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Browse Classroom Capsules and Notes

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Displaying 1031 - 1040 of 1214

The author shows that every triangle can be dissected into four (acute triangles into three) isosceles triangles, and that a triangle can be dissected into two isosceles triangles if and only if...
It is shown that any bijective function that maps circles and lines onto circles and lines is either a linear fractional transformation, or the complex conjugate of a linear fractional...
The author characterizes the set of possible limits of subsequences of a given sequence.
Two visual proofs of some exponential inequalities are presented.
Given any positive integer \(n\), find polynomial curves that have exactly \(n\) tangent lines which intersect the curve exactly once.

Solving Pell Equations using Fibonacci-like sequences

In the game of tennis, if the probability that player \(A\) wins a point against player \(B\) is a constant value \(p\), then the probability that \(A\) will win a game from deuce is \(p^2/(1 - 2p...

Solving an expected value problem without using geometric series

Another approach to trisecting any acute angle

Characterize positive integers which can be written as a sum of consecutive integers

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