Approaching one-third using only halves

Origami paper-folding has been a hobby of mine ever since I folded my first paper airplane. Coincidentally, origami is a rich source of all kinds of math problems in areas as diverse as geometry, algebra, calculus, and topology. One problem results from trying to fold a piece of paper into thirds. It's easy to fold a piece of paper in half, all you need to do is line up the opposite sides of the paper and crease. From there, it is easy to fold a paper into fourths, eighths, sixteenths, and so on, just by lining up different creases and folding. But what about folding a piece of paper into thirds? If you don't have a ruler handy, folding paper into thirds must be done by eye, which can lead to error. If only there was a way to reach 1/3 by only folding paper in half repeatedly. Can you think of a way? My friend Luke Nimtz did. See if you can figure it out. Answer is below.

STRANGE REVIEW

I recently wrote a STRANGE REVIEW for Brett Elizabeth Jenkins. You can read it over at her blog, The Angry Grammarian. Do it! Do it now I say!

Cheap and easy bike rack (for cars with spoilers)

About a year ago I went to Fort Wayne's Summit City Bicycle and Fitness to check out a bike rack for my car. I gave them the make and model of my car and they showed me the racks that would fit. The cheapest one they had was shaped a lot like this one below, but not as nice.

The bike rack they showed me costs around $160.  It looks cheap and is made entirely of plastic. I spent $40 on my bike, and there was no way I was going to spend 4 times that on a rack. I realized that I could make a bike rack myself that also looked cheap, was also made of plastic, but would cost much less.

Here is my bike rack. My brother, dad and I put this rack together on an afternoon and spent about $25. If your car has a spoiler like mine does, you can use a rack design like this one and save some money yourself.









We used:
15 ft of 3/4 inch PVC pipe
8 3/4 PVC slip tees
2 wire hooks
about 20 feet of nylon strap
PVC cleaning solution
PVC glue


Here is an exploded diagram. Every joint here is glued tightly, except at the places shown, which forms a hinge that allows the rack to fold. You'll want to make your own measurements so the rack fits your car, and your bike. This bike rack is 20 inches wide (this is too wide for some bikes) and the legs are about 2 feet long from the hinge. The bike sits on wire hooks that screw into the outermost slip tees of the hinge.

To attach the rack to the car, I put two of the legs of the rack underneath the spoiler of the car, with the other two legs standing on the bumper. To secure the rack, I used nylon strap with a hook on one end. I throw the hook end into the trunk, close the lid, and pull the strap tight. (You could also just tie a large knot in the strap instead of using a hook.) I have another length of strap, with a loop in it, tied to the inside of the top of the trunk lid. I use these straps to tie down the bicycle and keep the rack from moving or falling off the bumper. The excess strap is used to keep the front bike tire from flopping around in the wind.

I'd be happy to hear any design suggestions you have for this rack, or if you have other designs for other cars you can send them to me at joshuabfitzgerald (at) gmail.

Tips and tricks:

• I used a combination of 3/4 and 1/2 inch PVC, but the 1/2 inch legs seemed a bit wobbly. You may want to use 3/4 or even 1 inch pipe if you want it to be sturdier or if you have a heavy bike. 
• The PVC may scratch your vehicle. You could get rubber ends for the legs to prevent this.
• If you want to make your rack look less....homemade...you could always spraypaint it black.
• For added stability I often use two bungee cords that go from the top tube of the bike and hook onto the spoiler. If the PVC were sturdier (i.e., I used thicker pipe) I probably wouldn't need these. Better safe than sorry, though.

Some more photos:

 

Math for Farmers

Most math problems posed in school textbooks are created in order to use whatever new math concept the students are learning at the time. This leads to math problems that "fit" perfectly with the step-by-step process found in the textbook but don't relate to any real-life situation. However, here we have a real math problem, from a real person, working a real job, that illustrates some basic geometry principles.

My uncle, who is a farmer, asked me to solve this problem for him:

If it takes 15 minutes to drive a tractor around the perimeter of a field, driving at 6 mph, how many acres is the field? Try to figure this out on your own. If you don't know what an acre is, you can check this Wikipedia article. The answer is after the jump.

Bloginnings!

In case you couldn't figure out my clever title above, "bloginnings" is a new word combining the words "blog" and "beginnings." "Wow" is right! If you enjoy language-defiling word mashups and high school level grammar, then you've found the right blog!

I started this blog for purely political reasons. Here's how it all went down:

I'll be running for the office of President of the United States in 2012 as a member of the YouTube party. The paperwork is currently pending.

By the way, that's my good friend Brett Elizabeth Jenkins: poet extraordinaire, exceptional mitten wearer, and rugby ordinaire. You can follow her blog at The Angry Grammarian. Do it!

I intend this blog to be a semi-educational collection of weird science, interesting math problems, real-life adventures, and weekend garage projects. And other stuff. Probably.