# Golden Mean, Golden ratio in constructing items.

 Blog entry by Karson posted 04-19-2008 08:06 PM 18582 reads 21 times favorited 12 comments

The golden Mean or Golden Ratio is a number that people use when making items, buildings and furniture, They are determined a couple of different ways.

The number is used to determine proportions between pieces of the item being constructed.

One of the easiest to remember is to take 1 and 1 and then to add two consecutive numbers to get the next. The numbers in sequence are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. This might work if you were making something 89” tall and the width would be 55” wide.

A different way of calculating the number is take a calculator that has a square root function. Your computer has one. Enter any number 89, 22222, -45, .24876 etc. Take the square root of that number, add 1, take the square root again, add 1 take the square root again. Keep this up until the square root number never changes. You will get a number like this 1.6180339887498948482045868343656. If I add 1 to this number and do the square root again I get the same number.

You can take this number and multiply or divide it by a measurement and calculate the other one.

For example a box with a height of 4” the width on the side would be 4 X 1.618 = 6.472 your width of the end should be 6.472 or 6.5 inches. The top would then be 6.5 X 1.618 = 10.517. So the box dimensions would be 10.5” wide, 6.5” deep and 4” high.

For the bookcase that I was designing for the Challenge04, I estimated the height to be 54” high and 40” wide. Lets see how this would calculate out 54” divided by 1.618 = 33.37 or 33 3/8” But I was planning to put legs on it and I estimated them to be 10” for an overall case size 64”. Lets determine the width now.
64 / 1.618 = 39.555. That is within the range that I was wanting to build.

The base was estimated at 10” high. What then should be the width of the base at the side. 10 X 1.618 = 16.18” In my rough estimates I guessed at 15” for the case sides and about 16” for the top and probably the case bottom. All of these measurements are within the pleasing range for the eyes.

The shelves would be about 17.5” wide across the front. 40” – (1.75” X 2) – 1” = 35.5” Each shelf would be 17.75” wide. The spacing between the shelves then should be 17.75 / 1.618 = 10.98”. Since a lot of books are 11” high, the spacing should be at least 11.5”

This is a way of determining measurements for items that you plan to build.

See Davids blog Furniture Design #1: Fibonacci gauge

You can search of other pages on LumberJocks that reference Golden Mean.

-- I've been blessed with a father who liked to tinker in wood, and a wife who lets me tinker in wood. Appomattox Virginia [email protected]