# An Enigma Wrapped In A Riddle by Bryan G. Nance

A prize will go to the first person to unwrap this mystery.

Meet John (pictured) – master carpenter, master craftsman, and part-time mathematician. John is my neighbor, and for the last few weeks he has been constructing this “structure” in his front yard.

I know that many of you are stressed-out over the SATs, ACTs, SAT IIs and EIEIO (a test only given by Professor O. McDonald), but you deserve a break today. Listen closely: drop the practice test book and back away slowly from the college applications and I promise you that no one will be harmed! Take a moment to examine John’s front-yard project. Drop me a line if you think you know what he’s building.

- Hint # 1: Put on your math-based thinking cap.
- Hint # 2: Since I have not seen any wildebeasts, sloths or rhinos walking 2×2 in the neighborhood, I can speak with some certainty that he is not Noah and said construction in not an ark.

Good Luck!

P.S. A prize will go to the first person to unwrap this mystery.

first!

First thing I thought of when I saw the pictures was a mobius strip. Then again, it took me a while to get the EIEIO joke… (what, there’s a test I haven’t taken?!? Oh no, I’ll never get into MIT now! Wait a second, isn’t that a song? Oh, wow.)

It kind of looks like a hyperbola.

It looks like a model of a hyperbolic geometry plane, like a huge saddle.

It reminds me of a big wooden version of “the Big Sail” (La Grande Voile) … he’s making an Alexander Calder imitation, perhaps?

Not mathematical enough I suppose .. it also reminds me of the description of Malcom’s chaos models in Jurassic park..

oh, but I’ve been looking at it as though it was one piece rather than two. Möbious strip seems more on the right track .. but I’d imagine something orientable..I’ll have to think about it

~Donald

I have to admit, I was holding a test prep book whilst I read this, and I did, indeed, drop it (for 45 seconds or so).

looks kind of like a paraboloid

Id have to concur with the entire Mobius idea, and maybe go a step further as to say its inverted???

It’s some curiously shaped hyperbolic paraboloid whose surface area can only be approximated with the special help of our good friend Maple! haha….Get it? Maple? …..Anyone?

Or, perhaps, it’s a giant-sized Pringle. Your choice.

ah yes the chaos model from jurrasic park is an interesting guess… to bad the movie didn’t include any of that stuff

could it be a large pi symbol? or maybe an excessivly large dog house.

actually i think it might be a blow up or something small… a cell perhaps

a Klein bottle?

it does look a lot like a hyperbolic paraboloid… hmm what could a giant saddle be used for?

I like the saddle explanation. My idea is that it is an unfolded torus.

Hi Bryan,

It definitely looks like a hyperbolic parabaloid! It might just be a coincidence that it is MIT in both cases, but you may find this article interesting. Cheers!

http://www.nytimes.com/2005/02/15/science/15origami.html

Perhaps the starting of a torus?

sinusoid or sine wave

Or a fool consumed by fear.

Yep, somewhere in the hyperboloid or parabaloid range…

A boat.

I win; we can all go home now.

p.s. I love Mr. Neha.

Definitely looks like a hyperbolic paraboloid. But Vika and Jai beat me to it…

Or perhaps a model of a piece of hyperbolic space.

The opposite diagonal bars on the opposite sides interest me… it seems like if each side was identified with its opposite then it would be a projective plane embedded in hyperbolic space?

A quadric (perhaps elliptic paraboloid or a parabolic/hyperbolic cylinder or a hyperbolic paraboloid)

The prize…

It wouldn’t happen to be automatic acceptance, would it?!!

=]

hmmm, looks like a pi symbol to me

A wooden structure…… or what Vika, Jai, Berkely, Louis, and others have said.

A hyperbolic paraboloid (saying that just makes you sound smart no matter what).

It is a pi symbol in the shape of a hyperbolic paraboloid.

A parabolic shape of some kind seems likely, but I’m going with a model of the chaos theory, although the chaos model I’ve seen the most is shaped like a ship’s propeller, not a hull. But kudos to Mr. John for one heck of a backyard structure!

I think that John is building a hyperboloid, kind of like the one at the bottom of this page: http://www.mit.edu/~esg/html/academics/math_current.html

If he is planning to leave the construction in his yard, then he might also use it to hang/support plants in a garden.

Thanks for the riddle!

I agree with it being a hyperbolic paraboloid, but it also reminds me of a drawing of the curvature of the universe I saw in a book somewhere. After looking at <a>this</a>, it appears to be a model of a universe with a negative curvature. Or perhaps he is just building a fiendishly complicated trellis.

Oops, address is http://en.wikipedia.org/wiki/Shape_of_the_universe .

