D49: Little Triangle bags

I'm beginning to suspect that paper-based projects will be best for days like these...

I was wondering about the geometry of the triangle bag I made yesterday.  It's the perfect width for a handbag for me, but it's too short to go over the shoulder: the hole is only forearm sized, not shoulder sized.

For at least one of the four sleeps since then, I've drifted off wondering about other construction ideas.  Folding bags from cones, semicircles and triangles so that theres just one or two seams.  I remember flipping the shapes around in my head and feeling fairly confident about the results.  Really, though, my brain doesn't dance with 2D-to-3D conversions, I need a mock-up of some sort, so today I've done up a few ideas with bits of paper.

Three different lengths, folded from the centre outward.
That 1:2 one is actually 5:12.

I thought I'd start with the rectangles and see how far I got.
I wondered if simply lengthening the strip would be enough. I already knew that the construction steps couldn't be the same as 1:3 (as it works in from the ends) and was curious about other arrangements.  Here are three rectangles of different ratios, all folded so that their centre is at the bottom of the bag.

I thought the lower the ratio, the wider the bag. The 1:2 5:12 and 1:4 both have a sort of 'left over' part, which is fair enough as it's just a bit less or more than the neat 1:3. Although a 1:1.5 (or 2:3) ratio bag may be even more shallow, the reverse is not true. As you'll see with the 1:5 examples below, I think fixing the width of the rectangle at 1, for example, determines the width of the bag to always be at least 1.4 (with a bit of give for the bias).

Left: Folded from the centre (symmetrically)   Right: Folded from the end with a triangle

I thought I'd try another 1:4, folding it from one end to create the same shape. This shows how the left over part was shifted entirely to one side, making a kind of envelope.

The symmetrically folded 1:4, in half.

I think this one is totally good to go! A neat little clutch, no?

Here is the 1:5 effort. The one labelled 'wrap' is folded from the end and has the extending end concertina-folded and tucked into the other tip. It would be asymmetrical and possibly sit on a shoulder really well.
The 'centred' one is the same size as the 1:4 clutch when folded in half. It would hold more, though, because the tube/body is deeper.

The one on the left is the same height as the 1:4.  The right one is asymmetrical.

I like this one very much and already have a lined version in mind as a gift.
That's all for today. Possibly more miniature geometric bags in the future.


*Teachers looking for ratio/geometry/prediction tasks are welcome to steal this post! ;)