For your viewing pleasure: Donald Duck Discovers Geometry!

I am busy preparing for the Timber Framers Guild Annual Conference next week: posters for the bus tour people  to consider at the Sandown Meeting House, a power point presentation for the session on the following day.

I have learned so much since I began blogging about geometry and construction that many of my diagrams have needed to be completely rethought and redrawn. I expect to learn more from the other speakers. I will take notes.

Meanwhile my cousin who is a Coastal Engineer sent me Donald in Mathmagic Land:



The cartoon is long, but fun and full of geometry. The Greeks play jazz and explore the Golden Section. Donald tries to play chess with Lewis Carroll's Red Queen. But it also features lots of those pentagons that Jay Cougar White Cloud has been telling me I need to learn about! I think he's right, I just haven't uncovered any yet.

Basic geometry - Sandown Meeting House revisited

I have just revised the post I wrote on the Sandown, NH, Meeting House.
 http://www.jgrarchitect.com/2014/02/sandown-new-hampshire-meeting-house-1773.html

I have learned a lot more about early New England geometry since I wrote about Sandown in February. I have been in the Sandown Meeting House, sat in the pews, climbed among the trusses, stood at the lectern in the pulpit. I have visited and explored the geometry of the Parson Capen House, 1683; and the Rockingham, VT, Meeting House, 1785-1800. I am reading Palladio's 4 Books.
I revisited the Sandown measured drawings, found simpler, cleaner geometries which could have been employed.
A new post would have let the old diagrams remain. They are better discarded. I really didn't want anyone to come across the old post through an internet search.  So I redrew and rewrote it.


People had looked at that post 84 times before I revised.
If you are one, please go back and read the new version.


Some of what I learned:

 - How to divide a square into halves; more importantly, why.
Follow the progression on the graph paper here: #1-#2-#3-#4 - counter-clockwise.
I saw how that geometry informed the Parson Capen House.

- What patterns happen when the square in question is divided both horizontally and vertically - see A, B, C, D, E.
- And all the diagonals added.
- And then, imagine 2 squares overlapping! Since this happens at all 3 of the meeting houses I've studied, I needed to think about it more carefully - see F, G.

- And if overlapping is reasonable, how about turning the square 45*, on its point?  See H. The circle surrounding the square is really unnecessary, and, I think, probably not used. Imagine G or H with all its diagonals as in F!
I presented some of that in my diagram for the doors of the Rockingham Meeting House.

Finally I have been trying to understand the influence of Palladio on American vernacular architecture before the 1820's in terms of geometry.
We seem to use squares as a base in New England, and daisy wheel circles in New York. We use 3-4-5 triangles, especially when building an addition. About 1800 the more urban builders seem to begin to explore the Golden Section and less traditional ways to use geometry.

Currently, I do not see builders north of Boston using circles before 1790.
And I will now be skeptical when I see what appears to be a Golden Section. The turned square - H above - uses diagonals just as does the Golden Section. But within the confines of the square, not as an extension.

The French Andrews House Geometry - Part 2 of 2

The geometry of the floor plan of the French Andrews house focused on the fireplace and chimney mass. Two squares determined the space and the surrounding post and beam frame.  (See Part 1)
Did the framer used the same pattern on the elevations.
He did.
The red squares in the center of the front elevation show this. Starting from the stone foundation, the width of the firebox is also the height to the 2nd floor - the location of the 2nd floor beam. The square above determines the attic floor - the placement of beam at the eaves. The top of the third box is at the height of the ridge pole.
Both sides of the front elevation are squares with one longer side determined by the radius of the circle which fits around the square.  For clarity I have only drawn the square with its diagonals on the west side and I have only drawn the arc in question, 1/4 of the circle.    

 The east and west elevations are identical except that the location of the 1st floor door shown here is the location of a window on the east side.
Again the square is the determining geometry. I could have overlaid my red squares in several different patterns which all worked. I chose this one because it shows how the arc hits the center of the window, the center of the original house, and the edge of the square is also the edge of the door frame.
The north side of the west elevation is a duplicate, reversed, of the one shown. Again I didn't draw it so that the pattern would be easier to read.

 This is a geometry for framing. The squares lay out beam and post locations, not necessarily walls and room sizes.

