# Browse Classroom Capsules and Notes

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Displaying 91 - 100 of 1211

The following is a short, simple, but not well-known proof of the well-known trigonometric identify $\sin(a+b) = \sin a \cos b + \cos a \sin b$.

The range of validity of the inequality for various values of $n$

In his work On the Sphere and the Cylinder, Archimedes showed that the volume of the sphere is exactly two thirds of the volume of the circumscribed cylinder. This article explores...

The importance of round-off errors, ill-conditioned systems, and interval analysis in the context of baseball statistics

Calculation of the minimum distance from a point to a curve

The author shows that the system characterized by

$x(t) = a_1 t^2 + b_1 t + c_1$
$y(t) = a_2 t^2 + b_2 t + c_2$
$z(t) = a_3 t^2 + b_3 t + c_3$

must lie in a...

Projectile motion on large and small scales in the context of problems from sports

Hands-on activities using balloons for a differential equations class

The Method of Undetermined Coefficients is approached by using linear operators and making use of patterns associated with matrix multiplication.  The authors discuss several pedagogical...

Relations between Romeo and Juliet presented as pairs of coupled differential equations