By Glen Whitney for the Museum of Mathematics
When last we left our intrepid hula-hoop-armed mathematical makers, they had just suffered a collapse of the Sierpinski tetrahedron midway between order 2 and order 3. What to do?
In clawing through the twisted wreck, we discovered three major modes of failure: First, the order 2 tetrahedron sagged badly when it was lifted up in the air. Second, the junctions between hula hoops, held by pipe cleaners, rotated into angles and orientations quite far from the desired tetrahedron dihedral angle. Third, a few individual hoops under a great deal of strain warped to the point of elastic failure and developed permanent kinks.
So we took measures to combat all three of these issues. First, the experimental build showed us which hoops were in tension and which in compression. Roughly speaking, all of the horizontal hoops are in tension as the pyramid tries to spread, and all of the sloped hula hoops are in compression. So, to alleviate the first problem (sagging), we just added twist-tie loops between nearby (but not touching) hula hoops to prevent them from spreading as far apart.
Second, we experimented with different materials to connect the hoops and settled on self-adherent compression bandage as the ideal: it provided a broad, high-friction junction that virtually eliminated the problem of one hula hoop rotating with respect to its neighbor.
And third, the prototyping phase showed that three individual hula hoops were taking the lion’s share of all of the compression load of the configuration. Namely, the three hoops which slant inward toward the center, just below the three bottom vertices of the top order-two tetrahedron, all deformed very badly. So to shore these up, we drilled two holes the same diameter as the hula tube in the side of 3/4″ schedule 40 PVC pipe, at a distance of one hula diameter apart. We cut the pipe past the diameter of the holes to create “jaws” that would grasp the hula hoops and hold the stays in place.
With these changes, a bunch of MoMath friends and staff got together again for a second practice. And this time, with a bit of tweaking, we managed to get the entire order-3 tetrahedron in the air (as seen in the opening image).
This experience yielded one additional lesson for the actual public construction: attaching the hoops symmetrically, so that the three initial attachment points divided each hoop exactly in thirds, was really important in the quality of the resulting tetrahedron. So we marked each of 256 hula hoops with pieces of compression tape at the one-third points. And finally, last weekend at the World Science Festival in New York City, our visitors actually constructed this giant Sierpinski tetrahedron, based on the careful groundwork we had laid in our practice runs:
More:
Hula Hoop Geometry, Part I
See all of our Math Monday columns
And we’re back with our thirtieth installment of Your Comments. Here are our favorites from the past week, from Makezine, our Facebook page, and Twitter.
In response to NEWS FROM THE FUTURE – Robot Fish Scan For Pollution, TimeSpike says:
What happens when sharks start eating these?
In the piece on the A Bed that Makes Itself, Cory remarks:
Where's the robot to pick the covers up off the ground? They obviously haven't seen how I sleep!!
In response to Gauging Performance Between Compressed Air Rocket Mods, user JWC has a novel idea:
I made a mod on the launcher by attaching it to a small air compressor. The compressor maxes out at 100 psi, which is well below the pipe's rating, so safety isn't an issue any more than with the hand pump. The other nice things about this setup is (1) We can rapid-fire rockets without anyone getting tired and (2) if the air compressor isn't attached the launcher won't hold any pressure – which makes it a nice, visual safety.
In the piece RobotGrrl's Heathkit Build Continues, glenn147 says:
Many Years Ago, in a Land Far, Far Away. This was the First Analog Meter, that I made at Home…
In the article Cool Superhydrophobic Surface Demos, user Michael Phelps writes:
How long before an olympic swimmer coats himself in that stuff before a key race?
Like these comments? Be sure to sound off in the comments! You could be in next week’s column.
Most of the fathers I know actually have very little in common with Demographic Dad. You know the guy I’m talking about, right? About five-nine, one-eighty? Likes big-screen TVs, neckties, and golf clubs? Largely an invention of greeting card publishers and retail marketing directors? Yeah, that guy. Between you and me, honestly, I don’t like him very much. In fact, he seems like kind of a doofus.
Fortunately, my real-life Dad is way cooler. He’s practical, mostly, but can cut loose and appreciate a gag gift, or one that’s mostly just a toy, precisely because it’s the kind of thing he’d never spend his own money on. He’s an engineer—tech-savvy and scientifically minded—but he’s been around long enough to see ten thousand gadgets come and go. He appreciates quality, more than novelty, and he would rather have a thoughtful, intelligent, hand-made gift than the latest iThing. He can buy that for himself whenever he wants.
In choosing projects for this guide, then, I have tried to forget about Demographic Dad and choose stuff that A) I would proudly make and give to my own father, and B) that can be made with relatively small investments of money and time. If you follow the news, you may have noticed that petty cash is a bit tight in general these days, and if you follow the calendar, you may have noticed that (as of this writing) you have six days until the 17th.
Avanti!
#10
Mini mint tin toolboxes
OK, that’s cute. My Dad is not often susceptible to cute, but I think he’d like one of these anyway. Especially if, as Gareth has suggested, you outfit it with an emergency field soldering kit.
#9
Make: Projects — The Fire Piston
Odds are exceeding small that your Dad (or anyone else), in today’s world, is ever going to actually have to resort to a fire piston to start a fire. So this is mostly a toy. But, as toys go, it’s a really cool one, especially if your Dad is mechanically and/or scientifically inclined. And it’s easy to make, too.
