What is a double cube proportion box?

Sounds like it's the size of two cubes side by side. Whatever dimension you use for the height and width, the length is twice that.

Some boxes look "nicer" than others. That's all it is about.

Over the years people have found that certain proportions in a box ( or=20 shape) seem more pleasing to the eye than other proportions.

For the root two box think about the length of the hypotenuse in a 45=20 degree angle Square root of two as I recall. So you can draw a 45 deg.=20 triangle, take the lengths of the sides, and use them as the proportions =

of the boxes. (Angles: 45, 90, 45) (Sides: 1 : 1.41 : 1)

The golden ratio 1.62 approx. is based on the Fibonacci series -- again=20 which as I recall can be derived from looking at the natural branching=20 of trees.

Just do a search on the Fibonacci series and the Golden Mean (ratio).=20 You should be able to find lots of stuff.

These proportioned are used in architecture as well.

Have a look on my web site. There is a country style clock which was=20 proportioned in root two ( 1:41 : 1) as to the various dimensions. It=20 was sorta like that in an original design, but I reproportioned it to=20 take the rule into account everywhere. It looks nicer now -- In my opinio= n.

Whether we have "learned" to like the proportions because a "wise man"=20 told us we should, or we like them because there is a natural affinity=20 for certain relations -- who knows? But people do like these proportions =

-- and that is what it is all about.

How do they work?

Well if you make a bottom dimension 10 inches, make the height 16 1/4=20 inches (1: 1:62 -- the golden ratio) -- or if you want root two, make=20 the height 14 inches. Sometimes I double one side if I want the object=20 to look stretched. Or I might design it in a size that is convenient to=20 imagine and then divide everything by two, or three or any other number. =

(Or multiply... :-) )

It's that simple (or complicated) if you like.

The doubling rule (double one dimension to stretch one aspect) will=20 always work I think. The mixing of ratio rules will probably create a=20 "frankenbox". Try it -- maybe it works though! :-)

Beauty is in the mind of the beholder.

Welcome to number theory and architecture junction.

--=20 Will R. Jewel Boxes and Wood Art

FWIW, first 3 members of a Fibonacci series.

Steve