sketch 13 - wordpress.com · fig. 76 a simple geometric or-nament in the courtyard of the Şehzade...

T h e c h a r m i n g o r n a m e n t f r o m t h e Ş e h z a d e M o s q u e | 1

►SKETCH 13

THE CHARMING ORNAMENT FROM THE ŞEHZADE

MOSQUE1 We started our walks in Istanbul from the most frequently visited

mosque, the Sultan Ahmed Mosque (1609-16) often named as the Blue

Mosque. Then we visited the magnificent Hagia Sophia (532-537), a wit-

ness of the Byzantine Empire. Each of these two places is special in some

sense. In this sketch we will go to the Şehzade Mosque, also known as the

Prince’s Mosque, another special mosque in Istanbul. This mosque, locat-

ed a bit off the busy tourist tracks, is special in many ways. I have never

seen a crowd of tourists in this mosque. Every time I go there, the place is

very quiet and it gives me pleasure contemplating its architecture as well

as some of the most beautiful ornaments – geometric and arabesque pat-

terns.

Fig. 73 The Şehzade Mosque (photo from the back of the garden).

1 This document contains fragment of the first edition of my book “Islamic Geometric Patterns in Istanbul”. The second, updated edition will be available in 2015.

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

Fig. 74 Floor plan of the Şehzade Mosque (right side) and its courtyard (left side of the plan).

In the middle of the courtyard, exactly in the center an octagonal fountain is located.

Source archnet.org, published with permission of Dr Gulru Necipoglu

The mosque has its own specific mood of contemplation, quietness, and

meeting with God regardless whether you are a Muslim or a Christian.

There is also a large and well maintained garden outside the mosque

where you can always hide from the noise of the busy street and the heat

in summer time.

The Şehzade Mosque has its own sad history. In 1543, the eldest son of

Suleyman, the prince (Şehzade) Mehmet died at the age of 21. Suleyman

mourned three days beside the coffin before allowing to be buried his son.

Then he ordered his famous architect Mimar Sinan to design and build a

mosque to commemorate his son.

In response to this order Sinan created a mosque that has an ideal sym-

metry in mathematical sense and a shape copying, and expanding on the

construction of Hagia Sophia. The shape of the mosque is based on a

square. On the upper level we have another square that is a basis for the

19-meter dome. Inside the mosque we a have huge space extending in

four directions. In Hagia Sophia the central space was extended into two

directions only. Inside the mosque on the bottom level we have a gallery

with 24 arches, in the upper level there are 12 arches, and above there are

4 arches supporting the dome.

0 5 10 20 m

http://symmetrica.wordpress.com/


The mosque has an ideal symmetry: the base has a square shape; another

square is in the top part of the mosque, and a circular dome in the middle.

The courtyard is also a square with 3 small domes on each side and one in

each corner. The fountain has the shape of a regular octagon. The con-

struction of this mosque shows how strongly Mimar Sinan was influenced

by the Italian Renaissance architects who believed that pure geometric

forms – circles, squares, and octagons – are ideal shapes for constructing

churches as they reflect the perfection of God. The huge dome in Sinan’s

construction is interpreted as a symbol of heaven and unity under God.

The central part of the Şehzade Mosque is almost identical in its geometry

to the Santa Maria della Consolazione church in Todi, Italy. The Şehzade

Mosque construction was copied in hundreds of mosques in Turkey and

all over the world.

Fig. 75 The courtyard of the Şehzade Mosque with some geometric ornaments

After this brief introduction of the Şehzade Mosque let us look for geo-

metric ornaments in this mosque. We can find many of them, but due to

the limited space in this book we will concentrate on a few of them only.

We will examine some of the ornaments that we find in the courtyard and

later we will look at the ornament on the minbar inside the mosque. The

ornaments in the courtyard were frequently copied and used in many

other mosques. We find them in many places in Istanbul. Let us start with

some of them.

The next two photographs show two very similar ornaments. Each of

them was constructed using circles and arcs, and each of these ornaments


can be created using a simple hexagonal grid. However, each of them can

also be created using a rectangular grid. This way the repeat unit will have

the form of a rectangle and it will be very easy to spread such an orna-

ment over a larger area. Finally, one can think about creating the repeat

unit in the form of an equilateral triangle.

Fig. 76 A simple geometric or-nament in the courtyard of the Şehzade Mosque. The ornament was constructed using multiple circles.

