Wednesday, September 19, 2018

Corn Crib as Geometry

A corn crib.
Little. 17 ft by 21 ft , about 18 ft to the peak.
New roof, south facade, and paint: c. 2015. Painting on going.
New concrete blocks for piers; old  concrete piers formed in wicker baskets.
Moved, maybe by oxen.
Door relocated for easier access on foot. The main door was on this elevation, about 3 ft above grade, ideal for access from a wagon.

This south wall was rotting away.
The corn crib deserved better.
During the repairs we found that it is timber framed, scribed, the main framing beams hewn, others cut with a sash saw.
It has log rafters. and may predate the c. 1810 the house.

The scribe marks are similar to others found in the neighborhood - a common framer? Or a common teacher of corn crib builders?

Click on the photographs to enlarge them and read 'II', 'IIII', and 'III' on the posts and the beams. 'III' shows how water in that joint wore it away. 

I measured it - the width, length and height; the size of the posts and beams, and their locations; the roof pitch, the slant of the walls. I drew it up and checked my notes for clarity. 

The plan and elevation are below. The sides were for corn, the center aisle for work, the back (lower) section for grain, tools, equipment.

The walls slope out to shed the rain and snow, and to keep the corn from locking in place. The beam running below the beam at the eaves supports the floor of the small loft above the back storage section. There is a ladder built into the wall for access.

This is a normal corn crib for this section of the Hudson River water shed where New York, Massachusetts, and Vermont meet.
It does not seem to be the usual way corn cribs are built in other parts of the country.  I plan to look more carefully.

How I 'found' the geometry:
Note: the geometry is right there. It does not need to be found. I need to recognize it!
Looking at the  floor plan I could see the posts in the upper section forming a square. I added the diagonal and then using the diagonal as a radius I swung an arc. It landed on the lower left corner of the crib.
This is a simple easy plan. The elevation should be as simple.
I tried a square based of the width of the floor (about 17 ft. wide). It didn't quite fit.
I tried a square based on the width of the walls as they meet the roof  (about 18 ft. wide). Again, not good enough.

The utilitarian corn crib's frame needed to be as straightforward as its plan. The geometry tell the carpenter where to put his frame - exactly. Not within  4-5 inches.  He will have timbers laid out on a framing floor. He will want lines (chalk lines or taunt twine) that tell him position, lengths, mortises.  He needs no frills here.

This is when I have a cup of coffee, clean up the office, walk to the mailbox. And come back to try something else, experiment, play. "What if I drew the 'square' using the angled walls? Why not?"

It works. The Lines cross above and beside the framing members. The trapezoid ends below the ridge telling the framer where to cut his joints on the rafters so they will lap each other. The side braces (dashed line) are easily located.
The Lines on the framing floor will be beside the posts and beams, just as they are outside the edge of the plan.
The Lines needed to erect the crib are as minimal as those needed to layout the floor.

Tuesday, September 18, 2018

Archimedes' Stomachion

A copy of The Archimedes Codex was recently loaned to me by a friend who found it interesting.
I agreed. I enjoyed the discovery, the history, the math and the science.

I especially appreciated the chapter on the Stomachion, a puzzle I had not seen before. My grandson and I had fun with all the solutions.

I already knew the square and the Lines of the Stomachion.  It is a geometric diagram used for layout and framing, part of Practical Geometry which was commonly used for construction least as far back as the 6th century BCE when it is mentioned in the Bible.

Archimedes in Syracuse, a geometer and engineer, would have known Practical Geometry as it was applied to the construction around him in the 2nd and 3rd Centuries BCE.

Here is a basic Practical Geometric  diagram, the Rule of Thirds,  drawn in 6 steps.

The points where two lines crossed were used to determine both design and structure: the size of a building and its frame, its ornamentation.

This drawing is messy... I will replace it.

I have drawn the Stomachion as a square. It could also be a rectangle or a trapezoid - but for those shapes there would be many less solutions.

In the second square I have extended the Lines in red. The dashed lines show how the small lines on the lower left corner and the middle right side were laid out.
The Stomachion uses both the division of the square into thirds and the division of the square into quarters.
The shapes are clearly based on the Rule of Thirds.

This drawing by Sebastiano Serlio, is from his book Architectura, published in France in 1537. He is discussing how to place a door in an existing facade. These Lines match the ones in the Stomachion.

Perhaps someone else has seen how the Stomachion relates to Lines, the Rule of Thirds, and Practical Geometry.  I would like to meet that person.

