One thing we enjoy doing is guiding a student through the process of problem-solving. Here is a problem from August that illustrates how to think through a complicated geometrical proof. In particular, this uses some circle theorems involving chords, secants, and tangents, together with a bit of algebra.
(A new question of the week) A question from the end of August led a student and a Math Doctor to an extra challenge, by way of an apparent typo in the problem. We particularly enjoy working with students who are willing to take on extra work in order to learn more than they need …
(A new question of the week) Some questions we get, while small, raise interesting issues. In a question we got last month, there are several little issues pertaining to how the final answer should be chosen; as is too often the case, it seems that a diligent student who cares about accuracy might be penalized. …
A Test Dilemma: Do As You’re Told, or Do What’s Right? Read More »
(A new question of the week) Often the hardest part of solving a problem is interpreting what it means. Math is precise; human language can be ambiguous, and assumptions can be hidden. Today, we look at a multi-variable calculus problem that looked enough like a classic single-variable maximization problem to fool the reader into not …
(A new question of the week) An interesting geometry question came to us in July, about the area of overlap between two squares. The discussion was not long, but leads to some interesting ideas.
(New questions of the week) We’ve had a number of brief discussions recently, which feel too small on their own for a post; but several happen to be dealing with similar types of issues. These four questions, all from July, involve limits or derivatives at edges or holes in the domain of a function. Let’s …
(A new question of the week) We have had a lot of interesting questions recently. This one involved inverse trigonometric equations that led to cubic and quartic equations. We’ll observe here one of the benefits of embedding the original discussion in a blog format where I can add information that will help you, the reader, …
Challenging Inverse Trig and Polynomial Equations Read More »
(A new question of the week) Last week we looked at a recent question about an attempt to write a proof using the contrapositive, which was foiled by difficulty in negating a statement. Two weeks later, we had another question about the same sort of issue, but with a different problem in the negation. In …
(A new question of the week) A recent question raised some interesting issues related to the contrapositive of a logical statement, and how to negate a statement, similar to some past discussions. What universe you are in makes a big difference!
(A new question of the week) A recent question (from May) about approximating the binomial distribution with the normal distribution led to some (accidental and otherwise) insights about the method.