What Your Favorite Polygon Says About You


Triangle. You’re simple, solid, reliable. While you maybe fear being thought unimaginative, you feel a special affinity for triangles: they’re the shape that introduced the young you to the term “obtuse”. Knowing the word gave you many times you could insult a younger sibling without their catching on, and after they did catch on, let you insist that you were just describing the triangle they were making by doing something or other, and then they punched you. Good times.

Rectangle. You were caught off-guard by the question and figured this was the safest answer. Nobody’s ever going to say your judgement is bad, just vanilla. But, you answer, vanilla is only the most popular flavor of anything on the planet, even better-liked than chocolate, pentagons, fresh garlic toast, and the glue on security envelopes.

Pentagon. You actually like five-pointed stars but you’re not sure if they count as polygons.

Hexagon. You read somewhere about how this was the most efficient shape and you’re going to stick with that even though you never learned efficient at what. Alternatively, you play a lot of area-conquest strategy games and just like thinking about all these many paths of hexagons and having at least twelve types of cards to keep track of things. Alternatively, you are a flock of bees.

Heptagon. You don’t know what a heptagon is but you like the old-timey 1920s-slang feel to any word that starts “hep”.

Parallelepiped. You so enjoy the sound of this word you don’t care that it’s a polyhedron, not a polygon. If asked to name an actual proper polygon you will try to distract the questioner. “Is that a flock of bees?” you might say, pointing to the city’s new hexagon district, which is very efficient but has lousy traffic signals.

Circle. You have never, not once, ever completed a task without an argument about what the instructions precisely mean.

Parallelogram. You like how it suggests a rectangle, but by tilting to the side one way or another it looks like it’s moving faster. Or like it’s braking really fast. You can’t get just any shape to look that lively.

Heptadecagon. You are a mathematics major and were crazy impressed by the story of how Carl Friedrich Gauss figured out how to draw a regular 17-sided polygon with straightedge and compass. You’re still so impressed by this that you’re angry they inscribed a 17-pointed star, instead of a 17-sided polygon, on Gauss’s gravestone. You’ve never seen a picture of his gravestone, and you haven’t ever looked up how Gauss did this 17-gon. “It was really easy,” Gauss once explained. “I just drew a 17-pointed star and then connected the points.” You’re nevertheless still offended on his behalf.

Chiliagon. You were paying attention that day in philosophy class where they talked about a regular 1000-sided polygon and how you couldn’t even tell that wasn’t a circle. Very good.

Octagon. But not the stop-sign octagon. The octagon you get by putting, like, one long skinny table off the center of another long skinny table, because it looks like that shouldn’t even be an octagon but it is, and anybody can count edges and see it is, and that’s just great.

Myriagon. You like that chiliagon idea but think it’s getting just a little too much attention so you’re going for a 10,000-sided regular polygon instead. This is the sort of thing people warn new acquaintances you do.

Trapezoid. You have loved this shape ever since you first heard about it, and were able to go home and ask your little sibling if they wanted to see a trapezoid, and they said sure, and you informed them that they were a zoid and you grabbed their arm and wouldn’t let go, and said now that’s a trap-a-zoid and they ended up yelling and punched you with their free arm. That spot on your arm was sore for weeks. Good times.

Megagon. You’re the person who dragged the philosophy class into arguing whether it mattered that the Trolley Problem wouldn’t literally happen exactly like that, instead of letting the class explore the point of the problem about whether it’s more ethical to actively cause or to passively allow harm. Sigh. Fine. You are unimaginably clever. Now go play outside.

Dodecagon. You were trying to express fondness for that 20-sided die shape and then halfway through remembered that’s a polyhedron but you were committed. Had you started out with polygons in mind you would have said “heptagon”. The dice shape is the “icosahedron”. The dodecahedron is the 12-sided die. This is how everything in your life goes.

Everything There Is To Say About Going Indoors


Ooh, and hey, now I can publish an Everything There Is To Say About Going In Doors essay by taking this and running it backwards. This is great, I’ll finally be ahead of deadline a little, only to mess it up!

