SKETCH 12 STARS FROM THE GREAT HAGIA SOPHIA 1

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1 SKETC 12 STARS ROM TE GREAT AGIA SOPIA 1 agia Sophia, or Aya Sofya in Turkish, is the largest Byzantine church in the world. Its current name is a shortened form of the full name The church of the oly Wisdom of God. The current building is almost 1500 years old. It was commissioned in 532AD by the Emperor Justinian I, and designed by a physicist, Isidore of Miletus, and a mathematician, Anthemious of Tralles. The construction was finished in 537AD. ig. 65 agia Sophia, or Aya Sofya in Turkish, is the largest Byzantine church in the world. Its monumental structure can be seen from a long distance. The shape of the building was a source of inspiration for designing many Ottoman mosques for many years. 1 This sketch contains fragment of the first edition of my book Islamic Geometric Patterns in Istanbul. The second, updated edition will be available in S t a r s f r o m t h e G r e a t a g i a S o p h i a 1

2 or years the church served as an Orthodox patriarchal basilica and cathedral of Constantinople with a short period from 1204 to 1261 when the church was converted to a Roman Catholic cathedral under the Latin Patriarch of Constantinople of the Latin Empire established by the crusaders. On 19 May 1453, the church was converted to a mosque and served as a mosque to the Muslim community in Istanbul until In ebruary 1935 the church became one of the most frequently visited museums in Istanbul. There are numerous publications describing the history and architecture of agia Sophia. My favorite one is the wonderful book Strolling through Istanbul by John reely, a professor from Bogazici University (Bosporus University), who has lived and taught in Istanbul for more than 40 years. agia Sofia was designed and built as a Byzantine church. Therefore it contains numerous decorations that are typical of the churches from this particular period of time. These decorations do not resemble the ornaments that we are discussing in this book. owever, after the church was converted to a mosque some of the later additions introduced a few geometric ornaments that are worth exploring. One of them is an incredibly large and nicely decorated minbar. ig. 66 The minbar in agia Sophia (Photo by Ercan Gigi) 2 A u t h o r : M i r e k M a j e w s k i, s o u r c e h t t p : / / s y m m e t r i c a. w o r d p r e s s. c o m

3 The minbar contains some intriguing ornaments on its sides. The ornament along the banister is similar to the one that we developed while discussing grids and stars. It contains a grid of connected hexagons and overlapping nonagons (regular polygons with 9 sides). This ornament is quite easy to construct and I leave this construction as a simple exercise to my readers. On the top of the minbar there is a slightly larger version of the same ornament. Each side of the minbar is covered by an elaborated ornament with complex nine-fold stars and crossing them regular dodecagons. In this chapter we will concentrate on the ornament from the minbar in agia Sophia. Therefore, we will have to take a close look at it and see how the ornament can be created. ig. 67 The geometric ornament on the minbar in agia Sophia The ornament is built using two major elements: a regular dodecagon shape and a star ornament inside of the dodecagon. There is also some filling inside the star ornament. ig. 68 One of possible grids for this ornament The grid suggests that the repeat unit should be a square with a star inside of it. Note, the dodecagon shapes do not touch the edges of the repeat unit there is a gap between them. Note also that some of the lines of the star ornament do not touch the edge of the repeat unit we will have to remember these facts while creating the ornament. inally, a very watchful person can notice that the long lines forming the shape of the star are not parallel. In our construction we will ignore this fact. Now, after this brief analysis of the ornament we can start developing it. We will divide our construction into three parts: creation of the regular dodecagon shape, creation of the star inside the dodecagon, and finally adding some finishing touches in the corners of the repeat unit. S t a r s f r o m t h e G r e a t a g i a S o p h i a 3

4 ig 69 Construction of the geometric ornament from agia Sophia minbar STEP 1: Creation of the regular dodecagon shape D E Draw a segment AB, and construct a square with AB as one of the sides. ind the center of each side of the square; connect opposite centers to get point O the center of the square. Use the point O and a center of one of the sides of the square to construct a dodecagon. We need only vertices of the dodecagon, but leaving its sides helps to understand the whole construction. O Draw a rectangular subgrid of vertical and horizontal lines passing through vertices of the dodecagon. ind two points of intersection of the subgrid: here points and. Use the point to create a dodecagon with the center in O and as one of its vertices. Make lines of this dodecagon thicker this is the dodecagon shape that we see on the original ornament. Use the point to create a dodecagon with the center in O and as one of its vertices. We will use this dodecagon in order to create the star ornament. inally in each corner of the repeat unit add the two short dashed segments. We will use them as a supplementary subgrid to limit the lines forming the star so they will not touch the edges of the repeat unit. A D O E B A B Now, you can hide the rectangular subgrid. We do not need it any more. In fact you can hide or remove the external dodecagon, and most of the existing points. We will do it later. Now we are ready to start the second step where we create the internal star pattern. 4 A u t h o r : M i r e k M a j e w s k i, s o u r c e h t t p : / / s y m m e t r i c a. w o r d p r e s s. c o m

