The Geometry of the Sanctuary Plan

(Figs. 127-137)

In the sanctuary north arcade, immediately in alignment with the High Altar, and high in the triforium (Fig. 127a), there are two tympana that would appear to be unique, each bearing a unique geometrical motif.  A somewhat similar one can be found at the far west end of the nave in the western transept (Fig. 113), and this will be discussed in due course.  Apart from these three all the many tympana in the cathedral are either  undecorated or decorated with a diaper all-over pattern carved into the fabric.   None display geometrical motifs except for these three tympana in the building’s extremities..

       In the sanctuary the bay furthest to the east displays a single circle (Fig. 128a), while in the adjacent bay to the west a most unusual design is displayed consisting of four circles arranged in the form of a lozenge, based on a rhombus (Fig. 128b).

       A further remarkable aspect of these two motifs is that they are not carved into the fabric but have been carved elsewhere and then carefully set into the masonry of the tympana.  The single circle is formed from two pieces of stone while the four-circle motif is made up of six pieces.

      The unique manner in which these motifs have been fashioned and set in place, their siting in the immediate vicinity of the altar, and the uniqueness of their form, not only within Peterborough Cathedral but within any other English cathedral, all combine to present a powerful sense of purpose.

      After photographs had been taken and relevant measurements taken it was possible to calculate the size of the motifs (Fig 129, Fig 130, Fig 131).  Without scaffolding it is not possible to achieve perfect accuracy, but in the event the only essential matter is the ratio between the two diameters and the ratio between the width and the height of the lozenge motif.  The calculations eventually arrived at a diameter for the single circle motif of 24 inches [61cm] (Fig. 131a), and a width of the lozenge motif of 41 inches [104cm].  From the photograph taken virtually at eye-level from the sanctuary gallery (Fig. 128b), the vertical dimension was found to be 50 inches [127cm] (Fig. 132).  The distance between the centres of the vertically paired circles was found to be 31 inches [78.7cm], while that between the horizontally paired circles was 22 inches [56cm].  The ratio between 31 and 22 is 1.41, which is Ö2, and from the discovery of this fact it was a simple matter to create the geometry of the four-circle motif (Fig. 133), although the construction does involve an especially elegant element, i.e. the points of tangency between the circles are provided by the intersection of the lines joining their centres with the horizontals of the inner square (Fig. 133a).  Such serendipity is quite unpredictable and almost incalculable.

      Thus we are presented with two purposefully designed and situated geometric motifs that have no apparent connection.   But when we combine the single circle with the quadruple motif at the same scale, the larger circle becomes an integral part of the lozenge geometry (Fig. 134).  The importance of this relationship lies in the fact that in order to create the larger circle the inner square of the quadruple geometry must be turned to create the octagram or octagon star.  The large circle then exactly circumscribes the octagon formed by the star (Fig 133, Fig 134).  The importance of this development in relation to the geometry of the whole cathedral plan will be presented in due course.

       When the complete geometry of the two combined motifs is applied to the ground-plan of the sanctuary, centred in line with the position of the circular motif in the triforium, and with the primary circle of the geometry drawn at the scale of the primary circles of the rest of the abbey plan, i.e. 87 feet diameter, we are presented with the geometry of the apse of the sanctuary (Fig. 135).

       Not only is the interior surface of the wall of the apse delineated, but the geometry of the exterior surface and the line of the glass are easily obtained.

       When the new geometry of the sanctuary is related to that of the choir (Fig. 136) we find that they are mutually related in the most simple manner, and as we shall see later, when they are both related to the geometry of the New building of 1500, all are mutually integrated in an equally simple way (Fig. 234).

       Thus we find that the geometry of the sanctuary has been purposely presented in  the carvings inserted into the triforium tympana in the immediate vicinity of the High Altar.  But it is presented in a form that only one versed in the art of ‘geometrie’ could recognise and interpret.   The designs are ciphers in an esoteric code, and as in many coding systems, the ciphers are presented as two separate artefacts that are meaningless as single items.  Only when the two are superimposed does the message come to light.  One is here reminded of the fact that in the organisation of the freemasons, then as now, coded signs played a vital role in covert communication.

        Turning now to the third motif at the west end of the church in the western transept, we find a motif known as the quatrefoil (Fig. 127b) that is very commonly found in medieval architecture.   In this case it is sited in the western face of the last bay of the nave gallery (Fig. 138).  Thus it marks the termination of the Romanesque church.   It also directs the viewer to look eastwards along the whole length of the Anglo-Norman building.   It can be seen properly only by facing to the east.   It is a geometric design and its geometry extends extends from north to south, whereas the geometry of the sanctuary motifs extend east to west.   The design, though common in medieval architecture is found nowhere else in the whole of the twelfth century fabric at Peterborough.    Thus it would appear, like the designs in the sanctuary, purposeful in its design and placing.

     However, when we compare the geometry of the quatrefoil with the geometry of the nave plan (Fig. 118, Fig 142), there seems to be a contradiction.  The carved motif presents a geometry developed from the ‘right’square, while the geometry of the nave is based on the ‘turned’ square and the octagon star.     Here again I believe that if the design is considered though the eyes of a medieval architect-geometer its meaning can be seen to be truly relevant.  The cathedral architects were Christians and every Christian building that they designed and built was dedicated to the Risen Christ the Saviour.   His sign was the octagon star found in virtually every medieval work of art related to Him, and the quatrefoil is essentially part of an octagonal design and only requires to be turned 45 degrees to achieve its octagonal completion (Fig. 139), and deliver its message, which, as will be seen, applies to the nave elevation.  

       Returning to the sanctuary, we have mentioned the important role played by the octagon, while at the far west end of the church we find the same emphasis.  Looking then at the whole geometry of the church plan, the essentiality of the octagon is evident throughout the building (Fig. 267).  In the transepts it divides their lengths into three equal chapel areas.  This can be achieved geometrically by no other means.  In the nave and choir it delineates the width from plinth to plinth of the arcade.  Later we shall find the octagon playing a vital role in the plan of the ambulatory retro-chapel of 1500.