I wondered how the lean-to was laid out, especially since it was added later and its floor plan used the 3-4-5 triangle, not squares, so that the wing would line up squarely with the existing house.
The lean-to elevation is also laid out with squares, but these begin not from the foundation, but from the first floor - which makes sense  - it was a given.

The roof pitch surprised me because it is so obvious: the diagonal through 2 squares. Given the pattern already established it came naturally and is steep enough when shingled with wood shakes to keep out the rain.

Sometimes when I see these patterns emerge I shake my head and look at myself askance, "Of course! What else would have worked so easily?"

 On the second floor plan are dotted lines indicating the exposed beams overhead. Using my calipers I scaled them and found they made a square. They are not the dimensions of the 'chambers' - they mark the outer edges for the placement of the posts and beams.
Next, drawing the arc based on the length of the square I marked where the arc crosses the diagonal - the Golden Section. All the windows in the south elevation (except the one above the front door, see Part 1) are placed by the Golden Section. The windows are not centered by the Golden Section as they would be a few decades later. Instead the line marks the side of the window. It tells the carpenter where to start to frame the window opening.

Enjoy how the stair hall space within the beams is also a square, although the hall itself is slightly wider as the walls have been placed on the other edge of the beams.

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.

The Locke Tavern, once a saltbox - Part 4 of 4

During the recent updating of the plumbing  for the Locke Tavern  the floor between the first and second stories behind the center chimney was removed.
I took this photograph standing on the first floor looking up at the exposed second floor wall between the old bathroom and the northwest bedroom while the carpenters worked around me. They were very pleased to share what they had uncovered. Here is what we saw:
* Modern plumbing running next to the chimney stack to the left as we expected.
* A diagonal beam with stud framing below and above that do not match up - ie: the beam was there before the framing.
* A door opening into the nw bedroom  - the white angle on the right.

The diagonal beam is the beam for the original roof over the back wing .
On the top edge of the beam you can see where the purlins were let in. Over that would have been laid the sheathing and then wood roof shingles.


The Locke Tavern once had a lean-to back wing. The space was served by a third fireplace set against the chimney block.
This house shape is referred to as a 'salt box'.
Sometimes these wings were added later, the new roof laid over the existing one, often at a slightly different angle. I have not yet seen how these 2 roofs join.



For readers who don't know about the  form: Here is a picture of a saltbox c. 1715: the John Kimball House in Ipswich Mass. The name was applied to this way of  extending a house much later, in the 1890's. It comes from the shape of a kitchen salt box of that period. Another name for this roof configuration is a "cat slide". 
I chose this house as an example because Kimballs also lived in Andover, Mass. The picture comes from the HABS archives.


This means the northwest wing was extended and a second floor added over the lean-to when the house was enlarged and updated around 1790.

How was the size of the lean-to determined? I think the master carpenter used  the geometry of the square and the Golden Section just as he did for the main house.
 In the diagram the lean-to is outlined in black (a). The square and its diagonal extended (the Golden Section)  determine both the left and right sides (b).
The center section (c) is more problematic. I wish I had been able to photograph and  measure it on site when it was open. The drawings I am using are of the house before it was opened up. Clearly the framing extends on each side of the chimney block with the kitchen fireplace set in between. There are posts in the outside wall and posts on each side of the chimney, at the back corners of the front rooms. Maybe the shape is a rectangle that has sides determined by the 3-4-5 triangle. But I don't know precisely.

It would have been so easy if the basic floor plan were a 3-4-5 triangle! But it isn't. The house measures 36 ft x 28 ft.

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

cobbler's house north of Boston, c. 1840 Part 2 of 4

Note: I have extensively revised the posts on this house. I thought at first circle geometry had been used even though it didn't quite fit. Then I tried using the 3/4/5 proportions of a right triangle. Those proportions do work. The new post can be found here: http://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html .
I have left this post because of its introduction to the house and the floor plan with circles.

Here is the farm house, a story and a half cape, the contemporary shape for 1840, but in the old fashioned pattern: center entrance, 2 windows on each side.

Its first owner is listed as a cobbler. There is a spot to the side of the house where a very small work shop probably stood. He may have made shoes for the community or done piece work for a jobber who took the work to a factory in a near by town. Often men worked in the shop  while women did similar work in the house.

In 1837, the market for wool which had made fortunes for New England farmers,- including the farms in this neighborhood - disappeared. Australia could produce wool cheaper. A 'Panic' ensued  - today we would call it a depression.

