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Bryan G. Nance

Nov 27, 2007

An Enigma Wrapped In A Riddle

Posted in: Miscellaneous

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 2x2 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.

Comments (Closed after 30 days to reduce spam)

first!

Posted by: neha on November 27, 2007

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.)

Posted by: Star on November 27, 2007

It kind of looks like a hyperbola.

Posted by: Claire on November 27, 2007

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

Posted by: 0 on November 27, 2007

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

Posted by: donaldGuy on November 27, 2007

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).

Posted by: 0 on November 27, 2007

looks kind of like a paraboloid

Posted by: Kim on November 27, 2007

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

Posted by: 0 on November 27, 2007

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?

Posted by: Ana L on November 27, 2007

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

Posted by: Ana L on November 27, 2007

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

Posted by: marcus on November 27, 2007

a Klein bottle?

Posted by: Chelsea on November 27, 2007

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

Posted by: vika on November 27, 2007

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

Posted by: nick on November 27, 2007

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

Posted by: Jai on November 27, 2007

Perhaps the starting of a torus?

Posted by: Stephen L on November 27, 2007

sinusoid or sine wave

Posted by: Louis on November 27, 2007

Or a fool consumed by fear.

Posted by: 0 on November 27, 2007

Yep, somewhere in the hyperboloid or parabaloid range...

Posted by: Stephen L. on November 27, 2007

A boat.

I win; we can all go home now.
p.s. I love Mr. Neha.

Posted by: Jess on November 27, 2007

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?

Posted by: Berkeley on November 27, 2007

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

Posted by: Louis on November 27, 2007

The prize...
It wouldn't happen to be automatic acceptance, would it?!!

=]

Posted by: Javi on November 27, 2007

hmmm, looks like a pi symbol to me

Posted by: Kim on November 27, 2007

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).

Posted by: Kevin X on November 27, 2007

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

Posted by: Chris on November 27, 2007

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!

Posted by: E Rosser on November 27, 2007

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!

Posted by: … on November 27, 2007

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.

Posted by: Merritt B on November 27, 2007

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

Posted by: Merritt B on November 27, 2007

@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

Posted by: donaldGuy on November 27, 2007

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....

Posted by: Lauren S. on November 27, 2007

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

Posted by: donaldGuy on November 27, 2007

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)

Posted by: donaldGuy on November 27, 2007

A large wooden structure.

Posted by: izzy on November 27, 2007

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

Posted by: SKishore on November 27, 2007

Totally random thought - a Klein bottle?

Posted by: Travis on November 27, 2007

A butterfly, it's a butterfly.

Posted by: Edgar on November 27, 2007

Godzilla?

Posted by: YHuang on November 27, 2007

@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?

Posted by: Merritt B on November 27, 2007

newton's cradle

Posted by: 0 on November 27, 2007

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...

Posted by: Karen on November 27, 2007

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.

Posted by: Collin on November 27, 2007

Mcdonald symmetric functions

Posted by: A. Noni Mus on November 27, 2007

I think that's a Torus.

Posted by: Zaira on November 27, 2007

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?

Posted by: Keshav P on November 27, 2007

Saddle roof?

Posted by: Javi on November 27, 2007

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.

Posted by: Calvin on November 27, 2007

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...

Posted by: butterfly girl on November 27, 2007

A replacement for a faulty part of the Stata Center

Posted by: anonymous on November 27, 2007

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 "2x2." 2x2 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.

Posted by: Will on November 27, 2007

It's a jungle gym. Come on.

Posted by: Brant on November 27, 2007

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

Posted by: intleyes on November 27, 2007

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 [2x2] theory ... I think (I'm basing this off the slightest knowledge drawn from wikipedia in the last ten minutes)

Posted by: donaldGuy on November 27, 2007

Hooray for vague Barenaked Ladies references! (I think)

Posted by: Marissa on November 27, 2007

Too bad he isn't building a geodesic sphere...