5 STEP 2: Creation of the internal star Use points of the internal dodecagon to create a subgrid of pairs of parallel lines like those on the picture. You should have four pairs of parallel lines. Construct 12 intersection points of the subgrid lines. These are the points forming a ring inside the small dodecagon. Note, each of these points is separated from the center of the dodecagon by a single line. Now we are ready to develop the star ornament. We will start by creating the shape of the star from the left-top corner of the repeat unit. This way it will be easier to demonstrate construction of the shape of the star. Use the new subgrid (solid thin lines) to add the three pairs of segments (the thick lines). Each pair contains two segments of the same length; the vertex of the angle formed by these segments is one of the points of the central ring of intersection points created a while ago. Note, what we did when a subgrid line goes through the lines of the supplementary subgrid in the corner of the repeat unit. The arm of the star does not cross lines of this subgrid, its stops on them. Construct lines of the star ornament in the three remaining corners of the repeat unit. Clean the subgrid of solid lines, leaving only the supplementary subgrid in each corner of the repeat unit. We will need it in a moment to finish the construction of the repeat unit. S t a r s f r o m t h e G r e a t a g i a S o p h i a 5

6 STEP 3: inishing touches Now, is the easy part use the supplementary subgrid to add the segments closing the star in each corner of the repeat unit. ere these are segments PS and QR. Do the same in each corner of the repeat unit. To finish this work you should hide the remaining subgrid lines, but you can leave the edges of the repeat unit. You can also hide all points if you do not plan to use them later to expand or modify the ornament. Our work is almost finished. Now we can use the repeat unit to create a larger piece of ornament and see how it compares to the original decoration on the minbar. P Q R S The next figures present different versions of the ornament. ig. 70 The ornament from the minbar from agia Sophia We created only the edges of the ornament. We did not create any fills or even interiors of the stars. This way it is easier to compare the original ornament shown on the photograph with our construction. ig. 71 Another version of the ornament from the minbar from agia Sophia. 6 A u t h o r : M i r e k M a j e w s k i, s o u r c e h t t p : / / s y m m e t r i c a. w o r d p r e s s. c o m

7 As we said at the beginning of this chapter agia Sophia was not built as a mosque. Therefore the number of geometric ornaments typical of Islamic art is very limited. owever, we still find some interesting geometric ornaments to explore in agia Sophia. In the following photographs I show some of them. ig. 72 Selected geometric ornaments from agia Sophia An ornament on the metal door (below left) although it is not exactly in the same style as the examples we have examined before, we can still notice stars, circles, and a perfect octagonal rotational symmetry in it. The marble shelf (below top-right) this ornament is very similar to one of our first ornaments that we developed in this book. This is also exactly the same ornament that we have seen along the balustrade of the minbar. Below this ornament there is a frieze of small shapes and each of them was created from circle arcs. inally below the frieze there is row of small muqarnas. The photograph (below bottom-right) shows the decoration of the ceiling in one of the top arcades in agia Sophia. There are multiple geometric elements in the form of friezes or rosettes. Each of them was developed with the help of circles, triangles and other geometric figures and each of them shows multiple symmetries. Each of the ornaments shown in the photographs can be recreated as a geometric construction using similar methods to those we have already used in this book. S t a r s f r o m t h e G r e a t a g i a S o p h i a 7

8 CREDITS This document contains fragment of the first edition of my book Islamic Geometric Patterns in Istanbul. The second, updated edition will be available in All sketches were created using Geometer s Sketchpad, a computer program by KCP Technologies, now part of the McGraw-ill Education. More about Geometer s Sketchpad can be found at Geometer s Sketchpad Resource Center at All rights reserved. No part of this document can be copied or reproduced without permission of the author and appropriate credits note. MIROSLAW MAJEWSKI, NEW YORK INSTITUTE O TECNOLOGY, COLLEGE O ARTS & SCIENCES, ABU DABI CAMPUS, UNITED ARAB EMIRATES 8 A u t h o r : M i r e k M a j e w s k i, s o u r c e h t t p : / / s y m m e t r i c a. w o r d p r e s s. c o m