Help with Insane Paper Dimensions

[Cupcake]

I have been folding a lot of the models from Robert J. Langs "the Complete Book of Origami" and I am interested in folding some of the harder models, like the Bassist, Violinist and Pianist. However, I cannot figure out the dimensions for these.
I have already figured out that the Viking Ship with dimensions of 1:4.667 is 1:4 2/3. But I need help with the others. Here are the dimensions:

Violinist- 1:1.414
Bassist- 1:1.207
Pianist- 1:3.874

Thank you in advance

[origami_8]

Why don´t you just multiply the size you want the smaller side to be with the data mentioned and take the next measurable number?

Let´s say I want a violinist with the width of 25 cm, so the height would be 35,35 cm or equally 10" to 14,14".

By the way 1 : 1,414 is approximately A4.

For the pianist Lang describes a method how to get the needed length by beginning with a 1:4 paper and cutting of the exccess after folding a few steps.

[origamimasterjared]

1x1.414 = 1xsqrt2

Not sure about the bassist, but I know the diagrams showed how to get the rectangle for the pianist from a rectangle longer than 1x3.874 (Such as a 1x4)

[denori]

1 x 1.414 is (as jared says) 1 x sqrt(2)
All 'A' sized paper (and 'B' sized) is in this ratio, sometimes called the 'Silver Rectangle'

1 x 1.207 is 2 x (1+sqrt(2))

1 x 4.667 is 3 x 14

1 x 3.874 is roughly 8 x 31

[denori]

There's also a spreadsheet on my website http://www.origamidennis.co.uk/ that helps with this sort of thing.

It's in the Utilities section.

[Cupcake]

I have figured out that 1:1.414 is indeed a silver rectangle. But how do I figure out 1: 2x(1+sqrt(2))? Remember, I know only up to grade nine level math. Would it be 2:2.414?

Edit: I think I've figured it out now. Take a silver rectangle, add a square below it and multiply by two, putting them side by side. That would make the equivalent size paper, wouldn't it?
Heres what I mean:

[Fanatic]

You could actually do something easier for the bassist. Get an A4 sheet of paper and fold it diagonally like you're cuting a square. Cut of half of the protruding edge and there you have it!

[Cupcake]

I'm pretty sure i know how to make a 1:1.207 rectangle now. Make a silver rectangle, divide in half horizontally and vertically and make squares touching half in the bottom half (cut off paper from below the squares)

[Daydreamer]

I still don't understand why you make things much more complicated than they are. Just calculate, measure and cut....

[Cupcake]

I'm just to lazy to do things the easy way!

[the modern einstein]

3.874 = 500:1937

[the modern einstein]

Can we have any confirmation of a more simple logarithm for the bassist? - say X{y to the power of 2)?

[redheadorigami]

My head is full of BLAARRRGGH!!
Seriously, is the operation/pronumeral (sqrt) a number?
If so, what is it?

[the modern einstein]

Which operation are you talking about? The proportions we are trying to solve are listed on the top post - they are the numbers.

[redheadorigami]

What is the (sqrt) thing?