibonacci Numbers
  531. GCD(M, N) × LCM(M, N) = M × N [Java]
  532. Generalization That Solves the Problem
  533. Generating Functions
  534. Geometric Construction of Roots of Quadratic Equation [Java]
  535. Getting a Scout out of Desert [Java]
  536. Getting Your Rightful Share Back [JavaScript]
  537. Gheorghe Stoica's Problem from Gazeta Matematica Gireaux's Theorem
  538. Gödel's Incompleteness Theorem
  539. Golden Ratio is Irrational
  540. Graph and Roots of a Third Degree Polynomial [Java]
  541. Graph and Roots of Quadratic Polynomial [Java]
  542. Graph of a Polynomial [Java]
  543. Graph of a Polynomial Defined by Its Roots [Java]
  544. Graph with Nodes of Even Degree
  545. Graph without 3-Cycles
  546. Graphing Equations Is Useful
  547. Graphing Equations Is Useful, II [Java]
  548. Graphing Equations Is Useful, III
  549. Graphing Equations Is Useful, IV
  550. Graphing Equations Is Useful, V
  551. Greatest Difference in Arithmetic Progression
  552. Group multiplication of permutations [Java]
  553. 1/2 = 1
  554. Hadamard's Determinant Inequalities and Applications I
  555. Hadamard's Determinant Inequalities and Applications II
  556. Harmonic Serires And Its Parts
  557. 2006 Hellenic Mathematical Olympiad, Problem 4 [JavaScript]
