Railroad Warehouse Frame c. 1850, Richmond, VT

I first wrote this post in March, 2014. I have now updated it.

This is the model of the post and beam warehouse frame that Mark Goyette wanted to use as the frame for his new house.

Mark's model is not as tall as the original warehouse. He decided to lower the structure so that the ceilings for his house would be 9 ft. high instead of the original 13.

The warehouse was built along side the railroad in Richmond, VT, in the 1850's. It is square rule framed.
By 1850 the need for consistent dimensions in industrial applications had become obvious. Many different individuals owned the various railroads. However, engines, carriages and box cars needed to transfer smoothly from one set of tracks to another - all the rails needed to be exactly the same width and profile to accommodate the wheels which also needed to be the same dimensions.

I was very interested to find out if this warehouse, built to service a railroad, was framed by geometry or the new idea of standard dimensions. Mark Goyette, who restored old cars professionally, was curious too; he had, after all, built the model in order to understand better what he planned to erect. So, I drew up the section of the warehouse to find out what was there.



Such a simple, elegant design!

The necessary width determines the square which determines the height.
The 3-4-5 triangles determine the roof pitch. 2  3-4-5 rectangles are the box. The location of the cross tie  is set by the intersection of the square's diagonal and the triangle's hypotenuse.
The roof pitch is - in modern terms - a 9/12 pitch.




March 6, 2020 update:
 
The frame is 5 H bents. The bent shape looks like an H because of the  'dropped' plate - see the arrow.  This is how many barns and houses in southwestern Vermont in the Hudson River watershed were framed, and is a hallmark of Anglo-Dutch framing, 2 framing systems joined.
A Dutch frame would have bents about every 4 feet. An Anglo frame spaced the bents between 15 and 20 ft.  These bays appear to be 12 ft. apart.
A Dutch frame has the bent's plate framed into the post on the side, below the plate that carries the rafters. An English bent has both plates joined to the post at the the top, at the same height. This requires a more complex mortise and tenon joint.

Finding this hybrid frame in an ordinary service building, built by a corporation - not an individual framer who has moved upstate and taken his framing traditions with him  - in northern Vermont in 1850, is surprising and interesting .
   

Thanks to David B. AdolphusTravers for the photograph.

Tuckahoe Plantation, Richmond, Virginia, 1733-50

Update: August, 2023. This post needs revisions. 

In the last 9 years I have learned a great deal about practical geometry.  I have also read Material Witnesses, Camille Wells' book, published in 2018 by the University of Virginia Press, about domestic architecture in Early Virginia. She writes about Tuckahoe in great detail. 

I will leave this as I wrote it in 2014 until my new drawings are ready for publication. 

 

I visited Tuckahoe Plantation recently.  I wanted to see more brick work, after studying the walls of Gunston Hall.

The Tuckahoe Plantation Main House has brick end walls on the south wing, c.1733.  HABS has drawings that I could use, even though they are very small: 1/8"= 1'-0"

The  Plantation is on a bluff above the James River.Originally visitors came by boat. I came by car, turning off a narrow road onto a dirt lane lined with trees and pastures for horses and cows. Finally the buildings appeared, and parking for my car.  I liked entering on foot at a slow pace. There are few signs, and no visitors center. I was almost the only person on the grounds and enjoyed it all, even as I was studying the buildings, thinking about them carefully  I hope to go again for a thorough tour of the house (open only by appointment).

The upper photograph is of the south wing facing the James River. The second is the west wall of the south wing.



As the floor plan shows the House has two wings joined by a Great Hall. It is also surrounded by stately trees and shrubbery, therefore hard to photograph as a whole. The end walls of the south wing feel much more hand wrought than do the walls of Gunston Hall. There is also a subtle brick pattern, dark and light. The North Wing end walls are not brick.
The foundation (above grade) for the house is brick, but the north wing, added in 1750's does not seem to have a basement - no windows or doors, only vertical slits in the walls. I wondered if this difference, as well as the change in chimney construction, would also be visible in the geometry, whether it represented a change in how the north wing and possibly the Great Hall were considered, laid out, and built.