[OK, I know what you’re thinking and believe me, this is better.]

If you find that exiting doors until you get out of doors doesn’t work for you? Try opening a home-repair store and holding a good sale on doors and door frames. It’s a bit more work, but that’s what it takes.

[It’s not like I couldn’t reverse every word in every sentence like I said I could do last week.]

  • Look around for that free weekly paper they used to toss somewhere near your house but that you never see anymore. You don’t remember when they stopped tossing it nearby. Did they stop printing it? Did they get upset that you only read it to see what articles were made funny by copy-editing errors? You could write their editor to ask, but you don’t know their address, what with not having a paper. There’s no way to figure this out.

[It’s just not pretty is all.]

  • Start up singing “Everyone knows it’s windy” by the Association. Continue singing until you notice your neighbors looking at you, wondering if this is also talk about the weather. It’s not but you can understand where they’re coming from. It is from next to your place.

[I’m not being lazy in this. ]

  • Spend up to fifteen minutes examining that tree where last summer you saw a raccoon crawl out of a knothole that seems way too small for it.

[I tried reversing all the words and it just made me seasick.]

  • Test how far you can get from home before your WiFi stops being detectable. Alternatively, see if you can figure out where the WiFi signal with the really funny name comes from.

[I know, you’d think it would just make things sound like Yoda but that just seems like it’s hacky in a way I don’t like.]

  • Go back indoors.

[And I tried just reversing the sentences within each paragraph and that left me a bit queasy too.]

  • Agree with the neighbors that the weather is. This is a fun activity that improves relations with your neighbors. For some reason. Humans work all weird.

[It isn’t as if I can’t commit to a bit.]

What is there to do when you’re outdoors? There’s a world of things. Some options include:

[I mean, “baffling experiment in formalism passed off as humor” is almost my signature mode.]

If you find yourself indoors, you can get out of doors. Think hard of the last time you were outdoors, and exit at least as many doors as you entered to get where you are now. If you see a shortcut — some path that would skip some door or other — well, it’s your business. I wouldn’t risk it. You might overshoot the outdoors and get to the out-outdoors and that’s some weird space.

[But believe me there’s no way to make, like, “Detection outdoors in course advanced an need you’ll” readable at length never mind funny. ]

Thing about going out of doors is you can only do it if you start indoors. Thus, are you indoors? The way to know for sure is to apply a three-dimensional analog to the Jordan Curve Theorem. This is one of the foundational elements of multivariable geometry. So there’s no way to know. We have to infer from evidence. Check around you. If you find around yourself a fireplace, a cuckoo clock that is not oversized and does not feature comical figures poking out on the quarter-hour, a game show taping, or pictures on the wall of beloved yet vaguely identifiable relatives, there’s a good chance you’re indoors. If you find a herd of zebras or a ukulele festival or a golfatorium? These often indicate being outdoors. A giant cuckoo clock with comical figures poking out on the quarter-hour is often a sign you’re at an amusement park, and it might be indoors or outdoors. You’ll need an advanced course in outdoors detection.

[Anyway I won’t do this again unless it turns out that it worked brilliantly and everybody loves my weird mix of trying a thing that didn’t actually work.]

The outdoors is very like the indoors, with one fewer set of doors to go through. Also the outdoors offers weather. This is an exciting feature in which, instead of being comfortable, it’s too hot. Or it’s too cold. Sometimes you’ll be in a devious place and it’ll be too medium instead. There’s no guessing what the temperature will be like, except by checking a forecast. Plus weather offers the prospect of rain or snow or clouds of ladybugs or some other daft thing. There are places where you can say, “if you don’t like the weather, wait five minutes”. This is everywhere except Singapore. In Singapore it’s always 92 degrees Fahrenheit and muggy outside monsoon season, which is 1:30 to 3:30 pm every day.

[I feel like such a fool except this easily took me like four minutes less to write than a wholly original piece would have taken.]

Going out of doors is very like going in doors, except it works the other way around. Now if I had written Everything There Is To Say About Going In Doors, I wouldn’t be behind deadline. I could just print that whole essay with the words in reverse order. Too bad.