  558. Hlawka's Inequality
  559. Horner's Method [Java]
  560. How Jost Burgi Computed the Sines of All Integer Angles in 1586
  561. How to Ask an Embarrassing Question
  562. How to define a permutation? [Java]
  563. How to write an equation of the union of two sets
  564. However You Solve It ... A Wonderful Equation
  565. Hung Viet's Inequality
  566. Hung Viet's Inequality II
  567. Hung Viet's Inequality III
  568. Hung Viet's Inequality IV
  569. Hyperintegers and Hyperreal Numbers
  570. Identities with Triangular Numbers
  571. Imad Zak's Cyclic Inequality in Three Variables
  572. Imad Zak's Cyclic Inequality in Three Variables II
  573. Implementation of Base Conversion
  574. Importance of the Absolute Value
  575. Improving an Inequality [JavaScript]
  576. Improving on an Escalator [JavaScript]
  577. In Calculus too 1 = 0
  578. Inclusion-Exclusion Principle
  579. Inclusion-Exclusion Principle: an Example
  580. Inequalities and Quadratic Forms
  581. An Inequality for Mixed Means
  582. An Inequality from RMM with a Generic 5
  583. An Inequality from RMM with Powers of 2
  584. Inequality 101 from the Cyclic Inequalities Marathon
  585. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
  586. Inequality (1 + 1-3)(1 + 2-3)(1 + 2-3)...(1 + n-3) < 3
  587. Inequality 1 + 2-2 + 3-2 + 4-2 + ... + n-2 < 2.
  588. Inequality by Calculus
  589. Inequality for Integer Sequences
  590. Inequality for Integer Sequences II
  591. Inequality for Mixed Means
  592. An Inequality from Gazeta Matematica, March 2016
  593. An Inequality from Gazeta Matematica, March 2016 II
  594. An Inequality from Gazeta Matematica, March 2016 III
  595. An Inequality from Gazeta Matematica, March 2016 IV
  596. Inequalities with Double And Triple Integrals
  597. Inequality from Math Magazine 2009
  598. Inequality from Math Phenomenon
  599. Inequality in Acute Triangle
  600. Inequality of a Series of Square Roots
  601. Inequality with Constraint from Dan Sitaru's Math Phenomenon
  602. Inequality with Csc And Sin
  603. An Inequality with Exponents [JavaScript]
  604. An Inequality with Finite Sums
  605. An Inequality with Integrals and Rearrangement
  606. Inequality with Logarithms
  607. Inequality with Powers And Radicals
  608. Inequality with Three Linear Constraints
  609. Inequality with Three Numbers, Not All Zero
  610. Inequality with Two Minima
  611. Infinite Discent for x4 + y4 = z4
  612. Infinitesimals. Non-standard Analysis
  613. Infinitude of Primes
  614. Infinity As a Limit
  615. Inflection Points of Fourth Degree Polynomials [Java]
  616. Inheriting Inequality
  617. An innovative recurrence
  618. Integer Iterations on a Circle [Java]
  619. Candy Game (Change Discharged) [Java]
  620. Integer Iterations on a Circle III [Java]
  621. Integer roots of integers are irrational
  622. Integer Triangle That Sums to Cube
  623. Integers and Rectangles [Java]
  624. Integers and Rectangles: a Proof by Induction [Java]
  625. Integers and Rectangles: Two Simple Proofs [Java]
  626. Integers With Digits 1 and 2 and Residues Modulo Powers of 2
  627. Integral in Normal Distribution
  628. Integral Is Area
  629. Integrals of a Function And Its Inverse
  630. Interest Calculations [Java]
  631. Integral of a Piece-wise Function
  632. Irrationality of k-th roots
  633. Irrationality of sqrt(2) via a Difference Equation
  634. Is GLOBALHELLFRY a Prime? [JavaScript]
  635. Is the Triangle Inequality Necessary?
  636. Is There a Limit?
  637. ISBN Encoding [Java]
  638. Irrational number to an irrational power may be rational
  639. Is 0.999... = 1?
  640. It's All About Powers of 10
  641. Iterations on Monotone Functions
  642. Jensen's Inequality [JavaScript]
  643. Ji Chen's Inequality
  644. Joachimsthal's Notations
  645. Jumping Isn't Everything [Java]
  646. Kaprekar's Iterations and Numbers [Java]
  647. Kulikowski's Theorem
  648. Kunihiko Chikaya's Inequality
  649. Kunihiko Chikaya's Inequality with a Constraint
  650. Kunihiko Chikaya's Inequality with Parameter
  651. Labeling Subsets
  652. Lagrange's identity, Proof