So the owner of this house was cautious and frugal. The house is small. Its windows are tiny with 27" x 22' sash - the part that goes up and down - in an era when most sash were about 30" x 30".



In my last post I wondered if my measurements were off. So I checked, redrew very carefully, and then laid out the circle geometry: 2 circles with the same radius, each circumference running though the center of the other. My last post includes a diagram of this.

It is off, just barely. If the house were 4" smaller the circles would overlap as they should on their centers.

Locke Tavern geometry, part 2 of 4

The geometry of the Locke Tavern is based on the square, but it is interesting to see how the circle that fits around the square was used.


On the front facade, I have labeled the circles 'c' . The length of half the diagonal is the radius of the circle. The edge of the circle determines the space between the two squares, how the squares relate to each other. It is also where the front door is.
The men who updated the house in the 1790's clearly recognized the original pattern: they worked with it, using the square's diagonal to determine the size of their additions.

This is not design based on the 6 part geometry of the Daisy Wheel. The layout may have begun with a circle, but its use seems subservient to the square.
We know that house-wrights brought their knowledge with them from not just the 'old country' but specifically from their old neighborhood. And they passed their way of building on to their apprentices. Differences based on the origin of the colonists are visible in timber framing, barn and house layout. They are also visible in little things, like the shape of trunnels - the wood pegs that hold mortise and tendons together. Is this another regional variation?




On the floor plan the arc of the square -marked 'c' - of the smaller room to the left includes the chimney stack.

So, is that fireplace part of the 1740 house?
The room needed heat. But in cold New England fireplaces were never built outside the frame, even in half houses, where the second part came later.
Was there a little entry to the left, since enlarged?

I doubt this room was part of an earlier house (that the front is a newer wing) as it lacks southern orientation.

All this, of course, makes me wish I knew more about the construction of that part of the house and its foundation.
Ah, the joy of being present when things are taken apart!

Luykas Van Alen House, 1737, Kinderhook, NY, Part 1 of 4

The newsletter of The Society for the Preservation of Hudson Valley Vernacular Architecture arrived this week,Vol. 14, No. 10-12. Walter Richard Wheeler described the documentation before the Luykas Van Alen House in Kinderhook, NY, was restored.

Here is a partial view of the HABS drawing reproduced in the newsletter.

(1934, HABS, Adam Van Alen House, Kinderhook, NY, E. J. Potter, delineator. Please see the foot note for explanations and caveats.)

This morning I took out my compass to see what I could learn about the design of the house.

I used the HABS 1934 floor plan for my base drawing. As this house was built by people of Dutch descent who would have known Dutch framing systems from the Continent (NOT England) I was uncertain about what I would find. I looked first at the main house, the 2 rooms with fireplaces on the left. The floor plan fits within the circle.

Then I looked at the wing - the right side beyond the stair. It is thought to be a little later, perhaps beginning as a barn. Here the layout is more complex: (A) is the arc from the length of the wing. It intersects the continuing length of the house at the location of the partition. (B) is the arc of the width of the house and wing. Its length seems to determine the placement of a beam beside the stair. Its diagonal (C) may determine the location of the door and steps into the room on the end (the north room, on the right in the drawing). One would enter the room on the corner of its square, the room itself is the Golden Section.

Footnote: I also found the beams to be located at points determined by circle geometry. However:

The drawing I am using is very small, About 10 ft = 1 inch. As a architect I consider this to be 'schematic' - definitely too small for construction. The elevations in John Stevens' book are only about 1"=20', much too small to be able to identify a relationship between the plan geoemtry and the elevations. The next step is to print out the HABS drawings which are available on-line.

I am also thinking about how the circles were actually used. The builders might have drawn the first circle on the ground where they intended to build. Or maybe not.

2/3/2-12: I am not really comfortable with this analysis. I have decided not to delete it until I have better understanding. But read it with skepticism!

HABS: Historic American Buildings Survey

http://en.wikipedia.org/wiki/Van_Alen_House is an excellent introduction to the house. It includes a photograph which shows the main house and the wing.

The best book on Dutch 'Colonial' construction is Dutch Vernacular Architecture in North America, 1640-1830, John R. Stevens, HVVA, NY, 2005
.