Everything There Is To Say About Going Out Of Doors


Going out of doors is very like going in doors, except it works the other way around. Now if I had written Everything There Is To Say About Going In Doors, I wouldn’t be behind deadline. I could just print that whole essay with the words in reverse order. Too bad.

The outdoors is very like the indoors, with one fewer set of doors to go through. Also the outdoors offers weather. This is an exciting feature in which, instead of being comfortable, it’s too hot. Or it’s too cold. Sometimes you’ll be in a devious place and it’ll be too medium instead. There’s no guessing what the temperature will be like, except by checking a forecast. Plus weather offers the prospect of rain or snow or clouds of ladybugs or some other daft thing. There are places where you can say, “if you don’t like the weather, wait five minutes”. This is everywhere except Singapore. In Singapore it’s always 92 degrees Fahrenheit and muggy outside monsoon season, which is 1:30 to 3:30 pm every day.

Thing about going out of doors is you can only do it if you start indoors. Thus, are you indoors? The way to know for sure is to apply a three-dimensional analog to the Jordan Curve Theorem. This is one of the foundational elements of multivariable geometry. So there’s no way to know. We have to infer from evidence. Check around you. If you find around yourself a fireplace, a cuckoo clock that is not oversized and does not feature comical figures poking out on the quarter-hour, a game show taping, or pictures on the wall of beloved yet vaguely identifiable relatives, there’s a good chance you’re indoors. If you find a herd of zebras or a ukulele festival or a golfatorium? These often indicate being outdoors. A giant cuckoo clock with comical figures poking out on the quarter-hour is often a sign you’re at an amusement park, and it might be indoors or outdoors. You’ll need an advanced course in outdoors detection.

If you find yourself indoors, you can get out of doors. Think hard of the last time you were outdoors, and exit at least as many doors as you entered to get where you are now. If you see a shortcut — some path that would skip some door or other — well, it’s your business. I wouldn’t risk it. You might overshoot the outdoors and get to the out-outdoors and that’s some weird space.

What is there to do when you’re outdoors? There’s a world of things. Some options include:

  • Agree with the neighbors that the weather is. This is a fun activity that improves relations with your neighbors. For some reason. People are weird.
  • Go back indoors.
  • Test how far you can get from home before your WiFi stops being detectable. Alternatively, see if you can figure out where the WiFi signal with the really funny name comes from.
  • Spend up to fifteen minutes examining that tree where last summer you saw a raccoon crawl out of a knothole that seemed way too small for it.
  • Start up singing “Everyone knows it’s windy” by the Association. Continue singing until you notice your neighbors looking at you, wondering if this is also talk about the weather. It’s not but you can understand where they’re coming from. It is from next to your place.
  • Look around for that free weekly paper they used to toss somewhere near your house but that you never see anymore. You don’t remember when they stopped tossing it nearby. Did they stop printing it? Did they get upset that you only read it to see what articles were made funny by copy-editing errors? You could write their editor to ask, but you don’t know their address, what with not having a paper. There’s no way to figure this out.

If you find that exiting doors until you get out of doors doesn’t work for you? Try opening a home-repair store and holding a good sale on doors and door frames. It’s a bit more work, but that’s what it takes.

Ooh, and hey, now I can publish an Everything There Is To Say About Going In Doors essay by taking this and running it backwards. This is great, I’ll finally be ahead of deadline a little, only to mess it up!

Statistics Saturday: Some Shapes Which You Ought Not Use As Dinner Plates For Your Trendy Restaurant


  • Triangle-base pyramids
  • Whole spheres
  • Saddle curves
  • Vertical walls
  • Great Stellated Dodecahedrons (unless you are serving a food that can be usefully jabbed on spikes, such as pancakes or lumps of cheese ripped out of a whole)
  • Square-base pyramids
  • Sierpiński sieves (that triangle-with-interior-triangles cut out thing, as while it’s a great shape it actually has no surface area, so it can only hold food by way of surface tension)
  • Bipyramids
  • Doughnut-shaped toruses (unless it is an edible container, like those soup-in-a-loaf meals, itself containing many small doughnuts within, in which case I would like to invest in your restaurant)
  • The Great Rhombicosidodecahedron not because no food could be placed atop it but because when word gets out you have Great Rhombicosidodecahedrons in your restaurant the health department will begin an inquiry which will ultimately clear you but which will generate needless amounts of bad press in the meanwhile.