  653. Lagrange interpolation
  654. Lamé's Theorem - First Application of Fibonacci Numbers
  655. Langford and Skolem Sequences [Java]
  656. Latin Squares [Java]
  657. Le Khanh Sy's Problem
  658. Leech Trees and Taylor's Criterion
  659. Legendre's Formula
  660. Legendre's Theorem - The Prime Factorization of Factorials
  661. Leibniz and Pascal Triangles [Java]
  662. Leo Giugiuc and Vasile Cirtoaje's Cyclic Inequality
  663. Leo Giugiuc's Cyclic Inequality in Three Variables
  664. Leo Giugiuc's Cyclic Quickie in Four Variables
  665. Leo Giugiuc's Cyclic Inequality with a Constraint
  666. Leo Giugiuc's Exercise
  667. Leo Giugiuc's Inequality with Constraint
  668. Leo Giugiuc's Optimization with Constraint
  669. Leo Giugiuc's Trigonometric Lemma
  670. Less than, Equal to, Greater Than Symbols
  671. Lewis Carroll's Game of Logic [Java]
  672. Light Bulbs in a Circle [Java]
  673. Lights Out [Java]
  674. Limit of a Recursive Sequence
  675. Linear Algebra Tools for Proving Inequalities
  676. Linear Algebra Tools for Proving Inequalities: Cauchy-Binet Formula
  677. Linear Function with Coefficients in Arithmetic Progression [GeoGebra]
  678. Linear functions
  679. Linear Programming
  680. Linear System with Parameter
  681. Listing All Combinations [Java]
  682. Listing all permutations [Java]
  683. Listing All Permutations: Johnson-Trotter Method [Java]
  684. Logistic Model applet [Java]
  685. Long Huynh Huu's Inequality and Solution
  686. Long Runs of Composite Numbers
  687. Long Up Short Down
  688. Looking your best
  689. Loop or Halt [Java]
  690. Lorian Saceanu's Cyclic Inequalities with Three Variables
  691. Lorian Saceanu's Inequality with Many Variables
  692. Lucas' Theorem
  693. Lucas' Theorem II
  694. Lucky Numbers [Java]
  695. Marian Dinca's Refinement of Nesbitt's Inequality
  696. Marriage Theorem
  697. Marriage Problem, simulation [Java]
  698. Math Lotto
  699. Mathematical Induction
  700. Mathematical Proof
  701. Mathematicians Doze Off
  702. Matrices and Determinants as Optimization Tools: an Example
  703. Matrix Groups
  704. Maximum Volume of a Cut Off Box [Java]
  705. Means [Java]
  706. Mediant Fractions
  707. Method of Markers II [Java]
  708. Michael Rozenberg's Inequality in Three Variables with Constraints
  709. Michael Rozenberg's Inequality in Two Variables
  710. Minesweeper Theorem
  711. Mini Lights Out [Java]
  712. Minimax Principle [Java]
  713. Minimax Theorem [Java]
  714. Minimum of a Cyclic Sum with Logarithms
  715. Minimum of Cotangents from Saint Petersburg
  716. Minumum Spanning Trees and Kruskal's Algorithm [Java]
  717. Minimum under Two Constraints
  718. Minus One But What a Difference
  719. Modular Arithmetic [Java]
  720. Monotone Convergence Theorem
  721. Monotone Number Sequences [Java]
  722. Monthly Problem 11199
  723. Much from Little
  724. Muirhead's Inequality
  725. Multiplication
  726. Multiplication of Points on a Circle [JavaScript, GeoGebra]
  727. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  728. Napoleon's Relatives [Java]
  729. Negative on the left, positive on the right: how come?
  730. Nested Radicals
  731. Nested Subsets
  732. New Proof of Euclid's Theorem
  733. Newton's Method [Java]
  734. Newton's and Maclaurin's Inequalities [JavaScript]
  735. Hung Nguyen Viet's Inequality with a Constraint
  736. Nine Squares [Java]
  737. No Flipping without End [Java]
  738. NonSquare Matrix as a Tool for Proving an Inequality
  739. Number 8 Is Interesting
  740. Number Comparison - from the 1969 Canadian MO
  741. Number sequences and Pigeonhole [Java]
  742. Number System With Base 36
  743. Modern Vietnamese Classic
  744. On Dedekind Cuts
  745. On the Games of Hex and Y
  746. On the Intersection of kx and |sin(x)| [JavaScript]
  747. On the Intersection of 1+x and e^x and Trigonometric Consequences [JavaScript]
  748. One Dimensional Ants
  749. One Inequality - Two Domains
  750. One Trigonometric Formula and Its Consequences
  751. Optimization in Four Variables with Two Constraints
  752. Optimization with Many Variables
