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Browse Classroom Capsules and Notes

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Displaying 1021 - 1030 of 1214

The author gives a synthetic geometric proof answering the question in the title of the paper.

The author uses the golden matrix ring \(Z(A)\) generated by \(A= \left[ \begin{array}{cccc} 0 & 1 \\ 1 & 1 \end{array} \right] \) to prove certain identities involving Fibonacci...

The Fermat point of a triangle is used to present simple geometric proofs of the inequalities in the title of the paper.
The area under the segment of a parabola is found via the volume of a pyramid.
A few simple models in the fields of neuroscience and high voltage engineering are presented and discussed.

The tangent of the sum formula is proved by using an inscribed quadrilateral whose longest side is the diameter of the circle, and the diagonals are perpendicular to the pair of oposite sides...

The author shows that every Heron triangle is similar to one with sides \(r + 1/r\), \(s + 1/s\), and \(r - 1/r + s -1/s\) for rational numbers \(r\) and \(s\) greater than one.
The author gives geometrical proofs of a number of identities for the Fibonacci numbers.

A 1932 Erdos conjecture on packing squares into a square is shown to be equivalent to a more general conjecture.

The authors give two proofs, one geometric and one algebraic, to provide insight into why the sum of independent normal. random variables must be normal.