Another Blog, Meanwhile Index

The Another Blog, Meanwhile index rose two points on reports that someone saw a pair of mice snuggled up against each other sleeping and one opened its eye just enough to yawn and doesn’t that sound adorable? We thought it was adorable.

124

Caption This: Ray Walston Doing Things


Before we get to the main stuff. My mathematics blog? I had a couple more comic strips to talk about yesterday. Yes, one of them is Barney Google. I think you might enjoy it anyway. A lot of cartoonists did jokes about gambling last week, for some reason. Now:

Ray Walston pours a drink from a pyramidal glass into a shorter square-cylinder glass.
In this thrilling episode of Star Trek: Voyager, Ray Walston acts all cranky and asks why he has to talk to Neelix. I’m guessing.

Ray Walston Character: “Humans. Humans think of themselves as the supreme beings of their universe, the masters of their destiny — if not now, then at least, as beings who will be someday masters of their destiny. And yet as you explore the universe, its great potentials, its vast failures, its diversity of form and thought and expression, you come to a realization. The fatal flaw of the species, my friends, one I imagine that will never be overcome, is that humans are quite mediocre at discerning whether very different shapes enclose approximately equal volumes.”


Go ahead, top me with a better caption. I can take it, I’ll pretend.

The Big Picture


We’ve started looking at maybe buying a new TV. Our current TV is working fine, which has been part of the problem, since it’s your old-fashioned standard-definition tube-model TV screen hewn by Alan B DuMont himself from his shadowy hidden laboratory deep in the highlands of North Jersey. It was a fine TV in its time, and it’s clearly determined to outlast the entropic heat-death of the universe, but it’s starting to get annoying watching TV shows that assume screens are wider, like they are anymore. The Daily Show is pretty good about not putting stuff outside the bounds of the standard-definition screen, but it’s getting tiresome to guess what’s happening on the missing edges of Cona O’Brie.

The obvious change in TV technology since our old set was made has been the size, of course. There’s now no way to buy a TV set smaller than a tennis court in area, which will demand we rearrange the living room so it fits. We might have to have a carpenter come in and take out the stairwell, and just get to our bedroom by way of a rope ladder, trampoline, or perhaps a very patient giraffe (possibly mechanized). On the bright side modern TVs are only half as thick as other units of the same model, so if we buy a flatscreen we’ll be able to slip it in-between the wall and the paint on the wall.

The other thing is that shapes have changed. Picture-tube TVs all had that slight outward curve made. That curve was great as you could just place a large enough number of picture tubes near one another and automatically form a ball of television sets thirty feet across, allowing anyone to create an art installation about the disposability of modern pop culture whenever they wanted. But then they started making screens flat, so that every TV show you looked at seemed to be weirdly impacted in the middle, like someone had smooshed Bob Barker right in the belly. They’ve fixed that now, by finding a pre-smooshed host for The Pric Is Righ, and I suppose they’ve worked out what to do for other shows too.

And now the stores have innovative new shapes, too. The big one at the store last week was screens curled inward, giving us the experience of watching a couple seconds of a waterfall then a roller coaster then fireworks then the Grand Canyon while staring at the inside of a bowl. I guess that’s got advantages in how it makes the picture look curled inwards, and how the eyes of the Best Buy sales associates follow you wherever you go until in a fit of shyness you curl up behind the bin of $4.99 games for the Wii.

