TILTED GEOMETRY

IN NO TIME.

Duncan Jolyon Burden has posted to his blog an entry titled "GEOMETRY IN ARCHITECTURE AND ART - PART 3"

Geometry in Architecture and Art - Part 3

In his blog post Duncan rehearses his discovery of a geometric christogram of three classic geometric shapes found by him in a last-course painting by DAVID TENIERS II called "St. Paul and St. Anthony in the Dessert".

I have decided to investigate Duncan's shape-sifted seal in this saintscape and see if its existence is a solid certainty, or a smoke with no fire.

All images used by me in my post here can be found in my Flickr Album found here

https://www.flickr.com/photos/657576...57652439421670

Artwork by David Teniers II. Dread geometry by Duncan Jolyon Burden.

Duncan's use of thick, bold lines, to high-light the geometry, thought perhaps, by the reader, to have been used by Duncan to help the reader to view the geometry, can also hinder the readers ability to view and judge the veracity of Duncan's divined device.

In the image that I have borrowed from Duncan's Blog, you can see that in Duncan's final example, the square is stretched vertically, and is not a square of sides of equal length, and its thick lines are coloured a bold and attention grabbing yellow. So the square is out? So what? Accidental? Or developed deliberately by the devising geometrer to distract the reader with a big yellow square?

Let's now investigate Duncan's plane sight solution to Teniers II's painting "Raven With A Bun".

In this painting by Teniers II, Duncan has set his Tilted Geometry of a circle, a triangle, and a square, placed in occultation. The equilateral triangle has a vertex, or corner, locked to the top-left corner of the square. From this corner, the triangle swings to the right to overlap the square.

The edge, or side, of the triangle opposite this vertex, forms a diagonal line through the square, that bisects the two adjacent sides of the square, through the centre of each side.

This arrangement of the triangle and square mean that the height and breadth of the square in the painting can be easily determined, and the perimeter of the square quickly found, and Duncan's geometry imitated.

In Duncan's Tilted Geometry, Saint Paul's index finger is the centre of the shape of the square and the triangle. The saint's rested staff marks the diagonal edge of the tilted triangle. The diagonal edge of the triangle bisects the bottom edge of the square directly below the centre of the square.

If a vertical line is drawn from the tip of the index finger, which is the centre of the square, down to the staff, this line will be half the height of the square, and therefore half the breadth of the square.

The length of each side of the square will be twice the length of that line, and the line falls directly on to the middle of the bottom edge of the square at the staff.

By following these steps, the reader can replicate the size and location of Duncan's square, and the circle the square is bound by.

Artwork by David Teniers II. Geometry by ME, after Duncan.

Artwork by David Teniers II. Geometry by ME, after Duncan.

## Bookmarks