Fig. 77 Another geometric or-nament in the courtyard of the Şehzade Mosque. The ornament was constructed using multiple circles and arcs.

Let us start developing the first of the ornaments shown in the photo-

graphs. For this example we will create a rectangular repeat unit. It will

be a rectangle with given length of its longer side (horizontal). We can

imagine that ancient masters usually got the size of the area they had to

cover and then they had to fit an ornament in this space. Therefore, start-

ing with the repeat unit of a given size makes a lot of sense.



Fig. 78 A rectangular repeat unit ABDC for the geometric ornament from the Şehzade Mosque.

Note the overall design is based on a hexagonal grid. Therefore we can easily draw two equilat-eral triangles on our design, each of them with one side vertical. Their heights are equal to the longer side of the repeat unit. Note also the other side of the repeat unit is equal to half of the tri-angle side.

We can easily notice that if we start from the length of the repeat unit,

here it is the segment AB, then we will have to construct two rotated equi-

lateral triangles with a given height. This very simple construction is

shown on the next figure.

Fig. 79 Construction of an equilateral triangle with a given height

Start by drawing a segment AB and a line perpendicular to it passing through one of its ending points (here through point A).

Draw two circles with radius equal to AB and centers in A and B respectively. Points of intersection of these cir-cles mark as G and H.

Draw segments AG and AH.

Draw a line passing through point B and perpendicular to AG and another line passing also through B and per-pendicular to AH. Points of intersection of these two lines with the vertical line mark as C and E.

Triangle CBE is the equilateral triangle we need and AB is its height.

Now, we are ready to proceed with our construction. We will have to start

from a segment AB, and then develop two equilateral triangles with

heights equal to AB.

D

A

C

E

F

B

E

C

H

G

A B


Fig. 80 Construction of the rectangular repeat unit

STEP 1: Construction of the outline of the repeat unit

Draw segment AB and construct an equilateral triangle CEB with AB as its height.

Use points C and B to construct another equilateral tri-angle CBF. You should obtain two equilateral triangles with a common side and parallel heights.

The rectangle ABDC will be our repeat unit, and now we have to fill it with the pattern.

Divide each side of the two triangles into 3 equal parts (large yellow points) and then each external 1/3 of the side divide again into three equal parts (small points).

We will use these points to create a circular subgrid.

STEP 2: Construction of the pattern for the repeat unit

From each of the vertices of both triangles draw two circles – one passing through the large point obtained from the division of the side into three equal parts, and another one passing through the small red point ob-tained by dividing external parts of sides into three smaller parts.

Finally use these circles as a subgrid to draw only this part of the ornament that will be inside of the rectangle.

The repeat unit is almost ready. Now you have to hide all unnecessary elements.

Below I show the final shape of the repeat unit.

The next figure shows an ornament obtained by multiple reflections of the

repeat unit created above.

A

D

E

P

Q

C

B

F

A

D

E

P

Q

C

B

F



Fig. 81 A geometric orna-ment from the courtyard of the Şehzade Mosque

Construction of this orna-ment can easily be modified to obtain the ornament shown in the second photo-graph.

The second ornament from our photographs requires exactly the same

approach, with a few minor changes. Here the repeat unit is a rectangle

with the short side horizontal and long side vertical. Therefore, it is con-

venient to treat segment AB as half of the base of the equilateral triangle.

The remaining part of the construction does not contain any special diffi-

culties. The sequence of figures below shows selected stages of the con-

struction.

Fig. 82 Construction of the second ornament from the Şehzade Mosque

The repeat unit of the ornament can be taken as rectangle ABDC, where AB is half of the base of an equilateral triangle. The angle between diagonal BC and base AB is 60 degrees.

In order to create the repeat unit, we will have to construct two equilateral triangles with par-allel heights, here triangles EBC and CFB.

STEP 1: Construction of the outline for the re-peat unit

Draw a segment AB and create an equilateral triangle EBC where AB is half of the base.

Then create another equilateral triangle CFB by drawing two circles with radius CB and cen-ters in C and B.

Find the center, point D, of the segment CF and connect it with the point B.

Rectangle ABDC will be the outline of the re-peat unit.

C

A B

D

E

F

D FC

E A

B


STEP 2: Construction of two subgrids

In exactly the same way like in the previous construction divide each side of each triangle into three equal parts and then each external 1/3 of the side divide again into three equal parts (small points).

Use these points to create a circular subgrid.