Here are the diagrams. The geometry does change.

I have drawn 3 green diamonds on the South Wing (They could be 3 squares, same proportions.) To the center one I have overlaid the red square and added the diagonals of the half squares which cross at the walls of the South Hall. The points of the diagonals also determine the window openings. The rooms are not quite square.

Both of the North Wing rooms are square - noted by green squares with their diagonals. The squares divide in thirds - red lines in upper square. Then  a new square - drawn in red - is extended to determine the width of the North Hall.

The Great Hall is 2 squares crossed. I've drawn one in green, the other in red. The space where they cross is the entry, the crossing determined by the squares divided into thirds.

I wondered if the brick end walls would be 3-4-5 triangles, which would be structurally sound. They appear to be - see the green diagonal on the south end wall. The window and door sizes and placements do not neatly fit the pattern.

The Great Hall elevation is crossed squares - in green, just as its plan is. The edges of  the squares mark the edges of the windows. The diagonals' crossings mark the height of the door, the centers of the door panels.

The North Wing end wall is 2 squares - in green, divided in halves and thirds - in red. This also continues the floor plan geometry. The roof pitch comes from  the frame - not quite a 12/12, determined by the geometry, not by numbers.

The North Elevation can be looked at two ways.
On the right I have drawn the square (the diamond which marks the centers of  the square's sides) beginning at grade, including the foundation. The left edge is at the door frame.
On the left side I have drawn a square with its diagonals. The length of the square is the height of the wood frame of the wall of the wing; it does not include the foundation. That square ends at the edge of the paneling for the entrance, which are noted on the floor plan.

I do not know enough about the framing for this house. In the Northeast I have seen and worked on many buildings from this period and have knowledge of standard framing and regional variations. I can show how the geometry determined the framing and therefore the design. I wonder if Tuckahoe's framing changed between 1733 and 1750.


Part of my reason to visit to Tuckahoe was to see its intact measured one and  two room houses that looked in the HABS drawings very much like the houses Henry Glassie wrote about. I will write about that next.

Gunston Hall, Mason Neck, Virginia

updated 5/14/2014

Gunston Hall was built from 1755 to 1759 by George Mason as a home for his family on Mason Neck, Virginia.

Gunston Hall in February, 2014,  photograph by Justin Wilcox, through Wikipedia.
The drawings are from the HABS collection.

Gunston Hall, Return to Splender, the 50 page booklet published by the Board of Regents in 1991, came to me from a friend who knew I would like the pictures, the excellent recounting of the history of the house and its restorations, and the HABS drawings. She was right.

The booklet relates how George Mason began the building himself and then had his brother find and send  William Buckland from England to help him finish the work.

I was intrigued by the fact that George Mason, a very well educated man, realized that he needed help. I wondered if I could see why by looking at the drawings. He knew enough about construction to begin. What happened? Would the expertise William Buckland brought to the work be visible?



George Mason knew about what kind of  plan would fit his family and their life. He knew how to build with stone and brick, how to set a foundation, cap a window, taper a gable, frame a roof. He knew enough geometry to use 3-4-5 triangles and their permutations.

Remember that the diagrams can be enlarged by clicking on them.

The plan  is 4 triangles, or 2 rectangles with 2 sides 3 units long, 2 sides 4 units long. On the right side he has divided the rectangle in half to make his two formal rooms. He has laid out the diagonals of both smaller rectangles. Where they cross he has placed the wall at the edge of the hall.

Note that the rectangles do not meet at the center of the main doors, but to the right side.

The left side of the house was the family dining room and the Masons' own room which Ann Mason also used as office as she managed much of the plantation.

Here a hall separates the rooms.To determine the width George Mason divided the rectangle in half lengthwise and then added the diagonals. The center point is the location of the inside of the wall to the hall. Where the  diagonals cross to the other side of the brick wall, the corridor walls begin. Note that the stair width is also determined by another division of the rectangle and its subsequent diagonals.

