
Topology Explains Why Automobile Sunshades Fold Oddly (2009) - ColinWright
https://arxiv.org/abs/1205.4797
======
mauvehaus
This is the same way you coil a bandsaw blade, which has the dubious advantage
of having two readily distinguishable edges. When coiled correctly, all of the
teeth face the same way in the coil.

You can actually repeat the coiling process on a bandsaw blade one of two ways
(theoretically, there are probably more, practically, if you have blade long
enough to need to, please invite me over so I can ogle your saw):

1\. Repeat it with the whole 3 coil loop, which gives you a 9 coil loop.
Uncoiling without injuring oneself is a bit tricky, as bandsaw blades are
quite springy, and it's hard to uncoil the blade in two discrete steps one
it's in a nine coil loop.

2\. Gather the three coil section to one side (or equivalently, extend one of
the three coils) giving the gathered section about 1/3 the total size of the
exteneded section, then repeat the process with the exteneded loop in one hand
and the gathered coils in the other yielding a _five_ coil loop. It's still
tricky to get the whole thing uncoiled in 2 discrete steps, but you've stored
a bit less energy in the coils of the blade and it's somewhat less hazardous.

I wouldn't suggest trying either of these with a 93 1/2" blade (the standard
size for 14" saws), but method 2 works well with a 162" blade.

I took a knot theory class in college and there are actually two
characteristics, twist and writhe, that are quantifiable and can be exchanged
by coiling and uncoiling (massive handwaving, bad terminology, etc. That class
was a long while ago). If you've ever taken a garden hose in a flat coil (with
all the coils in the same direction) and pulled it out without unwinding it,
you've enjoyed an illustration of this.

~~~
jameshart
Twist and ‘writhe’ also explain the counterintuitive ‘roadie wrap’ method for
coiling long wires - where alternate loops are reversed, introducing twists,
but resulting in a wire that can be uncoiled smoothly by pulling one end - or
holding one end and throwing the coil.

~~~
bonestamp2
It also puts less strain on the wire, making it last longer. This is really
important in say a TV studio, where the cable that connects a camera can cost
thousands of dollars.

~~~
throwaway2048
yes, the naive way of bundling a wire into a coil strains the wire just like
if you were to take both ends and twist them in opposite directions.

------
ragebol
There's pop-up tents with a even more interesting topology. It's always fun to
watch (semi-drunk) people try to fold up theirs:
[https://www.youtube.com/watch?v=0gp5C1dYtuA](https://www.youtube.com/watch?v=0gp5C1dYtuA)

~~~
GuB-42
What is interesting is to see the evolution of the system used to fold pop-up
tents.

The most successful tent in France is, by far the Quechua 2 second, by
Decathlon. Go to any festival in a country where Decathlon is present and they
will make up the majority of the camping ground (make sure to remember which
tent is yours!).

The tricky thing, of course is to fold them back. Over the years, instructions
have changed, the design also changed slightly to make it easier. In the
latest version, you just have to pull a cord and you are more than halfway
there.

All these improvements are not just for helping the customer. Decathlon has a
very liberal return policy, and they had to deal with a huge number of broken
tents because people didn't fold them correctly.

~~~
sudosysgen
Decathlon is one of my favorite stores. I used to go there quite often when I
lived in Europe/North Africa, and now that they came to Canada its quite
handy.

------
Lammy
Totally off-topic question, but is this website name “arXiv” supposed to be
pronounced like “archive”?

~~~
caymanjim
Yes. From the Greek letter Chi.

[https://en.wikipedia.org/wiki/Chi_(letter)](https://en.wikipedia.org/wiki/Chi_\(letter\))

~~~
Lammy
Neat. Thank you :)

------
steerablesafe
Very cool and digestible paper! Followup question: Is it possible to fold the
shade into _n_ loops for every odd value of _n_?

~~~
colanderman
Yes, see @mauvehaus's top-level comment [1] for a proof sketch. The idea is to
either treat the folded shade as an unfolded shade and repeat the process, or
to make one loop sufficiently large that it can be folded again independent of
the other loops. Either way, imagine taping the original loops together, since
they do not participate in future folds.

[1]
[https://news.ycombinator.com/item?id=24407572](https://news.ycombinator.com/item?id=24407572)

~~~
steerablesafe
Ah yes, with the second method you can always add 2 loops. The first method
only gives you 3^n though.

------
alisonkisk
Why do people publish in this awkward obsolete Letter-size paper format that
is hard-to-impossible to read on modern computer screens?

Who is going to print out "College Mathematics Journal"?

~~~
User23
Printing papers out is a great way to let your optic nerve do the work so you
can save your short term memory for comprehension rather than simply recalling
what the symbols are.

I absolutely love printing out shortish papers single sided and sticking every
single page in order on a poster board or wall. Our eyes are made for flicking
from one thing to the next, it works really well. And also highlighting and
other note taking is much more direct and intuitive in this format. I also
discovered I prefer a columnar format.

if I had a monitor that could display 18 pages at once at 12-14pt and was as
easy to annotate as using a pen or marker then maybe I wouldn't do this, but I
don't.