@Merritt

would you happen to be the same Merritt B that went to the VA Governors School at CNU this past summer?

if so… hi! (this is, obviously, Donald)

I still don’t know.. I agree that it looks like some form of hyperboloid .. but obviously thats too simple.. plus I’d actually have to agree with paraboloid over hyperboloid .. because two of the traces are parabola .. and the third is .. a rectangle? (which is obviously not a conic)

hmm .. this is a challenge …

~Donald

I’d say a hyperboloid that will *hopefully* focus sunlight into a super powerful solar panel, or at least focus sunlight onto his rather sad garden….

oops.. on closer examination .. the third trace (from above) is, in fact, a parabola … *shame*

and by parabola I mean hyperbola *more shame*

either we already have the answer (unlikely) .. or we need to think more outside the box (or calculus book .. as the case may be)

A large wooden structure.

I think that’s a Torus.

Yes. Being in mvc, this thing does look strikingly similar to a hyperbolic paraboloid. However, I would like to point out one thing: “said construction in (sic) not an ark.” I believe the “in” is and “is,” so the thing is not an arc, and thus not a hyperbolic paraboloid?

Saddle roof?

I would agree with everyone who said that it looks like a torus. Almost seems like it could be big enough to surround a decent portion of his house.

I personally feel John (the guy making this object) got bored, drew a random design on a piece of paper and decided to build it…

I wish it was a butterfly though…

A replacement for a faulty part of the Stata Center

I’m going to go ahead and say it’s a mini greenhouse. I think whatever he’s making is probably going to stay around the house, because it’s kinda hard to transport that huge thing… so yea. mini greenhouse.

Hyperbolic parabaloid seems like a good choice to me. The problem with the torus, Klein bottle, and Mobius strip answer is that, well…it doesn’t look like a torus, Klein bottle, or Mobius strip. The photos shown and the clues given are enough information to anwer the question–and so those shapes (or projections of shapes for the Klein bottle) can be ruled out, since there’s just not enough there to conclude that. Circular logic ftw!

Regardless, the use of the word “ark” is a good clue. The embedding in hyperbolic space sounds even better, simply since it’s not constructed “in an ark”–i.e., it’s not taken from the “arc of a circle/sphere/whatev,” and so it can’t be easily described using the Euclidean metric, or at all.

The other good clue, even if it’s a bit of a stretch, is the fact that no animals walk “2×2.” 2×2 could be the dimension of the matrix that would define the linear transformation on the plane to arrive at a projection of that shape in R^2–so, maaaybe it’s derived from something more complex–perhaps not from any kind of linear transformation?

And, as a total guess, the edges kind of remind me of what happens when you invert the complex plane via a Mobius transformation. (If that’s the case, what luck! ALL we will have to do is find the Riemann sphere somewhere hidden in the picture and we will have solved this veritably challenging mathematickal puzzle!)

Anyway, I’ll continue to think it’s use is a hammock. I need sleep.

It’s a jungle gym. Come on.

I think it is a very nice walkway/porch cover.

If we are looking for mathematical puns in the hints .. I’d also point out the word “neighborhood” (whether or not it has any significance)

I also thought some sort of transform might be involved … but unfortunately I have no experience with them .. the first one that came to mind was some sort of Fourier transfer… which also works with the butterfly concept… but that would also violate the [2×2] theory … I think (I’m basing this off the slightest knowledge drawn from wikipedia in the last ten minutes)

Hooray for vague Barenaked Ladies references! (I think)

Too bad he isn’t building a geodesic sphere…

My guess is either a) a hyperbola or b)a model one of those pairs of infinite cones from which all the conic sections are derived!

Either way, it looks really cool.

Lots of possibilities, though I don’t think I solved the riddle. The saddle is a adaptable metaphor, but I’m thinking the structure is not complete; it’s not a plane.

A complete 3D structure from the side view, would look like a double cone, but of course it’s hyperbolic. My best guess is an hourglass shape; when stood up in its rectangle frame the structure would be a giant hourglass.

Hm…I’m quite impressed with everyone’s answers, but to me the real question isn’t simply what

shapehe’s constructing, but rather whatpurposeit will be used for. Considering that the structure’s shape appears somewhat parabolic, I’d guess a solar panel array?Solar array sounds interesting, and what about some kind of solar oven?

archimedes death ray

A garage roof. Being a hyperbolic hyperboloid, it would be very strong for the amount of materials. That is certainly important in New England where we get plenty of snow. Also, its shape allows snow to slip off easily. http://en.wikipedia.org/wiki/Hyperboloid_structure has a good related article

*just hyperboloid not hyperbolic hyperboloid that would be a little redundant

Building off of my bus stop roof idea and Paul’s garage roof idea, it does seem that it would be used to cover something, most likely a car.

Probably it will go over his driveway, which appears to be behind and not in front of the house, so I don’t think any silly zoning codes would make it illegal.

A trojan horse to give to Caltech?

Hmmm…looks like part of a roller coaster.

Skate board teeter totter?

Noah’s ark, old mcdonald, wildebeasts, sloths or rhinos walking 2×2… hmmm… what do all these clues lead to?…

It’s for the show “Pimp My Ride.” It’s Santa’s sleigh.