On the right side the inside space is divided - it would be smaller than the outside space - into thirds to place the fireplaces in the center of the rooms. I think it is possible that this is one of the changes Buckland made.
Understanding that wall thickness can throw off symmetry comes from experience. Buckland had training as a finish carpenter (a joiner), but he was young, just 22. Mason was 30; he knew brick and mortar, not perhaps not the finer points of symmetry. Proving this supposition would only be possible if the chimney stack was opened and taken apart - not very likely! So this is truly conjecture on my part.



The end elevations continue to use the 3-4-5 triangle for its proportions.
The door is centered. The top of the brick walls is the top of the rectangle.  The gable repeats the triangles. The bricks end on the upper edge. The shape is square and sound, made possible by the 3-4-5 90* triangle which is always true.
I have noted with a strong dot on the upper diagonals how the window height and location are also determined by the diagonal intersections.

Note that the depths of the porches are also 3-4-5 triangles -  drawn in green.

So then to the main elevations, one facing the water, the other the road.

 We already know that the left and right sides of the house are not equal as George Mason wanted larger formal rooms on the right side.

 Here is where I think he got himself in trouble: the left side is truly not as long as the right - see the dotted red line. Look carefully and the dormers: they are balanced but not symmetrical, nor evenly spaced.

 Perhaps Buckland stepped in here, adding the windows on either side of the front door.
What he really did was divert the eye - he added the Gothic porch to the river front: inviting, decorative. with half circles and Gothic curves. We are drawn to the porch and ignore the symmetry.

March 18, 2023: I wrote this almost 9 years ago.  I now know a lot more about Practical Geometry. Please also see my most recent  post about the porch: 

https://www.jgrarchitect.com/2021/07/the-geometry-of-gunston-halls-north.html

I will not delete the following discussion of the porch design. I want a potential geometer to see that as we recover a lost skill we make assumptions and therefore mistakes. That's ok. It's part of the work..

 

Here and in the house his knowledge of Palladio and what was fashionable in England is obvious. William Buckland knew the classic vocabulary. The booklet shows how plain the walls were without his embellishments. His  use of geometry was also much more sophisticated than George Mason's.

The road front porch which we see today came later, after the Revolution. As roads and bridges improved visitors arrived by carriage, as well as by boat.
The center arch within the pediment, flanked by openings marked by classic columns and lintels, comes right out of Palladio's Books.
And it creates an inviting porch. It is scaled to people - we would like to standing there, hand on the railing, welcoming a guest coming down the drive.
 This layout that we now call  'Palladian' was already widely used in Virginia churches where it was referred to a 'Venetian Window'.

I have drawn the first square - set on the diagonal -  that comes from the height. From that comes the outside dimensions, the outside square, and the square turned 45*. The lines regulate the roof pitch, the floor, the line for the lintels. No doubt he adjusted the size of the square to fit the space.


Then the squares are divided in half and the diagonals added. Now the placement and the width of the columns is determined.

I add this diagram to show how the semi-circular arch in the pediment unfolds down the center of the porch to mark the top of the columns, height of the railing and lands on the first step above the foundation.

18th C. Virginian Folk Houses, Part 2

Please see 18th c. Virginian Folk Houses, Part 1, where I describe why I am looking at Henry Glassie's book, Folk Housing in Middle Virginia, 1975, U. of Tennessee.

NB: These 2 posts have been updated with new posts as of November, 2022.

I am using Dr. Glassie's drawings. I am thankful for the chance to look at the geometry to the houses, many of which no longer exist. But I can't verify when I have a question. For example, "Is the window right there or maybe a few inches over? That would fit the symmetry.... " "The drawing isn't quite square. Is that caused by
the printing or was it real?"

I would really like to have been there as the houses were built. Then I would know. I need Dr. Who's Tardis.

So, between now and the loan of the Tardis, I have decided to make some assumptions for this next house.

It is the Lesser Dabney house, figure 45, Type 3, House V.Dr. Glassie's book includes a photograph and several other drawings of the house. It was probably built after 1770.

The original house included the chimney, but not the shed on the right.





