Recent changes to Interactive Mathematics Miscellany and PuzzlesInteractive Mathematics Miscellany and Puzzles is a frequently updated site. Here are the most recent addtions. For other changes please visit the site.The Golden PentacrossA construction of the The Golden Pentacross and the tessellation of the plane
http://www.cut-the-knot.org/do_you_know/GoldenPentacross.shtml
Miguel Ochoa's Chords And TangentsLines AD,CB,CD are tangent to a given circle at A, B, and N, respectively. M is the midpoint of the arc AB opposite N; P=AB\cap DM, Q=AB\cap CM. Prove that PQ=AP+BQ.
http://www.cut-the-knot.org/m/Geometry/MiguelChordsAndTangents.shtml
A Tricky Integral InequalityA Tricky Integral Inequality: a double integral over a disguised triangle inequality
http://www.cut-the-knot.org/m/Algebra/TrickyIntegral.shtml
Quadrilateral InequalityQuadrilateral Inequality
http://www.cut-the-knot.org/wiki-math/index.php?n=Geometry.QuadrilateralInequality
Golden Ratio in a Butterfly Astride an Equilateral TriangleGolden ratio is observed in a special butterfly that sits astride an equilateral triangle
http://www.cut-the-knot.org/do_you_know/GoldenRatioAstrideEquilateralTriangle.shtml
Addition and Subtraction Formulas for Sine and Cosine IVProduct to sum formulas for sine and cosine by John Molokach
http://www.cut-the-knot.org/triangle/SinCosFormula4.shtml
Inequality by CalculusFour solutions to an inequality, all by Calculus
http://www.cut-the-knot.org/m/Algebra/InequalityByCalculus.shtml
Three Junior Problems from VietnamThree inequalities with si xparameters linked by a 3x3 matri xequation
http://www.cut-the-knot.org/m/Algebra/ThreeJPfromVietnam.shtml
An Integral Inequality from the RMMf'(x)=f'(1-x) on [0,1]. Prove that int(f,0,1) is not less than sqrt(f(0)f(1))
http://www.cut-the-knot.org/arithmetic/algebra/IntegralPlusInequality.shtml
Hlawka in Conve xQuadrilateralIn conve xquadrilateral ABCD, E is the midpoint of AC, F the midpoint of BD. Prove that AB + BC + CD + DA strictly greater than AC + BD + 2*EF
http://www.cut-the-knot.org/m/Geometry/HlawkaInConvexQuadrilateral.shtml