Add the two rays going from points C and B and perpendicular to the opposite sides of the tri-angle.

STEP 3: Construction of the pattern for the repeat unit

Use the subgrids to draw the pattern inside of the repeat unit.

Now, you have to hide all subgrids and all points, fill the spaces between the lines of the pattern, and the repeat unit should be ready.

If you are using a computer to develop your construction, then here are the original colors of the ornament: dark red (RGB: 160, 70, 40), dusty black (RGB: 100, 90, 90), and powder white for the lines (RGB: 195, 185, 175).

The next figure shows a geometric ornament created with the use of the

repeat unit from our construction.

Fig. 83 The second orna-ment from the Şehzade Mosque

A number of other ver-sions of this ornament can be found in Istanbul. One of them is an ornament with reversed colors – lines black, black fills ren-dered as white, etc.

After constructing these two, rather simple, ornaments from the Şehzade

Mosque let us look at something more difficult. In the next photograph I

show an ornament with charming from the courtyard collection. This one

is not precisely drawn and during a number of restorations some of the

D FC

E A

B

D FC

E A

B



lines got a bit curved while some other lines are still straight. However,

accuracy of this ornament is not our major concern.

Fig. 84 The charming ornament with ten-fold stars from the Şehzade Mosque

This ornament was created using regular decagons and stars based on the regular dec-agons. The interesting feature of this ornament is that edges of the stars form rather unusual angles. This makes an exciting challenge while constructing this ornament.

First, let us try to construct the grid of the ornament. By drawing lines on

the photograph we can produce a grid that is shown on the next figure. It

is very unusual – here we have regular dodecagons, flattened pentagons

and expanded hexagons. In fact the hexagons have four angles the same as

those in a regular pentagon. Now, we know what kind of problem we are

facing. It is a well-known fact that a regular pentagon, and consequently a

decagon, cannot be used alone to cover the plane. Every time we use dec-

agons to cover the plane there will be some gaps between them. There-

fore, we have to use some other polygons, regular or not, to fill these gaps.

This is the case in our example.

In our ornament all pentagons are flattened, this makes them not regular.

This ornament gives us an opportunity to experiment. By changing the

size of the regular decagons we can move points H and K closer (larger

decagons) or more distant (smaller decagons). At the same time the shape

of the pentagons will flatten or get narrower. For H=K pentagons will turn

into quadrilaterals. I suggest to my readers to experiment with the dis-

tance between H and K and construct different versions of this ornament.

In this book we will almost follow the construction from the photograph

exactly.


Fig. 85 The charming geometric ornament with dodecagonal grid

The rectangle ABCD can be a very convenient repeat unit. Points H and K in this ornament di-vide the diagonal BD into three equal parts.

Point O is the center of rotational symmetry. We can create only the top-left part of the repeat unit and then rotate it 180° about the point O.

The angle between AB and BD (diagonal of the rectangle) is 36°. Therefore, our first task will be to create the angle 36°.

Fig. 86 Construction of the 36° angle

Start by drawing segment AB. Draw a circle with

its center in B and radius AB. Construct a line

perpendicular to AB and passing through B.

Find the midpoint E of the segment BD and draw

a small circle with center in E and radius EB.

Draw another segment AE and find its point of

intersection with the small circle, you will get

point F.

Finally draw a circle with its center in A and

radius AF. Mark the intersection point of the last

circle with the large circle. The angle ABC is

36°.

Now, we are ready to proceed with the construction of the repeat unit.

Due to the unusual angles of the edges of the star the whole construction

will require more work and quite complex subgrids. Let us start.

Fig. 87 Construction of grids for the charming ornament

STEP 1: Outline for the repeat unit and the first subgrid

Draw a segment AB, and then construct the angle 36° in one of its ends, here ABD.

Construct two lines perpendicular to AB pass-ing through points A and B. Mark point of inter-section of one of these perpendicular lines with the arm of the angle 36° as D.

Divide segment BD into three equal parts.

Construct a decagon with center in D and one of the vertices in 1/3 of the segment BD. Draw diagonals of the decagon.

Find the center of BD and construct a line pass-ing through it and perpendicular to BD.

C

K

HD

A B

O

mCBA = 36.000°

C

F

E

D

A B

ED

A B



STEP 2: Construction of the second subgrid

Find a center of each side of the decagon (small points) and draw a line through each of them to the fourth to the left, and to fourth to the right, vertex of the decagon (dashed lines). It is enough if you draw these lines through points J, K, L, and M.

