Practical Geometry - Drawing a Square with a Compass, Part 1

Draw a square with a compass? !
Yes.
Here are 2 ways. There are several more.

Compasses make circles. Straight edges make straight lines. Together they can lay out whatever you can imagine.
 
How to Draw a Square with a Compass #1

1)   Choose a length: A-B.  It is also the radius: dashed black line A-B,  for drawing a circle with a compass.
2)   Draw the circle.

I have drawn these diagrams on graph paper, a reference to help show how the square grows.

3)  Switch ends. Hold the compass on B. Swing the arc from one side of the circle to the other: G-A-C.
Hold the compass on C. Swing the arc to find D.
Use D to find E; E to find F. along the circumference of the circle.


The circumference of every circle will always be divided into 6 equal parts by the radius of that circle. The length between each 2 points around the circumference will always equal the radius.

It's easy to draw a daisy wheel. 

However, to construct a square the petals are not needed, only the 6 points on the circumference.

4 )  F-G is the line. It is the same length as the one chosen at the beginning, just in a different location.

G and C are 2 points. that can be connected by a line.
So are F and D. 
They are the same distance apart so they are parallel.

A square has 4 equal sides.  (Just a reminder)
5)  An arc the length of  F-G swung from either F or G will mark  G-H and F-I the same length as F-G.  This is the same length as the chosen line A


 







A square drawn using Practical Geometry, using a compass.  
To check: lay out the diagonals. If their lengths are equal the square is true.   

This upstate NY barn was dismantled for reuse by Green Mountain Timber. It had a daisy wheel scribed on one wall.  The  barn laid out using the 6 points of the circle. The frame of the east elevation is drawn below.

The square frame for the door is in the center. Either side completes the rectangle of the circle.

My post describing this barn:

https://www.jgrarchitect.com/2020/03/a-barn-and-its-daisy-wheel.html




How to Draw a Square  with a Compass, #2

Draw a line.  Mark 2 points on the line.
Open the compass wider than the distance between the  points. Swing an arc across the line, below and above it from each point.
The arcs will cross at 2 points. Draw a line between those points. The new line will be perpendicular to the first line.

Then choose the length of the side of the square A-B. Mark it off on both lines.See the arc B-B.
Swing new arcs the same length (A-B)  from both B's.  See the dashed and dash/dotted lines. They cross at both A's.
All the sides are equal: a square.

St. Jerome's Catholic Church, East Dorset, VT, 1873, was laid out using that simple square  - including how the arcs cross each other. 

My post about it is here:
https://www.jgrarchitect.com/2016/12/st-jerome-catholic-church-east-dorset.html

Part 2 is here:  https://www.jgrarchitect.com/2020/01/practical-geometry-drawing-square-with.html

I explain these ways of using a compass,a straight edge, and a marker to lay out squares and rectangles when I give presentations. I add them here because such information should be readily available on line.

St Jerome's Catholic Church, East Dorset, Vermont

St. Jerome's Church in East Dorset, Vermont. was coming down. Only 4 towns away, not very far!  I would be able to see the frame. The weather was beautiful;  I was itchy for a drive.

Add to that my friend from the 2016 PTN Workshops, Lisa Force, was one of the crew.  Of course I went.

This is Lisa striking a pose in her haz-mat suit.

The church was built in 1874 for the Catholic stone masons who had come to Dorset to work in the quarries and shops. By 2010 it had only 6 members and a large, lovingly cared for cemetery. The church was closed. Naturally the roof leaked; mold grew.
Parishioners realized that if church were gone, the cemetery could expand. Enter Deconstruction Works   http://www.deconstructionworks.com/



Here is the church with asbestos siding: sweet, unexceptional.

















Here's what was uncovered: vertical sheathing - classic Gothic Revival siding.  Rustic, rural, right out of the pattern books! *
Able to be built of local lumber cut at local saw mills by local craftsmen, the design fit its pastoral country setting.




A dog house shed for the bulkhead had covered a section of the original siding, leaving it unchanged. The battens which had covered the joints  between the boards were still there. They were fat and curvy , creating strong shadows, beautifully following the lines of the windows.
I admire how those craftsman 140 years ago reinforced the shape and rhythm of the windows as well as the verticality of the church.

The interior had been renovated several times; the floor covering  updated, the ceiling lowered at least three times, the walls painted, most of the stained glass replaced, the alter reconfigured.

The iron tie rods may have been original  - or not. They are visible on the right:  the straight horizontal chords that run right through the curved trusses.

Those trusses simply took off half way up the wall. No base.While they were in front of the posts of the bays and symmetrical around the windows they were built up, not solid timbers.





Way up at the peak, in the gloom above all the framing for the drop ceilings, (and what we thought was the original ceiling) the trusses crossed.

So I came home to draw a hypothetical church with curved trusses.
Lisa critiqued.







This is how I think the church was laid out - a simple and elegant geometric design.

However, the designer, be he master carpenter or fledgling  architect, did not need to know much about Practical Geometry. The elevation  divides the square into halves and quarters The  radii of the 2 arcs is determined by the width of the church . Very simple, not complex,

That the designer understood how the frame could create the sense of the church became clear as the layers of interior improvements were stripped from the frame.

The arches do cross. They are part of all the ribs of the bays from the narthex and the nave to the apse. They are an integral part of the frame, well anchored to the posts and braced by the wall's framing.

We saw that crossings were exposed, visible.
They were carefully joined, their edges chamfered  The trefoils and quatrefoils were inserts. The whole assembly was painted in  subtle shades popular at the time: metallic gold on the trusses, brick on the tracery, and on the inside edge of the patterns: red!

Perhaps the colors have faded; the emphasis has not. They were designed and carved to be seen.

The carving, the tracery matched what we saw on the arches and inserts at the transition from the wall to the roof which we had photographed and discussed.  But we had not know what we were seeing. The parts: the strength of the arches,the delicacy of the tracery, and the shapes they created were invisible when they were painted white.  They had lost their grace, their power.












The church is now stripped to the frame. It was taken down completely in the spring of 2017.

I have not seen a geometric layout like this before. I will make measured drawings; then I look at the frame more carefully.





I own drafting tools from this period. They are drawing instruments, 2 compasses and a divider as well as pens and 2 scales, made for drawing with ink.
A Master Carpenter would have used compasses to draw this layout and design in the 1870's. There were not many craftsmen who called themselves architects in 1874. Possibly this design was developed by the local diocese for small communities like E. Dorset. However, I have seen no record nor another similar church. 



*    The image, "William T. Hanlett, BICKNELL'S WOODEN & BRICK BUILDINGS, 1875", is  from
      Country Patterns 1843 - 1883, edited by Donald J. Berg, Revised 2nd edition, The Main Street           Press,  Pittstown, NJ, 1986.