Besides these inverted-bowl shapes there’s exciting new concepts in solid geometry coming, such as the saddle-curve hyperboloid which wowed people at the Consumer Electronics Show. It expertly suggested the experience of horse-riding, what with how as you get closer to the screen it looms higher and higher over you, until you get right up close to it, at which point the it bites your hair, covers your head an inch deep in horse boogers, and stomps on your foot, which any horse-expert person like my sister will tell you is a show that the horse likes you and it’s all your fault anyway. I didn’t even know my sister watched that much TV, what with her horse-experting to do. Anyway, television boogers clean up easily, but cleaning them off leaves you open to charges you’re one of those people who announces “I never watch television” every four minutes, even to empty rooms.

Personally, I think the most exciting new TV shape is one that projects the image onto the contact surface formed in the tangent space M \times \textbf{R}^{2n+1} so that for any fiber bundle \alpha you can find a sympletic coordinate pair perfectly matching, say, the statistical entropy to the chemical potentials of the system. I think most of you agree with my assessment because you’re hoping if you nod vigorously enough I’ll stop talking what might be mathematics or physics or possibly some conspiracy theory linking Nikolai Tesla to the Knights Templar and go on to literally any other topic at all. (Hi, LFFL!)

Anyway, this is all very thrilling stuff and it makes me figure that I should go back to watching narrower programs on the old TV set.

Statistics Saturday: Counting On The Splendid Bowl


If current trends continue, then in the year … … there will have been as many Splendid Bowls as there are or were:
2020 Faces and vertices of the medial rhombic triacontahedron
2026 Days in January and February (non-bissextile years)
2026 Minimum number of games in the National Hockey League postseason (per rules in effect for 2015)
2027 Days in January and February (leap years)
2028 Counties in New York State
2031 Years between a Punxsutawney, Pennsylvania groundhog’s first being recorded to predict the weather and the predictive groundhog’s receiving the name “Phil” [1]
2034 Secretaries of State of the United States (as of 2015)
2044 Inches of height of Michael Jordan
2048 Games in a regular National Basketball Association season (as of 2015)
2049 Episodes of the original Star Trek
2054 International Astronomical Union-recognized constellations
2071 Maximum number of games in the National Hockey League postseason (per rules in effect for 2015)
2173 Recipients of the Nobel Prize in Physiology or Medicine (as of January 2015)
2331 Days in the year
2686 Species of Pokemon revealed as of 2015
9886 Elements of the sporadic Mathieu group M11

1: Wikipedia’s description is very breezy and chatty, causing me to doubt that the topic has been the subject of credible historical inquiry.

Statistics Saturday: A List Of Some Things Which Look Considerably More Dignified If Depicted Wearing Glasses


  1. Dogs
  2. Statues
  3. Rabbits
  4. Eggs
  5. Dragons
  6. Instructors
  7. Robots (the good kind)
  8. Trees
  9. Small rocks
  10. Squirrels
  11. Teeth
  12. Robots (the morally ambiguous kind)
  13. Ducks
  14. Dodecahedrons

Note: I mean eyeglasses. Drinking glasses is a completely different thing.

Explaining The Angles


I’ve been working on a biography of Donald Coxeter, one of the most important geometers of the 20th century. I mean reading it, since the hard work of writing it was already done by someone else (Siobhan Roberts), and the even harder work of being an important geometer of the 20th century was done by another person entirely (Donald Coxeter). Mine is really the easiest part except for the people who aren’t reading it, who can do that anytime and from anywhere. Anyway, I’d run across some of his work in references to H M S Coxeter, and a careful examination of the first paragraph pointed out that “Donald” is not one of the leading names with an initial H, M, or S.

Anyway, Roberts explains that Donald’s parents wanted to call him Donald, and they did, but “the birth certificate recorded his first name officially as MacDonald, after his father’s father”. Fine and/or dandy. His mother added “Scott” to honor another relative, and a godparent suggested that he should have his father’s name of Harold, too, and that’s why he was Harold Scott MacDonald Coxeter.

And I just admire how very much that looks as if it explained the situation.