 I have outlined the house in red.
There are 2 overlapping squares -'a-a-a-a' and 'b-b-b-b',  or 3 equal rectangles made up of 2 small squares each - 'a-b-b-a'. or half of the large square. This is where I am taking liberties - Dr. Glassie's proportions is not quite as true as I have shown them. The parts do not line up as neatly if I scale on his drawing. But when I make them neat - a couple inches either way, they fit in a simple pattern.

I have drawn the diagonals that determine placements with a green dashed line. The determining lines are a green dash and dot line. At the end of the ones I think are where they belong I have added an arrow. Where it doesn't quite work - but so close! almost! - I have added a question mark:'?'. The shed's dimensions are determined by the width, divided in 8 parts, and the length, the extension made from 3 of those parts. This results in 2 3-4-5 triangles and assures a square fit of the wing to the house.





Here is the roof frame of the Lesser Dabney house,
Figure 69, The Loft, a section through the frame of house V.
Dr. Glassie included the interior wall finish (I think). I have left out that line.



Thinking about how the roof would have been framed to sit on the walls below, I extended the line of the posts as high as the peak. Then I crossed the diagonals to make the square, and crossed the collar ties at their juncture with the rafters. The center-line of the square crosses at the top of the knee walls. the diagonals of the half square cross the diagonals of the full square at the ceiling joists.
I am sure there were other considerations: reinforcing the eaves where they kick out, and tying together the rafters at a point where they will adequately hold the frame, but leave enough head room to make the attic useful.





Both of these two houses are they were printed in Glassie's book, Folk Housing in Middle Virginia. I didn't adapt anything. The geometry was obvious and easy.

This is Figure 39, The Central Hall I House, West of the Blue Ridge. A.
It is in the Valley of Virginia. The right side, through the entry hall, is built with logs. The left side added later.
The pattern of the original house is familiar: the square - red solid lines - and its half squares - red dashed lines - with the intersections of the diagonals marking window openings, chimney width, placement of the wall between kitchen and entry hall, and the  1/4 width added to the square to give the entry hall enough space for a turning stair- green dash and dot lines.

Then the left wing was added. Its dimensions are the 3-4-5 triangle - black dashed lines - with the existing wall designated as '4'. Its center-line locates the windows - green dash and dot lines again.
The windows on the front wall are not quite equi-distant from the corners, but close enough to read as balanced.

Finally,  Figure 39, The Central Hall I House, West of the Blue Ridge, B. A house in Falmouth, Pendleton County, Kentucky.

Both rooms are square - red lines, their windows, doors, and fireplaces are on axis - green dash and dotted lines. The circle around the square - red dashed line - determines the width of the hall, the relationship between the 2 rooms. It could also be found by turning the square 45*. Those intersections also place the doors into the hall and the fireplace and closet in the left hand room - green dashed lines for the turned square.
This  house, if its chimney in the right hand room for a cast iron stove was built with the house, may date to the 1830's.

The French- Andrews House geometry, Topsfield, MA - Part 1 of 2

updated 1/ 2019: the geometry is not the Golden Section. It is the square and its diagonal which I have found in many later houses.


When I was thinking about the original salt box shape of the Locke Tavern, I looked at other early Georgian saltboxes I knew for a comparison.
I thought I would find a similar geometry that would reinforce what I had already seen. Instead I found another way to use squares and the circles that fit around them to organize a frame.

This house I have only seen from a distance. However, measured drawings for it are available on HABS. And
a website for the French Family includes many pictures and a time line.

http://www.loc.gov/pictures/item/ma1015.sheet.00002a/resource/
 www.frenchfamilyassoc.com/FFA/ARCHITECTURE/Topsfield.htm

The French Family site says the house dates to 1675. The HABS drawings, done for SPNEA ( now Historic New England) in 1933, say 1710. Abbot Lowell Cummings says 1718. In any case it predates the Locke Tavern, and it was built in the same neighborhood.
Here is what I can see about its construction by looking at its geometry.

 Notes on the drawings for the second floor say at the wall between the lean-to and the upstairs bedrooms: "rear wall old weathered clapboards... balance of wall is shingled". This means the lean-to was added; the exterior siding left in place. I have seen this in other early houses. It is not unusual.

