watervole: (maths)
I was folding a few origami boxes at the weekend and decided to try my pentagonal box again, and realised that I could no longer remember how to do it!

Fortunately, once I got home, I was able to work it out again with the help of a previous LJ posting I'd made.

So, this is mostly a reminder to myself if I forget again, but also for anyone else who really wants to know.The maths )
watervole: (maths)
The process of working out how to make a pentagonal box (with lid) was productive in more ways than one.

Having had to work out all the folds from first principles, as opposed to copying them from the book (a hexagonal box is two pages of instructions and you have to change some of them to make a nesting base), I've found that I can now do many other boxes without needing to look at the book.

I now have a much better understanding of what fold is producing what part of the final box (trust me, when I say that this is not intuitively obvious) and am much more confident at tweaking the instructions to produce different styles of boxes.  I've done three totally different triangular box styles now, in addition to the ones in the book.

Triangles are the most amenable to variation as you have more free paper to play with.  Hexagons and pentagons have (as far as I can work out) a very limited number of permutations as the way in which you have to join the pieces together doesn't allow for many frills.  This limitation may only apply to boxes that use less pieces of paper than they have sides (eg. the pentagon and hexagon both use two pieces of paper, wheras the triangle uses three), but I haven't yet tried looking into a hexagonal box that uses six pieces of paper.  There is a chance that it will prove impossible using square paper, as there will come a point when there won't be enough paper left, after folding the rim, to reach into the centre.

It's proving to be an interesting blend of geometry, occasional trig and general logic.  It's also one of the few things I can do at present that doesn't cause pain.  (I hurt my neck last week and although it has improved, it still isn't normal - even watching TV is uncomfortable)  The really annoying thing is that the pain is fuzzing my brain.  I look at an origami problem and make way too many stupid mistakes.  Last night,  I managed to convince myself that half of 3/4 was 1/3 !  (And it was several minutes before I spotted the mistake)

I want to stop hurting and I want my brain back!

If you want to see what I've been making, [profile] entorienwill have some of them for sale in the Orbital dealer's room.  The price will not reflect the time it takes to make them.   It's not uncommon for a box to take a couple of hours to fold and assemble - the ones with flowers and birds on top are staggeringly complicated.
watervole: (gold star)
As a few of you will know, I've been happily folding origami boxes of various shapes and sizes since Xmas.  They're complex enough to provide a good focus for relaxation and not so difficult that I can't do them when I'm stressed.  (the shoulder is so bad at the moment that cross stitch, my normal relaxation, is proving painful)

Gradually, I've been finding errata in the book I'm using.  Not too many of them, but enough to make me think about the mathematics behind the way they are folded and why particular folds are necessary to make a box of a particular shape.

The book gives instructions for square, hexagonal and octagonal boxes.  I've been thinking for a while about how to do a pentagonal box and finally succeeded in folding one this morning.  The process reveals several things about the design of some of the other boxes, such as the choice for the depth of the rim.

I had to cheat in one small respect.  Purist origami uses no rulers or protractors.  Playing around with the geometry, I realised that I'd have to measure an angle of 18 degrees to do the first fold (this eventually gets me to the necessary angle of 54 degrees between the base of a side and a line into the centre of the pentagon). 

Playing around with trigonometry, I think I may have found a way of getting an angle of  (almost) 18 degrees without having to use a protractor.  It relies on folding a piece of paper in three.  This isn't that easy to do, but a bit of trial and error will get you there pretty quickly.  Maybe later today, I'll try doing a box that way and see if it works.  (If it's more than a degree out, I'll probably end up with a hole in the centre of the box lid, or else a small dome).

After that, the hard part will be writing down the instructions in a clear manner.  There's some folds that aren't needed other boxes and I need to be able to describe precisely where they are.  I may need to co-opt Richard to draw the diagrams for me as I demonstrate step by step.

I'm sure someone must have done pentagonal boxes before, but I don't see any books that contain instructions on Amazon (one book has a septagonal box - more correctly 'heptagonal').

Has anyone else come across a pentagonal box?

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Judith Proctor

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