  753. Order. Well-ordered sets.
  754. Order and Chaos in Multiple Pendulums
  755. Ordinal Numbers
  756. Orthocenter in Complex Plane
  757. Outline Mathematics
  758. Problem 1 From the 2016 Pan-African Math Olympiad
  759. Problem 11867 from the American Mathematical Monthly
  760. Problem 2, the 36th IMO (1995)
  761. Problem 2 from the 2017 IMO
  762. Problem 3824 from Crux Mathematicorum
  763. Problem 3980 from Crux Mathematicorum
  764. Problem 4002 from Crux Mathematicorum
  765. Problem 4010 from Crux Mathematicorum
  766. Problem 4020 from Crux Mathematicorum
  767. Problem 4033 from Crux Mathematicorum
  768. Problem 4117 from Crux Mathematicorum
  769. Problem 4142 From Crux Mathematicorum
  770. Problem 4165 from Crux Mathematicorum
  771. Problem 4186 from Crux Mathematicorum
  772. Problem 6 from Dan Sitaru's Algebraic Phenomenon
  773. Problem 790 from Pentagon: an Inequality in Two Variables
  774. Problem From the 2016 IMO Shortlist
  775. Problem M317 from Crux Mathematicorum
  776. Proofs of Schweitzer's inequality
  777. Prove 2[sqrt(n) - sqrt(n-1)] > 1/sqrt(n)
  778. Sam Walters' Four Questions
  779. Same Integral, Three Intervals
  780. Samuel G. Walters' Congruence
  781. Simple Nameless Inequality
  782. Small Change Makes Big Difference
  783. Smallest multiple of 9 with no odd digits [Java]
  784. Snake Permutations And Their Number
  785. Solving a Peculiar Third Degree Equation
  786. The Basics of Infinite Descent
  787. The Joy of Homogeneity
  788. The Lucky Find [Java]
  789. The Mean Property of the Mean
  790. The Number of Judges and the Number of Votes [JavaScript]
  791. The power of substitution: solving an equation in a right triangle
  792. The power of substitution II: proving an inequality with three variables
  793. The power of substitution III: proving an inequality with two variables
  794. The Very First Functional Equation at IMO
  795. The Very Last, for 2014, proof of the Irrationality of sqrt(2)
  796. Three Colors on a Chessboard
  797. Three digit twister [Java]
  798. Who Has Beard? [Java]
  799. Outline Mathematics: Diophantine Equation I [JavaScript]
  800. p-adic Expansions
  801. p-adic Numbers
  802. Pairing Monotone and Convex Functions
  803. Parabola and Abutting Equilateral Triangles
  804. Parabolic Sieve of Prime Numbers
  805. Parity counting [Java]
  806. Parrondo Paradox Via Simpson Paradox [Java]
  807. Partial But General Case Of Fermat's Last Theorem
  808. Party Acquaintances [Java]
  809. Patterns in Pascal's Triangle
  810. Peano axioms
  811. Pennies in Boxes [Java]
  812. Percent
  813. Permutations
  814. Perrin Sequence
  815. Pi in Pascal's Triangle
  816. Pi in Pascal's Triangle via Triangular Numbers
  817. pi^e vs e^pi [JavaScript]
  818. Pigeonhole Principle
  819. Pinocchio as Epimenides
  820. Place Value [Java]
  821. Powers and Fractions Inequality
  822. Presence of the Antipodes on a Circle
  823. Prime Sums in Pairs
  824. Probability of Divisibility
  825. Problem 1 from the IMO 2009
  826. Problem 11804 from the AMM
  827. Problem A1, 69th Putnam Competition
  828. Problem A2, 69th Putnam Competition
  829. Problem of Divisibility by 5n
  830. Product of Diagonals in Regular N-gon
  831. Product Of Four Consecutive Integers
  832. Product of Simple Fractions [Java]
  833. Product of permutations [Java]
  834. Proizvolov's Identity [Java]
  835. Proofs Without Words [Java]
  836. Property of an
  837. Property of Quadratic Polynomials
  838. Property of the Powers of 2 [Java]
  839. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
  840. Pythagorean Triples [Java]
  841. Quadratic Function for Solving Inequalities
  842. Quadratic Inequalities on [-1,1]
  843. An Inequality Where One Term Is More Equal Than Others
  844. Quasigroups and block designs from triangular grid [Java]
  845. Rabbits Reproduce; Integers Don't
  846. Radicals, Radicals, And More Radicals in an Inequality
  847. Radon's Inequality and Applications
  848. Ramsey's Number R(3, 3, 3)
  849. Ramsey Number R(4, 3)
  850. Ramsey Number R(5, 3)
