fig. 8: Root proportions
A Root proportion is a kind of geometric proportion, which serves as a design tool. The root proportion regulates the order of patterns. In medieval architecture, root proportions were used to create architecture which was perfectly pleasing to the eye.
Durham Cathedral
Root proportions were typically used in medieval cathedrals, for example in Durham, UK. Although Durham Cathedral was built during the period of 1093-1133 and at that time mathematical knowledge of the irrational numbers and root proportions was quite limited, people in the Middle Ages had already acquired some awareness of the special quality of the ratios of root proportions, and even some sense of its implications 15 . Evidence such as in the ground plan of the south transept of the Cathedral (as shown in Figure 9) can be found that root proportions were used in the design and laying out of Durham Cathedral 15 .
fig. 9: Durham Cathedral
The architects who built the Cathedral used root proportions as they considered it was necessary for the structural stability and the visually harmonious and unifying relationship of its individual parts to the whole cathedral. Therefore, the use of root proportions in the medieval period was more for practicality purposes 15 .
Tessellating Tiles in Islamic Architecture
Furthermore, the sequence of roots also forms the basis of the production of the complex, beautiful tessellation tiles in Islamic design. Figure 10 illustrates the construction of eight-pointed geometry based on subdividing the square and rectangle. Typical patterns can be seen in the tile patterns at the Alhambra Palace in the Hall of the Abencerrajes, and of the Two Sisters 16 .
Islamic architects and artists placed a special role for the tiles design as the underlying geometry of the squared circle
fig. 10 Root proportions used in Islamic design tiles
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