# Classroom Capsules and Notes

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used in Course Communities. So far we have organized capsules for the following courses:

You may select topics within each course.

## Featured Items

##### Fibonacci-Like Sequences and Pell Equations

Solving Pell Equations using Fibonacci-like sequences

##### Proof Without Words: Area of a Parabolic Segment

The area under the segment of a parabola is found via the volume of a pyramid.

##### The Classification of Similarities: A New Approach

In plane geometry, if a similarity is not an isometry, it is either a dilative rotation or a dilative reflection. A new proof is given based on Apollonius circles.

##### A Geometric Proof of Machin's Formula

The author presents a geometric proof of Machin's formula, which expresses $\frac {\pi}{4}$ as the difference of two inverse tangent functions.

##### The Rascal Triangle

Inspired by the Pascal triangle, three young "rascals" from three different countries devise a number triangle based on a diamond recurrence formula.

##### Maclaurin Expansion of Arctan $x$ via L'Hôspital's Rule

Coefficients are obtained for the Maclaurin series for arctan $x$ using l'Hôpital's rule.