Search Classroom Capsules and Notes:

Classroom Capsules and Notes

New Capsules for One-Variable Calculus catalogs capsules appropriate for this course using the same topics as the corresponding resources in Course Communities.

Featured Items:
An Application of Geography to Mathematics The authors review the history of the evaluation of the integral of the secant as it arose as an explanation of the construction of Mercator projections.		Instances of Simpson's Paradox Comparisons of averages lead to intuitive contradiction.
Uncountable Sets and an Infinite Real Number Game A short proof of the well-known fact that the unit interval \([0,1]\) is uncountable is presented by means of a simple infinite game. The author also used this game to show that a (non-empty) perfect subset of \([0,1]\) must be uncountable.		The Telescoping Series in Perspective The author describes an application of the telescoping series, \( \sum 1/[n(n+1)]\), to the visual theory of perspective.
Proof without Words The picture proves Viviani's Theorem: that the sum of the distances from an interior point to the sides of an equilateral triangle always add to the height of the triangle.		A Serendipitous Applilcation of the Pythagorean Triplets Relates pairs of quadratic polynomials to Pythagorean triples.