The applet below depicts Chebyshev polynomials of the first kind Tn(x) = cos(n·arccos(x)), n = 0, ..., 50.
http://www.cut-the-knot.org/Curriculum/Algebra/ChebyshevTest.shtml
Divisibility criteria are ways of telling whether one number divides another without actually carrying the division through.
http://www.cut-the-knot.org/blue/divisibility.shtml
Fagnano's original solution used Calculus. But, once the answer became known, several purely geometric solutions were also discovered.
http://www.cut-the-knot.org/triangle/Fagnano.shtml
The skills of computing fast might be classified into three broad categories.
http://www.cut-the-knot.org/arithmetic/rapid/index.shtml
With three pins forming a triangle, either all vertex configurations are the same, or all vertex configurations are different.
http://www.cut-the-knot.org/Curriculum/Algebra/FirstProof.shtml
There are many patterns in the common multiplication table.
http://www.cut-the-knot.org/Curriculum/Algebra/Figurate.shtml
This site offers several examples where representing a number in a base different from the customary 10 may have a great advantage.
http://www.cut-the-knot.org/recurrence/conversion.shtml
An old adage has it that those who understand compound interest are more likely to collect it, those who don't more likely to pay it.
http://www.cut-the-knot.org/arithmetic/interest.shtml
A Mathematical Droodle
http://www.cut-the-knot.org/Curriculum/Geometry/SymmetryInCircle.shtml
Count the number of vowels and consonants in the sentence below. You can modify the sentence by clicking on the numbers in parentheses.
http://www.cut-the-knot.org/Curriculum/Algebra/LetterCount.shtml