## Bradford Wool Exchange windows

The Bradford Wool Exchange completed in 1851 is apparently an example of ‘Venetian Gothic’. It now houses a Waterstones branch with a Starbucks upstairs.

The upper gallery has lanterns or ‘dormer windows’ set in the roof to provide extra light. These windows have an unusual pattern of panes – a modified triangle contains a circle of 7 circles, and then a Star of David . The 3-7-6 ratio formed here is unusual as the 7 and 6 don’t fit well together.

The sketch above does not show the proportions of the outer frame as I remember them (guess who didn’t think to take a photo). In the sketch, I have taken the radius of the arcs as the length of the side of the equalateral triangle that circumscribes the central circle. This radius *not constrained* by the pattern. The ring of circles and the Star of David are as they have to be to fit into the large circle – they are *mathematically determined* so my fallible memory is not stressed too much – all I have to recall is the fact that the 7 outer circles were radially determined and that the central circle was filled with the Star of David.

You see the star of David in quite a lot of Victorian buildings, not all associated with Jewish organisations, the symbol was widely used before the state of Israel came into being.

Focussing on the ring of circles (see above), you can calculate the radius of the outer circle, each radial circle and the inner circle with a little GCSE trigonometry. The steps go as follows…

- Draw a regular heptagon
- Let the circle cicumscribing the heptagon have radius R and the radius of each small circle in the ring be r
- R is the hypotenuse of a right angled triangle, and r is the side opposite the half angle at the centre
- The ratio r/R = sin(360/14), so r = R.sin(360/14) = 0.4338.R
- The large circle that contains the ring of small circles has radius given by R + r or R.(1 + sin(360/14)) or about 1.4338R

Turning the formula round, if you pick a value for the outer circle, say Outer, then

- R is Outer / (1 + sin(360/14))
- The radius of the Inner circle (the one that holds the Star of David) is R – r or R.(1 – sin(360/14)

Now, the geezers that drew out the cutting patterns for these windows would not have whipped out a set of log tables and calculated any of this in the 1850s. My guess is that they would have constructed the heptagon using a ruler and compass method or by measuring with a ruler and a protractor, then completed the rest of the construction and finally measured up the ratios to produce a full size pattern.

The roof is celebrated in verse by Joolz Denby

“I go to the Wool Exchange, that Temple to

the trade that made the city famous;

high up under the canopy of its arching,

ribbed roof that vaults to a ridge

like a mediaeval galleon upturned,

and beached on a city street,

painted wooden archangels crowned in antique gold pray

with knotted, steepled hands.

Once they were mute witnesses to the swirl and play of money

on the trading floor beneath them,

now the city seraphim watch ordinary people

buying books and drinking coffee;

but they don’t mind – they stretch their stiff, gilded wings

over everyone, young and old, and we’re all in their charge.”

Then again….

“stark against the huge backdrop of the clouds stand

the monumental sandstone buildings,

the Wool Barons proud and unflinching legacy,

palaces of trade that couldn’t be built now,

will never be built again by modern hands

no longer trained to patience and the skills

that turned the primeval bones of earth into carvings

as dense and intricate as nature herself.”

...or perhaps rather than a lack of patience or skill, you have to *pay a decent wage* for labour now as people want a roof over their own head, a pension rather than the workhouse and a bit of colour and some possessions? It strikes me that the *mathematical* input into some of these old buildings, as well as the use of daylight, could be blended with modern construction techniques. I miss the use of symbols and meaning in modern buildings.