I added a new page to my Web site. It's a visual proof that the integral of y=x2 from 0 to b is indeed b3/3.Some interesting things about this proof:It was discovered by Jacob Regenstein, a high school student.It does not involve any algebraic manipulation.It shows a dramatic example of how integration increases the degree… Continue reading Integrating y=x^2
One topic that has nearly vanished from my teaching is the solving of inequalities "by hand". There are several reasons for that choice:The techniques are difficult to teach and difficult to learn, because they are so close to the ones for the solving of linear equations, but differ in one crucial case.It is difficult to… Continue reading Solving Inequalities
This is another post about sessions I attended last weekend at the Asilomar Northern California CMC conference. (To read the whole set, start here.)Kevin Rees presented two variations on a classic volume optimization problem. In the traditional problem, you start with a square piece of cardboard, cut off congruent squares at the four corners, and… Continue reading The third dimension!