Regulating Lines #3 - Architecture

In November, 2009, Laurie Smith gave a workshop and a lecture at The Timber Framers Guild Eastern Conference in Saratoga Springs, NY.
Laurie Smith is a designer and a historic design researcher from Wales who is investigating the use of geometrical design in medieval Britain, documenting the use of circles and 'daisy wheel' geometry in the design of houses, tithe barns, and cathedrals. Ely Cathedral is pictured here.
His work is thorough, fascinating and thought provoking. Some of what he has written has been published in Timber Framing, the Journal of the Timber Framers Guild, www.tfguild.org.

My professors in architectural history had been in Europe after WWII. They told us about cathedrals in which the 'mark' (similar to a signature) of the stone mason could be seen on the parts of the columns. The marks were derived from the Golden Section.

Vitruvius, the Roman architect and engineer who wrote De Architectura, (On Architecture) in 10 books, writes about geometry and proportion, including the description of man as the basis for design that Leonardo da Vinci drew as the outstretched man in the circle. (I use a print by Cesare di Lorenzo Cesariano, c.1521, here.)

Peter Tompkins' Secrets of the Great Pyramid spends several chapters explaining how the pyramids are designed using the golden section. His book has much information about ancient Egyptian astronomy and
mathematics.
I didn't know about this book until a friend put his copy in the mail to me. Thanks, Bill. You'll get it back!

Arthur J. Lawton, and some others, researched the use of the square and its diagonal in Pennsylvania Dutch construction. It was published by the magazine, Pennsylvania Folklife, in the 1970's.
Section, its permutations, and the resulting regulating lines.

Regulating Lines - an Introduction

The feed-back from my post on the regulating lines of Lorenzo has been considerable. So I am putting forward for your consideration what I know about geometry and pre-Industrial Revolution design. Mainly:

Regulating lines are not mystical or mythical. They are not magic.They are simply geometry applied to design and construction.

They began as an accurate way to measure and layout design when people had only simple tools: a point, a line, and something to mark with. The line could have been string, a rope, a chain. The marker could have been chalk, charcoal, a stylus on wax or wet clay.

Find some wet sand, a beach perhaps. Make a knot in a length of string. Tie a stick to the other end. Use your thumb on the knot to hold the end of the string on the sand. With your other hand pull the string taut and trace an arc in the sand with the stick. You have begun to use geometry to design.

Geometry can be read by 'illiterate' people, or rather: People can be literate in geometry without knowing numbers or letters. It is a separate language which, like music, does not need translation.

I will list the sources I know of in art and architecture. I hope there is more I just haven't found, yet.

regulating lines for Lorenzo

The back cover of the brochure for Lorenzo, shows this picture accompanied by a good discussion of Vitruvius and his principles.

Unfortunately no one signed the article. I would like to discuss the ideas, especially 'regulating lines', with the author, but I haven't yet found a way. So I am posting this here.

I don't think the star shows the regulating lines used to design the house. The star is not regular in shape. Shutters like the ones on the house in the photograph were not in use until about 20 years after the house was built, so those points are not important elements of the design. The pediment was also added later.

My sketch shows the basic elements of the original house: the shape of the facade, the pilasters which sit on brick pedestals that are part of the foundation, the arches which join the pilasters, the door with its sidelights and fan. The windows sit quietly between the columns.


Here are the regulating lines - superimposed in red - that I think were probably used to determine the proportion, rhythm, and details of the house. These lines were easily drawn with a compass ( or dividers), one of the tools we know house wrights owned in the early 1800's. The center block of the house is a square. The width of the wings on each side is determined by the diagonal of the square used as a radius. The three bays in the center box are also the same width as the wings, and are delineated by the pilasters. The importance of the pilasters is emphasized by the pedestals in the foundation wall, the arches which join them, and the placement of the posts topped by urns in the roof balustrade. Curves, circles, ellipses draw the eye: here to the 5 bays, the door.

The height of the entrance is determined by the center of the square. When the pediment was added, its height was determined by extending the arc of the diagonal. Its ellipse is the same curve as the fan light. Pretty simple: each piece is determined by the whole. The curves reinforce the concept.

I played with the arch over the windows. Hmmm. It was a structurally sound way to finish the brick pilasters and create a frieze. It emphasizes the bays and formal composition. But the curve? The photograph is too small to figure out where the radius of that arc originates.