It does mean that the front of the house, the chimney, the hall and the chamber were built first.

The geometry for the main house is the square and its diagonal. The entry and chimney block consisting of 2 squares (red x's in the center) The corners would be the location of posts and bearing for the summer beams - the beams which are in the center of the rooms.
The size of the rooms is determined by the extended square and its diagonal (dotted red line showing the square and the diagonal).

The front door is not centered. For a while I thought this might mean one side of the house was built before the other. But then I realized that for the door to swing fully open it had to be off-centered, and that I had seen this layout in other early small houses.
You can see in the elevation that the hall window above the front door is also not quite centered - but carefully placed to minimize the asymmetry so that it would not apparent at first glance.
Here I have to stop and appreciate the builder who understood how far off from the center of the door and then, from the spot equidistant between the 2nd floor windows he could position the window where it would least call attention to the discrepancy. A fine mind there, one which speaks to me today. He succeeded.
Now in January 2019, I am wondering if he framed the wings after the chimney block was determined, as the Parson Capen House seems to have been. This would mean the window geometry came first, the door location last.  

The lean-to dimensions were determined by the 3-4-5 triangle (the green triangle on the plan).
This made the framing square to the house - the joists, purlins and sheathing would fit neatly, the house would be tight.
From the drawings we can tell that the width of the house was already 45'-6". The depth of the house became 34'-6".
45.5' divided by 4 is 11.375'.
34.5' divided by 3 is 11.5' .
Was the master carpenter 4+" off? Maybe. But I do not know from what place he began his dimensions - the foundation? the outside of the frame? the outside of the sheathing?
Perhaps the house shifted in 200+ years between its construction and  its measuring, or was re-sheathed. And the measurements might be 4" off.

Luykas Van Alen House, 1737, Kinderhook, NY, Part 4 of 4

In January and February, 2012, I wrote about the geometry of the Luykas Van Alen House.
The daisy wheel of circle geometry fit the plan and elevations - mostly. The right hand side didn't work. Or rather, I didn't see a consistent geometry.
To see the earlier posts, search using 'Van Alen'. 

Since then I have toured the house twice.

Once arriving early, I had a private  tour with a knowledgeable docent. After the tour she handed me a 2" thick report on the house and left me happily engaged as she gave the next tour.

The house has been measured at least 2 more times since the HABS  documentation in 1934, and the field notes of Gerald Watland and MC Hopping in 1958. Each time the chimney configuration  on the north end of the house - the right end in the drawings - is slightly different. Recently the exterior chimney visible in the field notes has been removed along with the English fireplace.
The drawing here is from Watland and Hopping's field notes reproduced in John Steven's Dutch Vernacular Architecture in North  America, 1640-1830.
Note that it shows a traditional Dutch fireplace whereas the HABS drawing shows the later, remodeled English fireplace.

 Click on the drawings to enlarge them.

So.
Where might the original wall have been?

I have 2 suggestions. Both are shown on the second drawing.
1) The circle geometry - shown in red - used for the first wing (see Part 1) if rotated 90* could have been used to determine the north foundation wall before the firebox was rebuilt.
2) A 3-4-5 triangle - shown in green - might also have been used. It fits quite well.


The family history says the north wing was added or rebuilt to be living space when the son and his family joined the father. If the foundation was already here, as shed space, then the fireplace and flue would have been added to the existing masonry.
If the wing dates from the arrival of the son, the questions are: How did the builder make it square? How did he fix the proportions when the left wing was already there? To use the same circle geometry he would have had to set the radius. He could have done that by locating the center of the circle from the corners of the existing foundation. The length of that wall is the radius.
Or he could have relied on the 3-4-5 triangle to get his corners square.

Once the foundation is in place the next step is the first floor framing.
Here is the geometry:
Shown in red: The circles based on the interior width of the house determine the wall between the hall and the parlor, the north wall and the location of the floor beam in the hall.  The center lines -'a' and 'c' - locate the wall between the left and right wings and the wall at the parlor. The intersections - 'b' and 'd' - locate the hall floor beam and the edge of the exterior wall.
Shown in green: -The parlor needed closer framing. The space, a 3-4-5 rectangle, is divided in 4 parts which determine the beam locations - 'e' .
.