  851. Ramsey Number R(4, 4)
  852. Ramsey's Theorem
  853. Random Walks [Java]
  854. Rascal Triangle
  855. Rational Solutions to xy = yx
  856. Rearrangement Inequality [JavaScript]
  857. Recombining Permutations [Java]
  858. Rectangle on a Chessboard [Java]
  859. Rectilinear Paradox
  860. Reflection Lemma [Java]
  861. Riemann Rearrangement Theorem
  862. Riemann Sphere and Möbius Transformation
  863. Riemann Sums - Function Integration [Java]
  864. Right Replacement [Java]
  865. Rolle's and Mean Value Theorems [Java]
  866. Rolle's Theorem in Action
  867. RomanoNorwegian Inequality
  868. Rooks on a Chessboard
  869. Roots and Tangents [GeoGebra]
  870. Round Robin Tournament
  871. Russell's Paradox
  872. Solve A Fourth Degree Equation
  873. Sophie Germain's Identity
  874. Square Root of 2 is Irrational, Proof 29
  875. Square Roots and Triangle Inequality
  876. Squares in Pascal's Triangle
  877. Squeeze Theorem
  878. Sum of Absolute Values [JavaScript]
  879. Sum of All Natural Numbers
  880. Sums of Binomial Reciprocals in Pascal's Triangle
  881. Squeeze (Sandwich, Pinching ...) Theorem (Lemma): an Example
  882. Scalar Product Optimization [JavaScript]
  883. Scheduling and Critical Path Algorithm [Java]
  884. Schur's Inequality
  885. Scrub Tile Puzzle [Java]
  886. Second Pair of Twin Inequalities: Twin 1
  887. Second Pair of Twin Inequalities: Twin 2
  888. Self-descriptive Strings [Java]
  889. Self-documenting Iterations [JavaScript]
  890. Self-reference
  891. Seven integers under 127 and their Ratios
  892. Seven Terms Periodic Sequence
  893. Shapley-Shubik Power Index [Java]
  894. Shapley-Shubik Power Index Calculator [Java]
  895. Shifting Digits and a Point of View
  896. Ship-Dock Theorem
  897. Shuttle Puzzle Practice II [Java]
  898. Sicherman Dice
  899. Sierpinski Gasket and Tower of Hanoi
  900. Sierpinski's Gasket and Dihedral Symmetry [Java]
  901. Sieve of Squares [Java]
  902. Σ2-n = Σn·2-n
  903. Signs and Sums in a Sequence [Java]
  904. Signs in a Matrix [Java]
  905. Simple But Uncommon Equation from 1968 IMO
  906. Simple Cellular Automaton [Java]
  907. Simple Graph Practice [Java]
  908. Simple Inequality with a Variety of Solutions
  909. Simple Inequality with Many Faces And Variables
  910. Simple Somos Sequence - a Russian Olympiad problem
  911. Simple Somos Sequence Calculator [Java]
  912. Simple Yet Uncommon Inequalities with Absolute Value
  913. Simpson Paradox [Java]
  914. $\sin 1^{\circ}+\sin {2^\circ}+\sin 3^{\circ}+\cdots+\sin 180^{\circ}=\tan 89.5^{\circ}$
  915. Sine And Cosine Are Continuous Functions
  916. Sine of a Sum Formula, Proof Without Words
  917. Single formula to express any integer with digits 0-9 each used just once
  918. Sitaru-Schweitzer Inequality
  919. Six Balls, Two Weighings
  920. Size of a Class: Two Viewpoints
  921. Sladjan Stankovik's Inequality In Four Variables
  922. Sladjan Stankovik's Inequality With Constraint
  923. Sladjan Stankovik's Inequality With Constraint II
  924. Slider Puzzles [Java]
  925. Solitaire in Two Colors [Java]
  926. Solutions of F(x)=x and F(F(x))=x [JavaScript]
  927. Solve - an Olympiad Problem - in Your Mind
  928. Solve xx3 = 3
  929. Solve cos²x + cos²2x + cos²3x = 1
  930. Solving an Equation with Inverse Functions
  931. Soriteses
  932. Sorting Algorithms
  933. Sperner's Theorem
  934. Splitting piles
  935. Square Root of 2 as a Continued Fraction
  936. Square root of 2 is irrational
  937. Star of David Theorems in Pascal Triangle
  938. Stars in Array
  939. Steinhaus' Problem [Java]
  940. Step into the Elliptic Realm
  941. Stern-Brocot Tree
  942. Straight Tromino on a Chessboard [Java]
  943. Structure of Hyperreal Numbers
  944. Subsets and Intersections
  945. Subtraction Game [Java]
  946. Sums of the Elements of Three Element Subsets [JavaScript]
  947. Sum of Three Squares [JavaScript]
  948. Sums and Products, a Generalization
  949. Sums, Products, and 1-1 Functions
  950. Sums of Geometric Series - Proofs Without Words [Java]
  951. Sums of Power Series
  952. Sums Of Successive Squares
