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Browse Classroom Capsules and Notes

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Displaying 1 - 10 of 1211

The author reviews the evidence of authorship of Cramer`s Rule and comes to the conclusion stated in the title of the paper.

The fact that, for an equilateral triangle, the sum of the distances from any interior point to the three sides is equal to the height of the triangle is shown visually.

The author considers two infinite decimals, where the \(n\)th digit is the last non-zero digit of \(n!\), creating the number \(F\), and using \(n^n\), creating the number \(P\). The author shows...

The geometry of Archimedes` proof of a formula for a sum of squares is depicted visually.

In this note the authors present an elementary proof that the inequalities \( (1+1/n)^n < e \leq (1+1/(m-1))^m \) hold for \(n>0\) and \(m>1\), using only the arithmetic-geometric mean...

This capsule uses the determinants of matrices to study Fibonacci numbers. Specifically, the sum property of the determinant is used to derive identities between Fibonacci numbers.

This capsule project starts with computing average class size from the institution and student points of view. The results are drastically different. The author then tries to explain why this...

This  project uses a sampling problem to compute certain probabilities. In the process, certain binomial identities are established.

This capsule discusses rates of change related to a vessel obtained as a surface of revolution. The question is about the rate a bug must move on the surface as liquid is being poured into the...

This article provides a calculation of the number of pizzas with different toppings to point out the mistakes in a commercial by a national pizza chain.