Posted by: Collin on November 27, 2007

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.

Posted by: Shamarah on November 27, 2007

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.

Posted by: Anonymous on November 27, 2007

Hm...I'm quite impressed with everyone's answers, but to me the real question isn't simply what shape he's constructing, but rather what purpose it will be used for. Considering that the structure's shape appears somewhat parabolic, I'd guess a solar panel array?

Posted by: Paul on November 27, 2007

Solar array sounds interesting, and what about some kind of solar oven?

Posted by: Travis on November 27, 2007

archimedes death ray

Posted by: V on November 27, 2007

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

Posted by: Paul on November 27, 2007

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

Posted by: Paul on November 27, 2007

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.

Posted by: Collin on November 27, 2007

A trojan horse to give to Caltech?

Posted by: L on November 27, 2007

Skate board teeter totter?

Posted by: 0 on November 27, 2007

It's for the show "Pimp My Ride." It's Santa's sleigh.

Posted by: 0 on November 28, 2007

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.)

Posted by: ag on November 28, 2007

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!

Posted by: MX on November 28, 2007

a decorative Pi symbol

Posted by: HK on November 28, 2007

@ L

You made my day! wink

Posted by: Edgar on November 28, 2007

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

Posted by: Utkarsh Sharma on November 28, 2007

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.

Posted by: 0 on November 28, 2007

everybody is really guessing..wow!!!

Posted by: 0 on November 28, 2007

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

Posted by: Amour on November 28, 2007

just noticed another clue: "unwrap this mystery." now to just find something mathematical that involves something with 2x2 but not an ark...

Posted by: Keshav P on November 28, 2007

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.

Posted by: Zev Chonoles on November 28, 2007

A garage for his wheelbarrow

Posted by: EV on November 28, 2007

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)

Posted by: Keshav P on November 28, 2007

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

Posted by: Hyun Jin on November 28, 2007

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.

Posted by: milena '11 on November 28, 2007

Hmmm...looks like part of a roller coaster.

Posted by: Janice on November 28, 2007

Noah's ark, old mcdonald, wildebeasts, sloths or rhinos walking 2x2... hmmm... what do all these clues lead to?...

Posted by: Leko on November 28, 2007

He is obviously board! Get it? He He

Posted by: mtd on November 28, 2007

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

Posted by: Manders '13 on November 28, 2007

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.

Posted by: Keshav P on November 28, 2007

Nice work, Da! wink yer kid

Posted by: Name Spelled Backwards on November 28, 2007

does wthe winner get automatically accepted?

Posted by: 0 on November 28, 2007

42

Posted by: tom on November 28, 2007

it looks flammable. LOL. smile

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

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.

Posted by: Justine on November 28, 2007

IT SI A GIANT WOODEN WAGINA LOL! ;D

SER I HAV NO IDEAS.

Posted by: Kamur INDIA on November 28, 2007

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.

Posted by: Rena on November 28, 2007

Unwrap, hmmmmm.

How about a wooden Xmas bow for the holidays?

Posted by: Polarisking on November 28, 2007

A miniature of MIT's Great Dome

Posted by: Louis on November 28, 2007

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

Posted by: Lydia on November 28, 2007

Gyroscope?

Posted by: Nick on November 28, 2007

Hey could it be the skeleton of a vulcano?
(So in a way a hyperbola without the top)

Posted by: Thomas Fronk on November 28, 2007

A box/other container for a present.
Yes, I'm dull and simple.

Posted by: Nick on November 28, 2007

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

And Paul: Does one really need a reason to be building a hyperbolic paraboloid? Hm?

Posted by: harrison on November 28, 2007

It's obviously the graph of cosine in 3D.

Posted by: Craig on November 28, 2007

It's obviously the graph of cosine in 3D.

Posted by: Craig on November 28, 2007

Oops, sorry about the double post. Itchy trigger finger I guess.