Finally the window placement:

Here the 3-4-5 triangle determines the size of the space, the location of the windows and door, maybe even the depth of the side walls of the English hearth. That may be later. If so not a valid dimension. Here the red lines show the 3-4-5 triangles, the green: a right triangle (half a square). The dotted black line is the center line through the wing.

C. 1825 workman's cottage, north of Boston

This small house, built about 1825, was one of several built on a country road across from a factory.
Today a park has replaced the factory. The house is in-town. Over the years wings have been added on 3 sides. I have cropped the photograph in order to focus on the original  house.

The post and beam frame includes recycled beams. 2 have beaded edges - probably recycled from the best room of a pre-1760 house.









Here is its section - a slice through the house showing its basic layout.









Here is the 3-4-5 triangle used to determine the size and location of the walls, the pitch (angle) of the roof                       










Here is the 3-4-5 triangle used to locate the 2nd floor joists and the ceiling joists.
The dot and dash triangle determines the height of the collar ties (ceiling joists). Its
vertical leg crosses the first triangle at the location of the second floor. The second floor window locations are also set by this line.
All this also makes me think that the house frame was laid out in the traditional way, on a flat space called a framing yard and then dismantled and re-erected on site. Contractors lay out rafters in this same way today as they frame a roof.  They use the floor of the house just below the roof as their framing yard.








Here is the floor plan. I've noted the chimneys. The lathe and plaster box around the lower one includes modern plumbing, heating and electrical systems.









And here is how the 3-4-5 triangle was used to layout the floor plan. Just as the exterior sills and walls were placed inside the box determined  by the triangle, so the beams on either side of the stair were placed inside the box. The walls, set above the beams, are on the inside edge.

The chimney locations are set by the triangle, but the windows on the opposite wall are not. They are centered on the rooms.




The windows on the side walls are located by a square -  in green - based on the shortest leg of the triangle.

Cobbler's house north of Boston, c. 1840 - Part 3 of 4

I have just finished writing about the Arnold House: how it uses the 3-4-5 triangle as a regulating principal and how it is almost but is not the same as the Golden Section.

If you don't know what that is, please read the posts on the Arnold House. Thank you.

I said the same thing about this house: it 'almost used Circle Geometry', but didn't. I realized I needed to look again.

I do love the grace of the Golden Section and Circle Geometry.
But look at how the 3-4-5 triangle fits.
(A)  marks the diagonal of the rectangle created by the 3-4-5 triangle. It's half the house. The other side matches it.
(B) marks the corner of the smaller room on the right, its size determined by the triangle. The larger rectangle forms half of the house footprint. The room's proportions are determined by the proportions of the house itself.
The back wing, a rectangle that matches the 2 front sections, is a little longer. (C) shows how the extra space is determined by half a 3-4-5 rectangle.



I rather hoped the end elevation wouldn't fit the pattern!
It does.
(A) shows the rectangle created by 2  3-4-5  triangles. It fits the size of the house, easily giving the master carpenter the dimensions he needed for post and beams. It even determines the roof pitch! Not a 9/12 or a 10/12 pitch, ratios commonly used today, but the 3-4-5 triangle.

However, the floor heights, the window placement, the elevations still seem determined by both circle geometry and the Golden Section.

The house's outline - its footprint, height and roof pitch - do seem governed by the triangle.

How nice it would be if I could teleport back to 1840, watch the house-wright at work, and ask questions!

My great thanks to Jay Cougar White Cloud for his good questions that pushed me to consider the simplicity of  framing with the 3-4-5 triangle.

For the next post, and a more thorough analysis of the house click here:  http://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html

Arnold House, Westfield, Massachusetts - Part 2

Here is the Arnold House around 1933.

And below is the measured drawing of the front done at the same time for the Historic American Building survey, a project of the WPA. The drawings and picture are available at the HABS website.


In the upper left corner of the drawing I have added the 3-4-5 triangle with its 90*, right angle. To see why I think this house was designed using that ratio see the previous post, Arnold House, Part 1. Click on the illustrations to enlarge.

