*A simple characterization of the condition that, for an integer-sided triangle, one angle is twice another.*

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*An alternative to partial fractions for certain integral calculations*

*Using substitutions to derive equations for the ellipse and hyperbola*

*A polar coordinate proof of the fact that the focal radii of an elipse (hyperbola) make equal angles with the tangent.*

*An extension of the fact that \(1/n!\) is the content (volume) of a particular \(n\)-dimensional simplex*

*Simple proofs of the formulas for the derivatives of \(\sin x\) and \(\cos x\) when \(x\) is acute*

*Using a generalized Fibonacci sequence to determine the expected number of tosses of a fair coin to first obtain \(n\) consecutive heads*

*Examples of an elementary transcendental function having three different kinds of asymptotes \(x-a-0, y-b=0, y=mx+c\) and defined by one single equation in its domain of definition*

*A simple, natural way to geometrically read off the complex roots of a real quadratic equation*

*Using the Arithmetic-Geometric Means Inequality and the Mean Value Theorem to show that the maximum value of \(x^{1/x}\) occurs at \(x = e\)*