Posted by: Craig on November 28, 2007

It is a mega-bird feeder.

He is going to cover the frame with wood, and then drill holes into the cover. He will put bird seed or yummy vegetable plants under it, and then sit back to watch a living example of the Pidgeon Hole Principle, as more birds flock to the feast than he has drilled holes!

Posted by: Erika on November 28, 2007

...or its a cage for his pet pidgeons.

Posted by: Erika on November 28, 2007

Harrison - you're right, he doesn't necessarily need a reason. But guessing what it might be for adds an extra...shall we say...dimension to the problem, eh?

Posted by: Paul on November 28, 2007

A Fractal Geometry! (By Mandelbrot, Benoit B.)

Posted by: MarcoMV on November 28, 2007

If the word "unwrap" has significance.. one way it could is if this has something to do with an instantaneous phase of a complex function which is used in signal processing

I don't know .. it could be relevant

http://en.wikipedia.org/wiki/Instantaneous_phase

Posted by: donaldGuy on November 28, 2007

mathematical symbol of the infinite?

Posted by: MarcoMV on November 28, 2007

Well, not to be all un-original or anything, but it does look like a hyperbolic paraboloid....or, now that I look at it more, it looks like half of a one-sheet hyperboloid.

as for the purpose...I was thinking of some kind of reflector, but only because we've been doing optics in physics lately. That doesn't really work for me though, as I can't think of why the heck he would want a hyperboloid or paraboloid reflector...

Or it could be some type of sundial. The curvature might have something to do with the varying angle of the sun between summer and winter. Seems simple enough...

Or, I believe this was said before, he could be building a roof for something. Perhaps for a shed, garage, or doghouse...I don't know. But a hyperboloid would quite effectively eliminate the need for any gutters.

Posted by: Johonaton on November 28, 2007

One more thing...if the supports around the hyperboloid are the beginnings of a shed, that hyperboloid would fit nicely as a roof.

Posted by: Johonaton on November 28, 2007

By any chance is he building some sort of solar captivation device or a complex solar panel? I mean, I realize it's Massachusetts and the picture alone shows the structure semi-covered in shade, but a hyperbolic-paraboloid would function to provide more even energy production throughout the day. Perhaps I've just started relating everything in my life back to global warming (hey, maybe I just don't like the idea of drought, rising sea levels and extreme devastation in the third world).

Posted by: Krishna on November 28, 2007

Hey Krishna, are you the same Krishna from the SAT class in Ft. Worth?

Posted by: Leko on November 28, 2007

Paradigm shift - how is an enigma wrapped in a riddle? Or rather, what's the riddle, and how is it an enigma?

Posted by: Travis on November 28, 2007

@ Leko

are you the Leko from TX HAS this summer?

Posted by: Collin on November 28, 2007

a condom for treebeard anyone?

Posted by: ronaldolycra on November 28, 2007

The title (an enigma wrapped in a riddle) and the line "P.S. A prize will go to the first person to UNWRAP this mystery." seem to hint that wrapping has something to do with it, and one can see in the pictures that the two halves are shaped slightly different, which makes the idea of some kind of parabaloid or hyperbaloid questionable. Perhaps it is some sort of three dimensional model of some data.

Posted by: Craig on November 28, 2007

It's obviously a saddle for the world's largest mechanical bull. End o' story.

Posted by: Will on November 29, 2007

And as far as the word "unwrap" goes, it seems like to me that that means it can be continuously deformed--i.e., it's homotopically equivalent to something else.

Posted by: Will on November 29, 2007

the design is that of a wooden boat........I win

Posted by: 0 on November 29, 2007

I zink i goch it!
hold ur breath..........
it's actually a christmas present for PAUL from EDLA!!. Edla's dad is bryan's neighbour and edla asked him to make a special version of the calabi yau manifold for paul, so that sweet paul could spend his vacations counting the dimensions and thinking about edla!!