#8
Make: Projects — Making a Diddley Bow
As a young man my Dad seriously considered becoming a professional guitarist. He still enjoys playing from time to time, and though he might prefer to call this particular instrument a “monochord,” he would have just as much fun playing it as David “One String Willie” Williams does in this video Mark posted on Boing Boing awhile back. “One String” himself wrote our how-to guide, and it doesn’t take much more than a board, a piece of wire, a glass jar, and a couple of nails.
#7
Make: Projects — Bulletproof Binder
Dad does not yet inhabit the Paperless Society. Nor, for that matter, do I. This thing is a pretty easy afternoon’s build if you have an old vinyl binder to cannibalize and a piece of sheet aluminum around, and its heavy-duty/industrial vibe will appeal to pretty much anyone who appreciates quality. A scrap road sign works great for a cover, but please don’t steal one for this project. Having to bail your butt out of jail, yet again, is a somewhat less-than-ideal Father’s Day treat.
#6
Make: Projects — Easy Lift Extension Ladder
If your Dad’s extension ladder is without a rope lift, or the rope lift doesn’t work very well, this easy mod from Martin Schmidt will A) show off your mechanical engineering savvy and B) make Dad’s life easier every time the ladder comes out. In the guide, Martin shows you how to replace the conventional single-pulley rope lift with a double-pulley system that halves the force required to extend the ladder. Smart!
#5
Weekend Project: Spider Rifle
Total DIY classic. Easy to make, useful, and fun to use. Dad likes to have the right tool, on hand, when the right job presents itself. And when the job is bug extraction (as it so often is out in the hill country where my folks have set up camp) this is the right tool. Equip your version with a buttstock so Dad can scratch notches into it with a hunting knife.
#4
Make: Projects — You Have Just Been Poisoned
These are easy to make, always get a laugh, facilitate the consumption of beer, and promote awareness of one of the greatest TV spy shows of all time. And just last week, etchworld started carrying the stencils in their catalog again for $2.00 apiece. Order today and they should arrive in plenty of time to etch a glass or two before the 17th.
#3
Make: Projects — Quick Easy Wire Rack
If you’re reading this site, Dad has probably been letting you run wild with his tools, workbench, and supplies since you were old enough to break things. And lose them. And leave them in a state of terrible disarray. Which he patiently cleaned up. Many times. Show him how much you appreciate that by returning the favor: Clean his shop. Organize his tools or supplies. That cardboard box with the wire rat’s nest might be a good place to start.
#2
Make: Projects — Clay Pot Smoker
Based on a design by Alton Brown, this user-contributed Make: Project from Max Wainer is just so much win. Max sums it up quite well:
Barbecue is not the same thing as grilling. True barbecue involves cooking meat over low heat for a long time – often for many hours. I have a grill (a Weber kettle), but having to manage the fire for hours isn’t a lot of fun. Smokers like the Weber Smoky Mountain start around $300 – and don’t even get me started about the Big Green Egg ($700+!).
All you need are simple hand tools, a hotplate, a couple clay flower pots, a charcoal grate, and some bits ‘n’ baubles from RadioShack.
#1
Make: Projects — Red Magnetic Toolbox to Match Tractor
What’s that? Your Dad doesn’t have a tractor? Oh, it isn’t red! Well, if you can’t find a toolbox to match your Dad’s weird non-red tractor, you may just have to come up with something else to make for him. Something that is as uniquely suited to him as this thing is to my Dad. I made it for him back in 2009, and it’s still going strong. It sticks to the fender with eight padded supermagnets and carries tools that’ve been fixing tractors in my family for three generations, now.
Thank God I have a brother to carry on that tradition.
Happy Father’s Day, folks!
All forms of making, from electronics and crafts to DIY automotive, invariably produce some type of waste product. Not everything can be endlessly upcycled into something new. From exhausted batteries and spoiled paint products, to that unlabeled bottle of mysterious liquid in your basement, the question of what to do next with waste product and liquids in particular (oils, fuel, degreaser, etc.) can be challenging.
All of these products and more fall under the Household Hazardous Waste (HHW) column, and thankfully, most municipal governments and counties have facilities to properly handle HHW disposal and treatment (quite often including recycling). So whether you decided to flush your vehicle’s radiator DIY-style, or have spent hydraulic fluid from your homemade flight simulator or submersible, call up your local government or search online for a collection site near you. Likewise ask your nearby automotive store, gas station, or hardware store if they have a collection program in place. You’d be surprised to learn what they accept. When drop-off or pick-up events take place (pictured above), they have the added benefit of spreading awareness and building community.
Some tips about HHW and your DIY projects to consider:
- Never pour waste down storm drains, as they might connect with nearby rivers or streams.
- Ask yourself, “Would I dump this on or bury this in my yard?” Probably not.
- Don’t mix things! A good general rule to follow. Because, well, you never know!
- Keep liquids in separate, labelled containers.
- Befriend your local retailers, most of them will help you dispose of spent product properly. (For example I take batteries to a local hardware store, and metals to a nearby machining shop for recycling.)
- Most importantly, have fun making – then act responsibly with the world around you!
Do you have other pointers or tips to share? Leave a comment below.
This post is brought to you by the new OE Fine Wire Spark Plug line from Bosch.
Image courtesy armyenvironmental
No comments:
Post a Comment
Keep a civil tongue.