He is obviously board! Get it? He He

And why the particular animals “wildebeasts, sloths, and rhinos”? Could that be another clue?

to go along with the paper folding idea… maybe it is a hyperbolic plane because it is (un)wrappable into a sheet of paper. As far as the purpose goes, he is definetly trying to reprove Fermat’s Little Theorem.

When I first looked at this, I was thinking maybe some type of wooden awning-like thing in the form of a hyperbolic parabaloid, since it seems constructed in two pieces which would be easy to mount and since a lot of the houses seem to have these porches, so maybe he wants to have the best house on the street. But, he couldn’t stick that in front of his house since there is the storm drain pipe is there. So I’m stuck. But I like this idea of the hyperboloid structure, except I can’t see it next to his house at all. (It just makes me think of the Dancing House, which is rather unrelated to all of this. I wish it was an ark though.)

Nice work, Da! yer kid

It certainly does look like an hyperboloid. Or a very cool looking trellis? A gigantic hourglass. Surround sound speaker system. There seem to be 2 distinct parts to this, and those poles look like they’re there just for support. Maybe part of the set of a play–someone come up with a witty title, quick!

does wthe winner get automatically accepted?

a decorative Pi symbol

@ L

You made my day!

It is the left part of a regular hyperbola, i mean the one which lies on left side of origin.

42

it looks flammable. LOL.

I’m stuck in 1.00. I know that I shouldn’t be on here, but I couldn’t resist. it looks flammable. LOL.

I’m stuck in 1.00. I know that I shouldn’t be on here, but I couldn’t resist. <3

do you guys need cookies anytime soon? I’m contemplating a giant cookie bake for the holiday season.

IT SI A GIANT WOODEN WAGINA LOL! ;D

SER I HAV NO IDEAS.

He’s building the sloping hills of a farm in his backyard – hence, the EIEIO hint. The farm is in the shape of a hyperboloid so that he can accurately take the derivative of vegetable size with respect to height grown.

Unwrap, hmmmmm.

How about a

wooden Xmas bowfor the holidays?A miniature of MIT’s Great Dome

Unwrap makes me think of Christmas…so clearly its a christmas present for someone, though how he plans on keeping it hidden…got me

Could this be the arch of a supporting bridge but then why would it be wooden?It could be the roof of a bus stop but it looks like that only from a particular view and not that much like one from the others.

Gyroscope?

Hey could it be the skeleton of a vulcano?

(So in a way a hyperbola without the top)

everybody is really guessing..wow!!!

A box/other container for a present.

Yes, I’m dull and simple.

Yep, definitely looks like a hyperbolic paraboloid… although I was beaten to it. About 17 times. Drat.

And Paul: Does one

reallyneed a reason to be building a hyperbolic paraboloid? Hm?It’s obviously the graph of cosine in 3D.

A Home for his Dog…. or may be a small skating bay for his own X-games….

just noticed another clue: “unwrap this mystery.” now to just find something mathematical that involves something with 2×2 but not an ark…

I’m imagining that a hyperbolic paraboloid of that size could be useful as a rain collector – the rain falling over the entire surface would end up flowing down to the two lower sides, i.e., if its z = x^2 – y^2, the water will flow to the y-axis, and then out to either side. That’s just my guess.

Could it be the function z=x^2-y^2 ?

Totally random thought – a Klein bottle?

A butterfly, it’s a butterfly.

A garage for his wheelbarrow

Godzilla?

@Donald

Hi, yes, same me (and I have not stopped believing, for what it’s worth).

@Edgar

Perhaps it’s some form of a Lorentz Attractor, although pic #3 shows both ‘wingtips’ pointing down, unlike the rendering done by my Mac’s Grapher, which is the only place I’ve seen one. It seems to be divided in the middle (pic #4), perhaps this is a clue – maybe it’ll be flipped?

newton’s cradle

by “unwrap this mystery,” i meant that it is probably a shape or whatever that’s wrappable (is that even a word? oh well, it is now)

My first thought was “a wooden hammock,” but then I realized that would be rather uncomfortable (hey, I’m on medication for an ear infection, bear with me).

Then I thought that he might be building the top to a gazebo. That would be a little bit more practical than hyperbolic geometry in his front yard. And it would make a rather nice gazebo for in the summer, maybe with some ivy hanging off of the side…

This may sound really weird, but anywho:

I think he is building a bus stop roof. If you notice, the two (parabolicky curvy sides) things do not appear connected, which can be seen in pictures 1, 3, & 4. I believe they are to be made as some kind of roof because the lips curve downwards in the center, but bank upwards to the sides.

(so if they do this then depending on how he puts it up it could increase the amount of shade available to those underneath, I think)

If they are meant to be parts of a roof, then they could be attached together at the top by poles where a bench could be placed underneath for people to sit under. To me, if it was built up like that it would look like those bus stops you see with roofs on them to keep the elements off you while you wait for the bus!

Or it is indeed, a giant pringle.

This is fun.

This is just a guess on my part with no mathematical support whatsoever, but…

It looks like an airfoil?

And… wow, all that math is pretty impressive… and utterly incomprehensible

Mcdonald symmetric functions