There u go!;-)

Posted by: rafael on November 29, 2007

oi bryan!...u got the spelling of wildebeest wrong.

Posted by: rafael on November 29, 2007

Hyperbolic Paraboloid to 'hack' the dome ... what else ?!

Posted by: Vihang on November 29, 2007

and yes..the dimensions will add up to 46!!
Sorry for the triple post!

Posted by: Rafael on November 29, 2007

It may be of some value to contrast Bryan's title of "An Enigma Wrapped In A Riddle" with the Churchillian description of Soviet Russia as "a riddle wrapped in a mystery inside an enigma." [Interesting reversal of the relationships, eh?] Combined with the persistent references to "wrapping" and the references to a diverse zoological field [sloths, rhinos, etc.]the terms lend themselves to a possible representation of some biochemical theme - possibly some form of DNA or RNA representation?

Posted by: Doubltap on November 29, 2007

cooling tower for his house
or
skateboard ramp for his grandkids.

(Moms can have fun too!)

Posted by: just a mom on November 29, 2007

Yup. Definitely a hyperbolic paraboloid. I didn't even know what that WAS until I googled the term when someone wrote it before. Yay for learning!

Posted by: Shantini on November 29, 2007

half of a dumbbell?

something that contains many parabolic curvatures?

I know it sounds strange

but if it is not an ark , this is the first thing that comes to my mind

Posted by: Ying Wei on November 29, 2007

I'm not sure what the structure is (though I like the Pringle suggestion)...


...I just really wanted the (2^7)th post. :D

Posted by: Matt, PSU '11 on November 29, 2007

Hmm, no one so far seems to have suggested that the structure could have moving parts. The third picture has the X-shaped cross-beams which could be used as a pivot. Then as far as "unwrapping" goes, it appears that the front half of the structure could be lifted up by moving the cross-beams about the pivot.

Also, I'm inclined to agree with Paul that it might be important to figure out the reason behind building the structure. Solar panels seem plausible from the pictures, but considering we're going into mid-winter in Massachusetts when the days are getting shorter, that hypothesis appears suspect. Nonetheless, I think that's a good approach to try to solve this problem. Form follows function. =)

Posted by: Arkajit on November 29, 2007

a wooden burrito? a pine cannoli?

Posted by: cc on November 29, 2007

Hey Collin, yeah it's me. HAS was so much fun this summer.

Posted by: Leko on November 29, 2007

Getting back to the farming concept (EIEIO)--is it some sort of storage container, like a silo? I'm reminded of the shape of nuclear cooling towers...although I have no idea why somebody would build a silo in a similar shape...??

Posted by: Travis on November 29, 2007

possobly 3d graph or a theoretical model of the universe

Posted by: Trenten'16 on November 29, 2007

It looks like a saddle for Babe the great blue ox. And John looks like Paul Bunyan.

Posted by: James on November 29, 2007

My guess is a Riemann surface?

Posted by: Ross on November 29, 2007

it looks like parabolas within a rectangular frame

Posted by: onome on November 29, 2007

Instantaneous phase of a sinusoid

Posted by: Louis on November 29, 2007

After way too much Wikipedia reading - a geometric representation of a unitary group of degree 2?

Posted by: Travis on November 29, 2007

I have a vague feeling that it could be a section of a minimal surface.

Posted by: Chi Feng on November 29, 2007

intersecting, opposite facing hyperbolas within a rectangular frame of some sort

Posted by: onome on November 29, 2007

D'oh! It's a wooden support structure for an obviously elaborate Christmas light set up of some sort.

It could be a herbolic parabloid shaped hill that a reindeer family could be mounted upon, and he would cover the "surface" with green lights to make it look like grass!

He's a holiday genious.

Posted by: Collin on November 29, 2007

I actually think it is a cross-section of a hyperboloid instead of a hyperbolic paraboloid. According to wikipedia, hyperboloids minimize the wind cross-section while retaining structural integrity with minimal material.

