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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 1212

A visualization of the triple angle formulas for sines and cosines is presented.

The limit of the geometric mean of the first \(n\) integers raised to the real positive power \(s\), divided by their arithmetic mean is shown to be \((s+1)/e^s\). An elementary derivation of...

The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...

The author gives a visual proof of the Pythagorean Theorem.

The author presents a geometric interpretation of Leibniz`s rule for differentiating under the integral sign, and gives an informal visual derivation of the rule.

Using basic linear algebra, the authors obtain a complete, easy to compute, winning strategy for the \(4 \times 4\) mini `Lights Out` game.

The Theorem “An infinite group is cyclic when each of its nonidentity subgroups have finite index” is proved and discussed, and a test to show groups are not cyclic is ...

The author gives a proof of the title as an application of Lagrange`s Theorem, allowing the theorem to be presented in the first semester of an undergraduate abstract algebra course.

A visual representation of the title is presented.

The author provides a combinatorial explanation of a `striking`result from Herbert Wilf`s book “generatingfunctionology” , equating the likelyhood of certain permutations with the...