Woodworking Math Turtle
Golden Rectangle
Help from acient Greeks

Kepler QuoteAs a wood worker you have many opportunities to design furniture, cabinets, houses, etc. How many times have you wondered about the best way to determine the dimensions and proportions that would look just right.

The ancient Greeks, Phidias in particular, have some help for you. We need to first look at something called the Divine Proportion.

What is the most aesthetically pleasing way to divide a line. In half, thirds, quarters? Art theorists speak of a "dynamic symmetry". From the ancient Greeks to Western art, the answer is the Divine proportion.

A line divided in a divine proportion is divided such that the ratio of the length of the line to the longer segment equals the ratio of the longer segement to the shorter one.

AB/CB = CB/AC Refer to the figure below. It turns out that this ratio is always equal to 1.6180339887... (close to 1 5/8). This number is commonly called the Divine proportion, or Phi (after the Greek sculpture Phidias who utilized this proportion in his work).

Divine Proportion

This proportion has been found in many areas of nature. From growth patterns in flowers and plants to the rise and fall of the market for a stock analyst. If you are interested in studying more about this ratio from the mathematician's perspective, I suggest you start with the study of Fibonancci numbers, which starts with the story of multiplying rabbits.

Other geomtric figures based on the Golden Ratio and Golden Rectangle.

Right now, I would like to move onto the two dimensional form of the Divine proportion - the Golden Rectangle. Here are the basic steps to construct the golden rectangle

Step 1 The construction starts with creation of a square of any size.
Step 2 Next step is to divide the square in half.
Step 3 Mark point G on the same line as the bottom of the square such that FB = FG. One way to do this is to use a compass to draw an arc of a circle with center at F and radius of FB. Point G is the interestion of the arc and extenstion of line CD.
Step 4 Complete a rectangle with the intersection of top of square AB and perpendicular extension of Point G. We then have rectangle AHGC.
Step 5 I remove the intermediate construction lines to show our resulting rectangle and the ratio of the long to short side.

The sides of the Golden Rectangle are the same ratio as the Divine Proportion. The Golden Rectangle can be used to help design furniture which is not only functional but pleasing to the eye.

I encourage you to send me your questions via my email address John Sommer. I will include your question and explanation on this site.

..more to come
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