Posted by: Chi F. on November 29, 2007

It's definitely Santa's new sled.

Posted by: 0 on November 29, 2007

Possibly an octacube, or some similar 4D shadow?

Posted by: Carolina on November 29, 2007

I think it's a present bow.
Or a helicopter propeller.
Or a hyperbola.
Or a hammock.
Or a fence.
Or a hat.
Or the beginnings not of a Trojan horse for Caltech...but of a Trojan BEAVER for Caltech!!!
DUN DUN DUN!!!

Posted by: taran on November 29, 2007

did anyone solve it?

how close is he to finishing this structure?

Posted by: 0 on November 30, 2007

Perhaps it's a finite simple group of order two?

(Couldn't resist.)

Posted by: Paul on November 30, 2007

Leonardo da Vinci's helicopter.

Posted by: MarcoMV on November 30, 2007

Paul, the finite simple group of order two link was GREAT! Thanks.

Posted by: Jane on November 30, 2007

The structure is definitely a section of a quadric.
It looks as if it is a lateral section of a hyperboloid rotated horizontally!

The hyperboloid in question may be described by

x^2/a^2 + y^2/b^2 - z^2/c^2 = 1

I wonder if it has any asymptotes.

I wish they taught this in Grade 12. Life would be so much fun!!!!

Posted by: Leo V on November 30, 2007

Hyperboloids and hyperbolic paraboloids are both saddle curves and look similar. The way you can tell this one is a hyperbolic parboloid is that there are a series of parabolic curves in the xz planes as well as in the yz planes. In the xy planes you have the long hyperbola sections that run parallel to the street as you move up the Z axis until you hit the asymptotes and then you get to the shorter hyperbola sections that run parallel to the driveway. If it were a hypeboloid, there would be hyperbolas in th xy planes as well as the xz planes, and the yz planes would be sections of circles or ellipses.

Parabolas are the better curves to build because there's no wasted wood. If you look at the wood grain direction and notice a glue joint down the middle of each board of wood parallel to the grain, maybe you can see why. Leo V, in the finished structure the asymptote lines are made explicit. Bryan, I hope you'll post a link to the answer soon!

Posted by: Jane on November 30, 2007

The suspense is killing me... maybe another clue perhaps?

Posted by: Leko on November 30, 2007

I think Laura S. may have guessed it correctly: an awning/arbor solar energy collector using architecturally flexible solar film.

Posted by: sunless in seattle on November 30, 2007

Hello All!

WOW! Never challenge the individual or collective math knowledge of the MIT blogging community. THe contest is over. In fact by post 3 the contest was over. To be gracious, the first 20 to correctly ID the structure will receive a prize. If you are

Find below a message from my neighbors Jane and John Kostick.
------------------------------------------------------

Hi, this is Jane writing, and that's my husband John whose creation you're discussing. I can't even begin to tell all of you how much fun we've been having reading all of these comments. The first prize should go to Ana L, who was the first to identify the shape correctly as a hyperbolic paraboloid. A prize should also go to, at the very least, Kim, Vika, Jai, Berkeley, Louis (for using the word "quadric"!) and probably some others but there are getting to be too many to keep track of. For figuring out what its use will be, a prize should also go to Merritt B for writing "a fiendishly complicated trellis" and Lauren S for suggesting it will "at least focus sunlight onto his rather sad garden...." That really made us laugh! Also, Karen for suggesting a gazebo and ivy and intleyes for seeing that it's a walkway cover. Also, Zev Chonoles for a good idea and Harrison for a great question/comment. Did I miss anyone? Let me know. First prize is a six-axis bronze star. The 19 runners up get a tetraxis. Bryan will contact the winners by email.

Now go to www.quadricdesigns.com to see a slideshow with more up-to-date pictures and find out what a tetraxis is!
-Jane and John Kostick

Posted by: The Nance Effect on November 30, 2007

I really like the sixth from last picture, showing the pergola and the tree...that seems like a really cool project!

