30 Jul

If you’ve come here as a result of a puzzling postcard you may have come across, welcome to Studio Infinity! We hope you’ll enjoy looking at some of the other content below as well, but here are the three posts corresponding to the problems you can find on those postcards, each of which links to a solution.

And, as I’ve mentioned here before, I invite you all to submit a problem or solution to Math Horizons Playground.

30 Jul

How does the value of the following improper integral compare to 1? I.e., is it smaller, larger, or exactly equal to 1?

(This problem was proposed to Math Horizons Playground by Mehtaab Sawney of Commack High School. And for all of you $\pi$-ists out there, $\tau$ is of course just the radian measure of a full circle, i.e., $\tau=2\pi$.)

Stumped? You can peek at the solution using the password “strapyb”.

30 Jul

30 Jul

For definiteness, the unlabeled points do in fact trisect each of the sides of the triangle.

30 Jul

30 Jul

What are the next few terms in this sequence of smallish numbers?

# 1 1 13131 131 131 131 1 1321 132131 131 1 1321 1321 13 ? ? ?

(And, of course, what’s the rule generating the sequence?)

Stumped? You can peek at the solution using the password “1p1a2s”.

30 Jul