# Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 981 - 990 of 1214

The author finds visually sums of squares and sums of odd squares.
Given positive integers $$n\geq 3$$, the author finds a single inequality condition for every $$r$$ of them ($$3 \leq r \leq n$$) to be the lengths of sides of a $$r$$-gon.
The author presents a geometric proof of Machin's formula, which expresses $$\frac {\pi}{4}$$ as the difference of two inverse tangent functions.
The author proves visually the law of cosines.

The author gives two applications of a method for finding a function $$g$$ such that $$f(g(x)) \geq f(x)$$.

The author visually expresses the cube of a number as an arithmetic sum.

A visual determination of the area of a right triangle is given using an inscribed circle.

An odd prime $$p$$ has $$(p-1)/2$$ quadratic residues mod $$p$$, and for relatively prime $$p$$ and $$q$$ there are $$(p-1)(q-1)/2$$ non-representable Frobenius numbers. The author discusses a...

An old and forgotten method for determining whether a quartic polynomial over the rationals is reducible is revived.
The Butterfly Theorem is generalized to include Sidney Kung`s Butterfly Theorem.