Posted by: Travis on November 30, 2007

Yay!!!! But how do we claim our prize? :O

Posted by: Ana L on November 30, 2007

I'm so excited! The website is awesome; John you have some really neat projects.

Posted by: Lauren S on November 30, 2007

Congratulations, guys =]!

Posted by: Carolina on November 30, 2007

Ooooh, cool! smile I looked at the website and those are, by far, the most interesting and creative uses of hyperbolic geometry that I have yet to see smile

Posted by: Karen on November 30, 2007

I think it's a circular paraboloid, a parabola curved around a circular cylinder with the axis oriented east-west. It will have a rail or pipe at the curved focus of the parabola, concentric with the cylinder. Regardless of the yearly season, the sun will focus somewhere on the rail/pipe, where he can either a) place a sliding solar absorber (could be a high temperature tolerant PV panel), or more likely b) the pipe will carry some fluid that will be heated only locally at the focus. Given the f/number and the aperture, if the fluid is water, he will generate a steam bubble rather quickly,which will push the fluid, and with the help of a check valve in the pipe, he will be able to pump hot water into a water heater storage tank.

If this is the case, the design is very novel and spectacular but rather inefficient because only a very small part of the supporting pipe/rail would be in focus from a very small area of the reflecting surface - the rest is idle. One could do far better with a simple E-W parabolic cylinder adjusted seasonally in small moves.

Posted by: Frank Michael on December 1, 2007

Thanks Jane, John and Bryan! This was a really neat competition! And good luck John with the structure!

Posted by: Jai on December 1, 2007

I'd say he's building a tree house for his grandchildren.

Posted by: Yangyang Guo on December 1, 2007

Hey Bryan,

I was the 7th person on this blog to say "hyperbolic paraboloid" in my entry. Though I thought it was a Pi symbol.

If I am considered a winner, please give my prize to Melis. She truly is an inspiration.

Posted by: Chris on December 1, 2007

It looks like an airplane wing! woooo airplane *wink*

Posted by: Stephy on December 2, 2007

what a disappointment! these are prospective mit students, you're asking. a hyperbolic paraboloid is in the first chapter of multivariable calculus.

Posted by: anonymous on December 2, 2007

@ Anon: Perhaps you've missed another important tenant of what it means to be an MIT student - creativity. It seems a little presumptuous (not to mention contemptuous) to presume that everybody who didn't answer hyperbolic paraboloid is somehow inferior to...well, you. In essence, you're trivializing all the other comments that spawned original and creative thinking. Being right is not all that matters- being willing to speak your mind and come up with something new is equally important.

Posted by: Travis on December 2, 2007

Hi Jane, thnx for looking at my answer.

BTW..I DID use the word quadric!!!! Really!!!!!

Look at my answer!!! Maybe I deserve a reward???

Anywhich ways....this was the the most fun filled "geometric mystery" ever!

Please do post pics of the completed structure!

I'm a grade 12 student from Dubai. After answering your question, I had a long conversation with my math teacher about quadrics and learnt a whole lot about them.

Cheers
Leo V

Posted by: Leo V on December 4, 2007

Leo, you definitely get a tetraxis too! John just finished making 20 of them, and Bryan will send them out. You can see more pictures of the pergola and other mathematical artwork at jjkostick.com and quadricdesigns.com

To see the tetraxis prize, go to www.youtube.com/jjkostick

Posted by: Jane on December 4, 2007

hi jane,
no brownie pts, for finding a spelling mistake?? ("wildebeest"),and it could have been a 'calabi-yau' manifold,cudn't it?
oh..i feel pathetic..but anything for a recognition frm MIT..however distant!!

Posted by: raphael on December 4, 2007

Wow.....thnx soooooo much JANE!!!!!!

This is way too cool!!!

