What is a double cube proportion box?

[needin4mation]

Hi, I am hoping one of you will be able to help me. I have a book, "Box-Making Basics" and in it it has some "classical or traditional proportions, these include the double cube, the root-of-two box, the

1:2:3 box, and the golden rectangle." (p.4)

I don't understand what the double cube is. In the picture it has 1 1

2 where the height is 1, the width is 1 and the length is 2. What does this mean?

I really don't understand what any of them are. the double cube one just looked the easiest to understand.

Thank you.

[Rich]

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.

[WillR]

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

power of accurate observation is commonly called cynicism by those=20 who have not got it.=94 George Bernard Shaw

[Steve Peterson]

FWIW, first 3 members of a Fibonacci series.

Steve