Pop Quiz: Philosophers


  1. Pythagoras:
    1. I know, right?
    2. The hypotenuse squared over the sum of the sides.
    3. E = mc2.
    4. Beanfields.
  2. Descartes:
    1. Pituitary glands.
    2. God’s too nice to make mad scientists?
    3. Mornings kill people.
    4. I yam what I yam and tha’s all what I yam.
  3. Nietzsche:
    1. Oh, dear Lord.
    2. Just set that down and come back when you’re at least ten years older.
    3. Or you could start punching that book right now.
    4. Both (b) and (c).

Colorful Troubles


I don’t get invited into focus groups much, not since I explained in a slender, carefully chosen, 12,350 words how Star Trek V is much better-directed than people think. I probably had that coming. So I was thrilled when the Department of Rainbows called to have me evaluate some new meteorological products they were test-marketing. All I had to do, they explained, was watch in the early afternoon as they tried out this new rainbow concept where the colors would be there, but faint, so you’d only see them against a light cloud in the background and you’d look up and suddenly, hey, a Neapolitan cumulus was hovering there.

It transpired that come the first test period I was inside doing some emergency alphabetizing of the refrigerator, which was absolutely the top priority because I started out thinking the DVD player had a awful lot of dust on it. Fine, their phone call was forgiving, and they referred me to a pilot project in Blu-Ray dust, which is dusty with such an incredible fidelity that vinyl audiophiles swear it makes records sound more authentically dusty than actual dust can.

The second period, though, I missed because I was looking at the wrong clouds and they could not believe that I don’t know a cumulus from an altostratus. I can’t blame my parents for this; in a package of childhood documents I found the certificate from a pre-kindergarten project which showed that I memeorized every possible kind of cloud there was, including the imaginary ones, in that way that only excitable four-year-olds just learning to classify things can. In my defense, when I was a kinder, “brontostratus” was too a cloud and I can’t be blamed for missing its reclassification as “the habit of looking at the wrong month on the calendar so getting the day of the week wrong”.

The third time I missed because I was explaining to our pet rabbit that if he insisted on barking like that people were going to think I was mad. He insisted that this was my problem and if he wanted to bark he was jolly well going to bark. (I alter his words a bit; he said something more like “certainly going to bark”, but the “jolly well” seemed to fit his huffiness more.)

And the fourth time, which is entirely my fault and I can only blame myself for it, I missed because I was hard at work coming up with ways to use the word “transpire” in casual writing in ways that pedants would find acceptable.

So, Rainbows got all upset with me, and I guess they’re right to be. I don’t know how much work is involved in bringing new rainbow concepts to the test-marketing stage but I’m sure it’s something. And they did all sorts of work trying to train me, too. For example they revealed you can always tell a cumulus from an altostratus by scanning the upper right corner with a price-check laser, or by trying to play middle C and seeing what note does come out.

What I really don’t know what’s going to happen with this. I was really hoping to make a good impression and maybe get into this group I hear’s trying to refresh heptagons. They’ve been clinging to that seven-sided thing for a long while and I think we’d have to stick with that, but that “hept” thing isn’t really working. People tend to figure it’s a fake prefix because it was created by agents for the Soviet government in 1930 when the country sought ways to sneak cash out of western governments.

As such the prefix doesn’t really mean anything, but it’s caught on among people who need to group together seven things in a prefix, as soon as they think of any. I mean, you can think of groups of seven things and find them all over the place, we just do well enough calling them “the seven things” and I don’t see that changing so much, so we need to find ways to bundle seven things into smaller groups that go at the start of things, you know, like, prominent colors in a rainbow. Oh, I bet the Department of Rainbows will like it if I point that out to them.

Vim, Vigor, and That Other Thing


I’m getting back into regular exercise. I don’t want to make people envious of my physique, but in the past few years I’ve got into the best shape of my life, not counting that year in elementary school when I was a regular heptagon. When I say the best shape of my life, I mean the best shape for me, though. I have the raw athletic prowess of a tower of buckets. Given a reasonable time to warm up and stretch, I can pretty nearly successfully tip over and plummet onto the floor. Next week I’m hoping to get to tipping and plummeting onto the floor while wearing weights.