Leo is just a screen name. I've always liked the name Leo. I am Lionel Vaz. This prize means a lot to me. It's more than just a prize!!!!!

I'm excited for two reasons.

Firstly, I'm am applying to MIT for fall 2008. As an interntional student, the competition for admission is fierce. But I have a strong belief in my will to succeed. This is prize just serves to re-affirm my belief. It's a milestone for me!

Secondly, math is my first love. What can be better than being rewarded for doing something you love the most????

A big THANKYOU to all you people.

Thankyou Bryan for posting this. I can't explain how much this means to me.

Its amazing...something as simple as a wooden structure has set of this "tsunami" of happiness within me. WOWWWWWW!!!!!!!!!!!!!!!

Cheers
Lionel.

Posted by: Leo V on December 4, 2007

After a bit of math-base researching I may not have figured this out. LOL! My son is the math whiz. Here's what I'm guessing. It's a representation of Kieren's concept of fractions as several interrelated subconstructs, not just a single construct. In the early 1980s, Behr et al suggested a theoretical model linking all 5 subconstructs (i.e., part-whole, rato, operator, quotient and measure). That what I believe this amazing structure represents. Thanks for keeping my gray/white matter functioning.

Posted by: Jay (Hopeful MIT Fall 2008 parent) on December 4, 2007

Sorry. The real credit for the answer was searching Google for "math-based"? EJ757761-Drawing on a Therotical Model to Staudy Students Understandings of Fractions.

Posted by: Jay (again) on December 4, 2007

a lot of one sided geometry answers.

Hmmm... He has no official porch, and it's hard to tell from the pictures exactly which shape it belongs to.

My best guess is a sun-roof seeing how the four poles are so uniformly distributed around the frame

Posted by: Johnson C on December 4, 2007

mhm.. I think he is making a parabola stand for his plants( pea, grape,etc.), so that the plants' vines can wreathe on the structure.

Posted by: angi on December 4, 2007

I'm one of the runners up, and I haven't received an email yet. I'm just wondering if they might have forgotten to put my email on the list, or if the emails just haven't been sent yet.

Thanks again for this intriguing contest!

Posted by: Zev Chonoles on December 6, 2007

I gave Bryan a bag of stars last night. He will send out an email requesting your mailing address and then send you a tetraxis.

Posted by: Jane on December 6, 2007

a surface that combines parabola and superbola can be a slider.

Posted by: 0 on December 10, 2007

Has anyone else heard from Bryan yet? It's been a while, perhaps he's run afoul of my spam filter.

Posted by: Merritt B on December 13, 2007

I haven't heard from Bryan yet, but it is slightly possible that he's backed up with paperwork from EA decisions...just maybe smile

You can always hope that he put it in your tube!

Posted by: Karen on December 13, 2007

I haven't heard from Bryan yet either, but I assume he is very busy reading our EA applications. Still anxiously awaiting the arrival of my tetraxis!

Posted by: Lauren S. on December 13, 2007

Hi, I just have a general question(s) about MIT. Im only a sophomore but already im looking at colleges because I realize which ever university I go to will be a commitment I want to have thought over GREATLY. Anyway, I do pretty well in math and sciences in my school and supposedly MIT is believed to be a geek/nerd or engineering/math/science school. I was wondering how strong the Humanities and Arts are @ MIT. Although this college is renowned for its advances in Mathematics and Sciences I wanted to learn more about departments such as Philosophy, Psychology, and East Asian Studies. I admire MIT because of its programs, the general opinions i get about the student life and stress as a opposed to Harvard,Yale, or Princeton (other options) and its philosophy that closely relfects my own view of the actual reason I would go to college and even bother LEARNING @ all. However, its reputation makes me at odds about whether or not it would be a good fit for me. I would really appreciate any advice/criticism/suggestions/comments...etc..

..Arigatou Gozaimasu (Thank you very Much =D)

Posted by: KUI on December 14, 2007

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