I was fooling around with some K’nex today (think of a mix between Lincoln Logs and Legos), and noticed something odd. Your basic K’nex kit comes with 5 different lengths of rods, and a handful of different types of connectors. I took one of the longest rods (which are color coded grey) and two of the second longest (red) rods, a 90 degree connector, and two 45 degree connectors. I put them together and formed a perfect right isosceles triangle.
I did this again with one red, and two rods that were one step smaller. And then again with the next step down. And so on until I got two of the very smallest pieces, and one of the second smallest piece.
Now at first glance, that’s not really much to get excited about. But, if you stop and remember high school geometry, you’ll remember Pythagoreans theorem. (The sum of the two sides of a right triangle squared is equal to the square of the hypotenuse, or A^2 + B^@ = C^2). That means that when the toy engineers were designing K’nex, and deciding what length to make all the rods and connectors, instead of making them just say 1 inch, 1 and a quarter inch, 2 inches, 3 inches, etch, they actually sat down and calculated how long everything would have to be in order to be able to form right isosceles triangles.
Well it only makes sense if you’re going to be building relatively large structures as you need the cross supports. Granted, I’m not an engineer. Just as Georgia Tech.
As said. it’s necessary if you’re going to have right-angle bracing (i.e. – you put diagonals across your squares occasionally to form triangles to make the structures rigid) It IS good planning and design, but you’d stumble upon it yourself right off the bat when you started building things.
K’NEX is made of white and colored Delrin plastic, by the way, which is a pretty tough plastic. Hard to break, doesn’t absorb water, and doesn’t react with most things. It’s alterating carbons and oxygens in its “backbone”, with hydrogen saturating the other bonds, and the ends stabilized with rings. Basically polymerized formaldehyde, with really long chains. (I worked with Delrin and other acetal plastics before I learned about K’NEX, and was glad to see someone doing something fun with it.)
K’NEX are totally awesome. I can’t wait until WhyBaby is old enough for them. Her brother made some amazing things, including a five foot tall ferris wheel. I think the instructions were for a 3-foot ferris wheel, but he “adapted” it. It was big enough and sturdy enough for the cat to ride in!
Well, okay, the cat “rode” about six inches before fleeing for his feline life, but in theory…
I have a large box of K’nex at home… I really should dig 'em out to play with 'em.
The best thing I’ve built with them was a five-foot-across geodesic sphere. The joints aren’t strong enough to keep the sphere, well, spherical, but it does stay together. It’s pretty cool being able to sit inside something I built out of little plastic sticks.
The ISO standard paper sizes used in Europe (and most of the rest of the world, really) use a similar trick. The largest size is A0, then A1, A2, etc. A4 is similar to our ‘letter’ size in the US.
The cool part is that the ratio of the width to height of each of these sizes is sqrt(2) - which means that two A4 sheets placed side-by-side make up an A3, two A3’s an A2, two A2’s an A1, and so forth.
When my wife was doing toy reviews, she got a very early set. The press info she got said that Delrin developed K’NEX to fill in dead periods. I don’t know their sales, but they seem pretty good.
And they are indeed great things to play with, the most stable building kit I know. I remember a truly awesome setup they had one year at Toy Fair, but I don’t remember what was in it.
I didn’t know that. Interesting.
“Delrin” is the brand name of the plastic – Dupont is the manufacturer. They spent a lot of time and money coming up with the process to ultra-purify formaldehyde, polymerize it, and tie off the ends with something that wouldn’t unravel. They were majorly pissed when a competitor made an almost identical plastic by going a different route (co-polymerization of cyclic ethers) to produce Celcon. But those guys never came up with anything as cool as K’NEX.
For reference, rod length is from shortest to longest: green, white, blue, yellow, red, grey.
In addition to the right triangles, if you link two together linearly, the connector is the right length so that they’re the same length as a connector two steps higher, that is, two greens make a blue, two whites make a yellow, two blues make a red, and two yellows make a grey. Personally, I find that even more impressive.
I beleive the same is true for TinkerToys (next size up is sqrt(2) as big)
The fact that two sizes up is 2x is a natural followon for that.
big = sqrt(2) * medium = sqrt (2) * small
big = sqrt(2) * sqrt(2) * small
big = 2 * small
