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.A System of Equations in DeterminantsFind all nxn matrices A such that det(A+XY)=det(A+YX), for all X and Y, and det(A)=1
http://www.cut-the-knot.org/arithmetic/algebra/EquationInDeterminants2.shtml
Powers and Fractions Inequality\sum(a^3b^3)/c^5 is not less than sum(ab)/c.
http://www.cut-the-knot.org/arithmetic/algebra/PowersAndFractionsInequalities.shtml
Miguel's Tangents: Modern Day SangakuIn equilateral triangle tangents from a point on the incircle to the three inscribed circles have the property that the longest one is the sum of the other two
http://www.cut-the-knot.org/m/Geometry/MiguelTangents.shtml
Miguel's Area of SquareThe area of a square is found via the perpendiculars from vertices to a tangent to the circumcircle
http://www.cut-the-knot.org/m/Geometry/MiguelAreaOfSquare.shtml
Proof by A. RobsonMorley's Miracle, Morley's Trisector Theorem, A. Robson's Proof of Morley's Theorem
http://www.cut-the-knot.org/triangle/Morley/Robson.shtml
Greatest Difference in Arithmetic ProgressionFor a given n greater than 0, find among all arithmetic progression {x_i} with sum(x_i)^2=1, the one with the greatest difference
http://www.cut-the-knot.org/Optimization/GreatestDifference.shtml
An Inequality in Triangle, VIIIsum(5a^2-b^2-c^2)/sqrt(m_bm_c) is not greater than 4sum(m_a)
http://www.cut-the-knot.org/triangle/InequalityInTriangle8.shtml
Hlawka-like Dinca's InequalitytHlawka-like Dinca's Inequality: x^a+y^a+z^a+(x+y+z)^a is not less than (x+y)^a+(y+z)^a+(z+x)^a
http://www.cut-the-knot.org/arithmetic/algebra/HlawkaDinca.shtml
Quadratic Formula: Completing And Not Completing the SquareDerivation of the quadratic formula for finding the roots of a quadratic equation
http://www.cut-the-knot.org/arithmetic/algebra/QuadraticFormula.shtml
An Inequality with Cot, Cos, and SinIn an acute triangle sum(cot^2 A cot^2B) is not less than sum(cos^2 A)/sum(sin^2 A)
http://www.cut-the-knot.org/arithmetic/algebra/CotCosSinInequality.shtml