# Tag Archives: math

## Polyhedron with 152 Faces, Including 60 Heptagons

### Image

# On Math Jokes (with a new re-telling of my favorite one, about a balloon race)

Math jokes are almost universally awful — or, at least, it seems that way to me, since I spend a lot of time around ninth graders. Hearing “Gee, I’m a tree” or “Pi are square? No, pies are round, and cake are square!” will generally elicit a groan from me, and each new cadre of students seems to think they invented these fossilized puns. An even worse “joke” is the giggling one should expect from, say, 7th graders, if one squares the number thirteen in their presence.

I do know exactly one good math joke, though. I didn’t hear it from a student. If you’re curious, read on. Only the embellishments are original; I didn’t make up the joke, itself, though, nor do I know who did.

My source for the image below is this fellow WordPress blogger’s photography blog.

So a physicist, chemist, and a lawyer enter a balloon race together. Theirs is the last balloon to leave, because the lawyer had been in court, arrived late, and caused a short delay in departure. The consequences of this were serious, though, for a sudden cross-wind blew them off course, right after takeoff. Soon, they couldn’t even see any of the other balloons in the race, and none of them recognized any landmarks in the landscape below.

Soon, they had no idea where they were, and started getting worried about making it to their next classes on time — or back to court, in the case of the lawyer. The chemist was particularly worried. “What are we going to* do?*” asked the chemist.

The physicist replies, “I have an idea!” He cups his hands, leans out, and yells, as loud as he can, “Hello! Where are we?”

The balloon flies on for at least two long, anxious minutes as the trio waits, silently, for an answer. Eventually, they hear, from a great distance, a voice. “Hello! You’re lost!”

The physicist looks at the other two, and says, “That, my friend, was a mathematician.”

“How,” asked the lawyer, “could you possibly know that?”

“Three things,” replied the physicist. He held up one finger. “First, it took him a long time to answer.”

“Second,” he continued, holding up two fingers, “the answer, when it finally came, was absolutely correct.”

A third finger joined the first two. “Third, the answer, when it finally came, was completely useless!”

# One Possible Definition of Physics

With my metaphorical “mathematics of sets” hat on, this is what physics looks like, to me. The further you go in the field, the more challenging the mathematics gets; also, the better (and more expensive) the toys become.

# Circumparabolic Regions Inside a Unit Circle

A circumparabolic region is found between a circle and a parabola, with the circle being chosen to include the vertex and x-intercepts of the parabola used, with the circle, to define the two circumparabolic regions for a given parabola-circle pair. There are four such regions shown above, rather than only two, because two parabolas are used above. The formulae for the parabolas, as well as the circle, are shown.

A puzzle which I will not be solving, I suspect, until I learn more integral calculus: what fraction of the circle’s area is shown in yellow?

# “Math Problems for Fun”: The Source of My Blog’s New Header-Image

I don’t usually post the work of others here, but, since I am now using this as my blog’s header-image (in slightly altered form), it seemed appropriate to make an exception for this cartoon, in its original format. I didn’t know that the cartoonists at *Cyanide and Happiness* monitored my life, but, clearly, that guy in the blue shirt is me!

# Tessellation Featuring Regular Pentagons and Regular Pentadecagons

Other polygons included in this tessellation include several types of rhombi, as well as triconcave octadecagons. The pattern is chiral, but the chirality is subtle. (Hint: look near the pentagons.)