On the left side I have drawn in red dashed lines the 3-4-5 triangle using the first floor as the base and the ceiling of the second floor as the top. A house-wright would have used that line to determine his top plate. See (A).

The center of the  resultant rectangle is marked by the red 'x'. The 'x' is the location of the second floor beam.
The right hand edge of the rectangle is the edge for the door, telling the framer where to locate the rough opening. The windows and doors do not appear to be determined by the elevation, but by the plan. See my earlier post on the Arnold House - Part 1.

As drawn on the right side - see (B) a red dash and dot line - the space on either side of the door is a square. But the windows are not symmetrical within the box. I tried using the Golden Section. It doesn't fit. Circle geometry - here a circle based on the square - almost fits: several inches too large.

Here I used the 'face' of the house clapboard from foundation to eaves, as I think the concern of the master carpenter would have shifted from framing to presentation - how the house appears to the community.

Two squares with the arcs from their circles would have fit across the front of the house, meeting at the middle of the front door IF the house had been 9" longer - 40 ft, not 39'-3", a true 3-4-5 rectangle. Was the foundation not true? The house-wright inexperienced or lax? If the wood was green would it have shrunk 9"? Or?

For reference I have added a diagram of a square with the circle whose radius is half the square's diagonal.


This house is no longer there. I would very much like to be able to see it,walk through the rooms, sense the proportions. I want to know if it feels differently because the ratio is mathematic, not geometric.


The 3-4-5 triangle is not the Root-Two Rectangle. The diagram here shows the difference geometrically : the triangle is marked off in red, the ratio (a square and the length of it's diagonal) in black.

 In algebraic language : (a x a) + (b x b) = (c x c)
                            (3 x 3) + (4 x 4) = (5 x 5)  or   9 + 16 = 25

For the Root-Two Rectangle to equal the triangle, if the side were 3 then  the diagonal of the square would have to equal 4. It doesn't.
                    (3 x 3) + (3 x 3) = 18   the square root of 18 is about 4.25


I think the evidence is too strong that the house-wright was using the  3-4-5 triangle to put together a traditional looking house. The fact that circle geometry almost works is just that - it is almost the same. But it isn't.

updated 12/31/15

Arnold House, Westfield, Massachusetts - Part 1

The Arnold House,Westford, Mass. c. 1800, was measured by Edward E. Jordan for the Historic American Building Survey.
On the first HABS sheet is written: "Note: house partly destroyed by fire during winter of 1933-34." I know very little about the house or the family. Probably the builder was Joseph Arnold who died in 1823.


While I was thinking about how this house was laid out, a friend asked if I had ever seen the 3-4-5 triangle used for design. Like the circle and the square it is independent of fixed dimensions. It is simply a ratio that always produces a right (90*) angle.


I had not seen it, but I began to pay attention.







So - look at this house. Click on illustrations to enlarge.

Note the outside dimensions -
 30'-6"  by  39'-3".
For a wood frame, post and beam, hand hewn house that's close enough to 30ft. and 40 ft. So for the 3-4-5 triangle the diagonal across the house, (A), should be about 50 feet long. It is.

Then look at (B), the diagonals of the front rooms. The same angle gives the dimension of the parlor. The diagonal (B) in the Living Room is not as clean, but still defines the size of the fire places and chimneys and the post location at the rear of the house. (C) determines the post location in the Dining Room.

The 3-4-5 ratio also gives the locations of the windows, at least one door and the size of the Room behind the Parlor.
Here I have added what I think was the original back wall of the Parlor for clarity (X). I have also used a red line with a dot for the rectangles created and the center lines of the doors and windows
(D) shows the Parlor window placement on the side directly on the center of the room, the front windows equidistant from the center.
(E) shows the window spacing in the Living Room determined by the rectangle turned on its side
(F) places the center line for the Dining Room window and door at the edge of the rectangle.
(G) determines the size of the Room behind the Parlor and the location of the stairs.

Next I will post the front elevation and add some ideas I have about the house design.