                            *                               *                          *                            *                           *

The Archimedes Codex, How a Medieval Prayer Book is Revealing the True Genius of Antiquity's Greatest Scientist, Reviel Netz & William Noel, De Capo Press, Great Britian, 2007. 

Monday, September 17, 2018

The Vail House, c. 1805, Bennington, Vermont


The Vail House was deconstructed this past summer for repair and reconstruction in another town.


It was once one of the most stylish houses in Bennington, its architraves and columns more complex than most local houses, its fanlight and surround unique to this part of Vermont. 
Similar details exist on a few houses across the border in New York.

The Victorian updating can be seen here - the double windows on the first floor, right, and the porch with curly brackets   Well executed at the time and then let go.
  I measured and photographed it about 4 years ago. I wish I had documented it more carefully. I have no image of the front of the house!

On September 16, I will include its  geometry as part of my presentation  'Practical Geometry' for the Bennington Historical Society lecture series at the Bennington Museum.

The family wanted a broad front hall with space for a sweeping staircase. This was the new style. The framer's answer was to  add 1/3 of the width to each side. The red square in the center shows how this worked. It was divided into 3 equal parts using the Rule of Thirds.
The house was to be 3 parts  deep and 5 parts wide. 

As you can see the division into 3 is not quite where the posts and beams are.
While the size was set by an addition of proportional lengths, the rooms were set by a different application of the Rule of Thirds . I call it 'Crosses Squares' .

 Each side is a square, the Rule of Thirds applied to each side makes the front rooms square, the back rooms long and skinny, The posts and beams are set where the walls will be. 
Usually the front hall will be the width of the extra third. Here you can see that it is wider.  Or perhaps the house is wider... slide those 
squares on each side towards each other about a 12" and the  crosses squares would mesh.

The floor plan is traditional for this part of Vermont: 2 square front rooms, a long skinny space in the back divided into smaller rooms, the plan of a salt box. I wrote about this in an earlier post:

 This is the west elevation. The shutters are a later addition.

Here is the Practical Geometry: a square in the middle, with the left and right sides 1/4 of the whole. The Lines locate the windows' size and placement. The sash themselves are squares, which is in keeping with the layout. The  decorative architrave's height is determined by the half of the square.

As I did not measure the exterior extensively I have not tried to layout the geometry of the corner boards or the frieze.
The photographs show that I have not accurately located the quarter circle vents in the eaves.  They are farther apart than I drew them, The proper location is probably on the 1/4 line of the square.
I think the roof pitch matches the Lines which divide the square into quarters - or the dash dot line I use to call out the left quarter of the house. This would be a logical choice:  a natural choice, using proportions the framer already is working with and also complementing the design of the house.  

Sunday, September 2, 2018

Practical Geometry - what our ancestors called this geometry

Practical Geometry.
It's what our ancestors called these diagrams I draw.

 Here is Peter Nicholson who wrote about Practical Geometry. His writings make clear that geometry was once an expected and necessary part of construction, used both by the designer and the artisan.

His first book, The Carpenter's New Guide, published in London in 1792.

He begins with a Preface, some of which I quoted in an earlier post:

Page 2 is copied here.

The use of geometry in construction was so accepted that Peter Nicholson waits until his third paragraph before he shares that geometry is useful in mathematics and science too.

By the time of his death in 1844, Nicholson had published 27 books in London, New York City, and Philadelphia.  More than 10 years later his books were still in print.

This portrait is in his updated book The New and Improved Practical Builder, published in 1837.

This time he writes a whole paragraph explaining Practical Geometry. Has he been asked to be more thorough? Have the new uses of geometry in science changed the perception of what geometry is? Have men become carpenters by necessity - especially in the New World - rather than by apprenticeship, and thus desire to educate themselves?

Here is the Introductory Chapter

The second paragraph describes the 2 branches of Geometry: Theoretical and Practical.
Now  the Theory of  Geometry is carefully described, including a reference to Euclid, but it is still one of the 2 branches of Geometry.
The other branch, Practical Geometry,
 allows "the architect to regulate his designs and the artisan to construct his lines". 

Later, on page vii, he writes, "There is no mechanical profession that does not derive considerable advantage from it."

first portrait: by James Green, 1816, now in the National Portrait Gallery, London
second portrait: the frontispiece of The New and Improved Practical Builder. Don't miss his compass.