Another useful Geometry Application. Furniture Using The Square Root of 2.

When I taught furniture design to college students one project assignment was to design a table that could be reduced by 50% and still be useful when the starting dimension wasn't needed. 

This is one useful solution that my students have used several times over the years.  It uses the Square Root of 2 (1.414213562373095) to create a rectangle that remains the same width to length ratio when folded in half. 

In this example I have a wood panel to use that is 24" x 36" x 3/4" thick.  If I use the 24" side as the width of my table top and multiply it by 1.41... I get 33.94....  So with 36" of potential length I have room for the kerf of a table saw or CNC 1/4" profile cut. 

The Whole Top

One half of this 24 x 33.94" top is 16.95 x 24. When rotate 90 degrees and centered over the base it is the same ratio as the starting dimension.

Half the Top

Soss hinges between the table halves are hidden when unfolded, but will be visible on the inner edge when folded in half.

Rotated and Centered

One challenge was to find a single point of rotation for the top that would keep the top centered over the base after being folded over and rotated 90 degrees. 

Project a line from the center of 1/2

To find a common point that will be in the same position between unfolded and folded/rotated draw a line 45 degree from the center of the side that will be on the bottom and rotated.  

Project the same line, but from the rotated/centered outline. 

Draw the same 45 degree line from the rotated view of the bottom half.  Where those lines intersect is the only point the top can be rotated about to remain centered over the base in both positions.

The inner outline shown in the 2 views above is the outline of a base that would be inset 20% from the large perimeter. You can see it is still inset a small amount under the folded top. 

Here is one option for a base.  The legs extend to the inner edge of the 20% inset outline. A bracket attaches  to one stretcher to provide a pivot position for the top to rotate about. 

Under the folded top.

Under the open top.

Need a larger table?  What is the largest rectangle of that same sq.rt. of 2 ratio that can be made from a 24" x 60" panel? Account for a 1/8" wide kerf on any cuts.  How much scrap will be left after cutting the two table halves?

As the table base is a little smaller than 1/2  of the table top, you could also make the folded half a drop leaf rather than just double the smaller top thickness. This side would hang down and block access to one side of the base, but if that is not important the table top will benefit from being the same height above the floor in both unfolded and dropped side positions.  

Leave a comment if you need any more information.

4D