  953. Sum without Adding
  954. Sums and Products [Java]
  955. Sums of powers of digits [Java]
  956. Superposition Principle
  957. Surreal Numbers
  958. Swapping Rows and Columns [Java]
  959. Sylvester's Problem
  960. Taking Games Seriously [Java]
  961. Tangential Chaos
  962. Telescoping Cubes
  963. Telescoping Squares
  964. Telescoping Sums and Series [JavaScript]
  965. Telescoping Tangents
  966. The ass and the mule [Java]
  967. The Averages of Sides and Angles in a Triangle
  968. The Basic Rules of Counting
  969. The Local-Global Principle
  970. The Regula Falsi - Iterated
  971. The Roads We Take
  972. The Size is in the Eyes of the Beholder
  973. Three Complex Numbers Satisfy Fermat's Identity For Prime Powers
  974. Three Dimensional Cross
  975. Three Junior Problems from Vietnam
  976. Three Variables, Three Constraints, Two Inequalities (Only One to Prove) - by Leo Giugiuc
  977. Tool for Constructing Orthogonal Latin Squares [Java]
  978. Tower of Hanoi, the Hard Way [Java]
  979. Train on Bridge [JavaScript]
  980. Tran Hoang Nam's Cyclic Inequality in Three Variables
  981. Transpositions
  982. Traveling Salesman Problem [Java]
  983. Treatise on Arithmetical Triangle
  984. Triangular numbers that are also square
  985. Trigonometric Identity for the Pi Day
  986. Trigonometric Inequality with Integrals
  987. A Trigonometric Inequality with Ordered Triple of Variables
  988. Trilateral Diagrams [Java]
  989. Trinary Tree(s) underlying Primitive Pythagorean Triples
  990. Tromino Puzzle: Deficient Squares [Java]
  991. Twenty five boys and twenty five girls around a table.
  992. Twin Inequalities in Four Variables: Twin 1
  993. Twin Inequalities in Four Variables: Twin 2
  994. Two Circles and a Limit [Java]
  995. Two Colors in Two Rows [Java]
  996. Two Cyclic Inequalities [JavaScript]
  997. Two Equations in Three Variables [JavaScript]
  998. Two Men of Tibet [Java]
  999. Two-Parameter Solutions to Three Almost Fermat Equations
  1000. Two-Sided Inequality by Dorin Marghidanu
  1001. Two Problems by Kunihiko Chikaya
  1002. Two Problems from a Serbian 7 Grade Math Competition
  1003. Two Products: Constraint and Inequality
  1004. Two Sequences Defined by Recurrence
  1005. Two-Sided Inequality - One Provenance
  1006. Two Solutions: One Correct, One Illuminating. An Example
  1007. Uncountability of the Reals - via a Game
  1008. Undefined vs Indeterminate in Mathematics
  1009. (Un)fair Division by Consensus
  1010. Universal Coloring [Java]
  1011. Universal Product Code [Java]
  1012. Unproperty of the Powers of 2
  1013. Unsolved Problem from Crux Solved
  1014. USA 1975 Problem 3
  1015. Vasile Cirtoaje's Cyclic Inequality with Three Variables
  1016. Vandermonde's Convolution Formula
  1017. Vandermonde Determinant
  1018. Venn Diagrams
  1019. Viète's Formulas
  1020. Voronoi Diagram [JavaSCript]
  1021. Ways To Count
  1022. Weierstrass Product Inequality
  1023. Weierstrass Substitution
  1024. What, how, and the Web [Java]
  1025. What 1, 6, and 14 Have to Do with 5?
  1026. What Is Algorithm?
  1027. What Is Determinant?
  1028. What Is Finite?
  1029. What Is Infinite Descent?
  1030. What Is Infinity?
  1031. What Is Limit?
  1032. What is so natural about "natural logarithms"?
  1033. What Is Space Completion?
  1034. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
  1035. When Two Segments Intersect? [JavaScript]
  1036. Where To Start? [Java]
  1037. White and Black Balls in Urn. 1 in, 2 out. What Color Remains?
  1038. Why 17?
  1039. Why Can't They Be All Different?
  1040. Why sin(x)/x tends to 1
  1041. Why The Number of Primes Could Not Be Finite?
  1042. Wilson's Theorem
  1043. Without Definitions: Why $\displaystyle\frac{1}{3}+\frac{2}{5}=\frac{11}{15}?$
  1044. Wonderful Inequality on Unit Circle
  1045. Word Problems [Java]
  1046. Wu's Inequality
  1047. $x_n=\sin 1+\sin 3+\sin 5+\cdots+\sin (2n-1)$
  1048. Yet Another Puzzle with Hats
  1049. Yet Another Simple Integral
  1050. Zeros and Nines [Java]

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