# Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 47

Ptolemy's Theorem states that the product of the diagonals of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) is equal to the sum of the products of the opposite sides...

The authors "describe two different methods for locating the centroid of a finite number of given points ... without using coordinates or numerical calculations". Some examples are...

Three propositions, involving integration and partial differentiation, one of them Fubini`s Theorem, are shown to be equivalent.

The author derives formulas for the coefficients of the characteristic polynomial of a square matrix in terms of the partial derivatives of its determinant, which is viewed as a function of...

Some popular optimal value and constraint problems, like fence-area problem and box-volume problem, are generalized to $n$-dimensions.

Using polar curves, the author defines "vertex solids", which include usual cones and paraboloids, and computes their volumes.

If a function of one variable has a unique critical point, then it is not only a local max/min, but global. Does the same hold for functions of two variables? The authors provide a...

A smooth surface in $\Re^2$ or $\Re^3$ has one critical point that is a local, but not global minimum. Must that surface have another critical point? While the answer in the 2-D version is...

Solid angle technique applied to find volumes of regular polyhedra

The author shows a relation between a Jacobian and a certain class of Wronskians.