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.Isogonal ConcurrenciesAn outgrowth of the concurrencies noted earlier in the Hofstadter configuration
http://www.cut-the-knot.org/m/Geometry/IsogonalConcurrencies.shtml
Cutting a Hole in HalfThe task is to cut with a single straight line a rectangle with a cut off smaller rectangle
http://www.cut-the-knot.org/m/Geometry/CutInHalf.shtml
Getting the first digits of Pi by counting collisionsGetting the first digits of Pi by counting collisions
http://www.cut-the-knot.org/blue/nicollier_galperin_ctk.shtml
A Median SurpriseAn exciting newly discoeverd property of medians
http://www.cut-the-knot.org/m/Geometry/LeeSwallows.shtml
A Property of AltitudesA Property of Altitudes - a property of altitudes that for a right triangle reduces to a well known identity
http://www.cut-the-knot.org/triangle/AltProperty.shtml
All about altitudesAll About Altitudes - a collection of several salient and useful properties of the altitudes
http://www.cut-the-knot.org/triangle/AllAboutAltitudes.shtml
Beyond PythagorasA picturesque generalization of the Pythagorean theorem
http://www.cut-the-knot.org/m/Geometry/BuratinoPyth1.shtml
Golden Ratio in Five StepsGolden Ratio in Five Steps starting with a right isosceles triangle
http://www.cut-the-knot.org/do_you_know/BuiGoldenRatio5Step.shtml
An Unusual Generalization of the Pythagorean TheoremAn Unusual Generalization of the Pythagorean Theorem: 1) true for any triangle, 2) reduces to the Pythagorean theorem
http://www.cut-the-knot.org/pythagoras/Pyth107.shtml
An Unusual Generalization of the Pythagorean Theorem, a VariantAn Unusual Generalization of the Pythagorean Theorem, a Variant: 1) true for any triangle, 2) reduces to the Pythagorean theorem
http://www.cut-the-knot.org/pythagoras/Pyth107C.shtml