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Browse Classroom Capsules and Notes

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Displaying 1031 - 1040 of 1135

The derivative of arctangent is derived directly from the definition of derivative by using some clever inequalities.
The author shows how to solve a class of analytic equations of matrix functions by using single-variable calculus and nilpotent matrices.
The author discusses several conditions that guarantee the correlation of the union of two bivariate data sets is greater than common correlation of the two data sets.
The authors show that a certain sequence unexpectedly converges to 8.
In this paper the radix sorting algorithm is used to explain why Geronne`s 3 pile card trick works. Generalizations are explored.
The limit of the ratio of the geometric mean to the arithmetic mean of certain sequences is studied, using Riemann sums.
Two proofs, one elementary, of the limit in the title are presented.

The authors investigate the occurrence of composite values of non-constant polynomials with integer coefficients evaluated at integer points.

A visual proof for the sum of octagonal numbers is presented.
The paper presents an elementary solution to the Brachistochrone problem.