Draw a circle with its center in D and radius DO. We will need it in a moment.

STEP 3 Construction of the third subgrid

Mark points of intersection of the circle with diagonals of the decagon, here points P, O, Q. Through each of these three points draw lines to the second left and second right point on the circle – on the picture these are thin solid lines.

STEP 4 Construction of the repeat unit

Use the existing three subgrids to draw the left-top part of the repeat unit (medium red lines).

Now, clean all lines of all subgrids, as well as everything that is outside of the boundaries of the repeat unit.

Rotate the resulting shape 180° about point O. You should get something that looks like the right bottom figure.

M

OKJ

L

ED

A B

Q

P

O

ED

A B

Q

P

O

ED

A B


Final repeat unit for the ornament

The next two images show two versions of a geometric ornament created

with this repeat unit.

Fig. 88 The charming ornament from the Şehzade Mosque

In this picture we only show out-lines of the ornament – no fills were created.

Fig. 89 The charming ornament from the Şehzade Mosque

The fills in this image mimic the original ornament.

As we said in the beginning of this chapter, our last stop in the Şehzade

Mosque will be the minbar inside the mosque. We already know that in

Q

P

O

ED

A B



many mosques the minbar is the place where we can find some interest-

ing geometric ornaments. The Şehzade Mosque is not an exception. The

glorious minbar has a long geometric ornament along the banister, anoth-

er ornament formed into a round medallion, and a beautiful golden ara-

besque with some dusty-read elements. We have already seen the long

ornament. It was in the Sultan Ahmed Mosque. We also find it in many

other mosques. Therefore, we will concentrate on the ornament in the

round medallion. At the first sight it looks quite simple, just a grid of 5

decagons filled with some spider net. But we know already that penta-

gons, and consequently decagons, are always trouble makers. Simply

there is no way to cover the plane with decagons or pentagons only.

Therefore, if a geometric design uses decagons, we then have to find a

good way to fill the space between them. And this makes the construction

so interesting.

We have to find a way as simple as possible to construct this ornament.

Accurately speaking we have to only create what we see in the photo-

graph without trying to extend it further. Let us look closely at the orna-

ment. There are many ways to approach this problem. Each of them is

tedious to a certain extent and requires constructing a few subgrids. The

most convenient way would be to create the triangle ABD (see the photo-

graph) as a very unusual repeat unit, and then create multiple reflections

of the repeat unit about its sides.

This way we will obtain a new, large decagon filled with a spider net of

lines.


Fig. 90 The minbar in the Şehzade Mosque



Fig. 91 The ornament on the minbar in the Şehza-de Mosque

We will construct the repeat unit in a form of a triangle, here the triangle ABD.

Note, the triangle as well as the ornament have quite uniform angles: 36° and 36°/2=18° .

Here: ABC= BAC=DAC=36°, ACB=3x36°=108°. All this means that construc-tions of 36° and 18° angles will be the most fre-quently used in this work. We already did the con-struction of the 36° angle. The angle of 18° is just half of it.

As we said the construction of the ornament requires creating a few sub-

grids. Therefore in order to simplify it as much as possible we will create

the ornament around the point C first and then we can use the same ap-

proach to create parts of the ornament around points A, B and D.

Fig. 92 Construction of the ornament around the point C

STEP 1: Draw the segment AB (it is the radius of the medallion). In points A and B construct angles 36° and construct triangles ABC and ACD

Now divide each angle of the triangle ABC into 18° wedges. Mark the two points of intersection of rays shown on the picture and draw three circles with centers in A, B and C, and passing through the marked points.

STEP 2: Creation of subgrids around point C

Divide each angle around point C into 18° wedges. We have our first subgrid.

Find the point P that is half way between C and B. Find the center of CP (point Q), find the cen-ter of QP (point R), find center of CQ (point S) and finally find the center of CS.

Draw two larger circles each with center in C, and radii CR, CQ, and a small circle around the point C. This is our second subgrid.

D

B

A

C

D

C

A B

S

RQ

P

D

C

A B


STEP 3: Polygonal parts of the ornament and third subgrid

Use the two large circles to construct two deca-gons – you need to create only the part inside of the triangle ABD.

Use the third circle to create a subgrid of seg-ments joining every second point on it. This will be the third subgrid that we will use to create the star pattern around point C

STEP 4 Creation of the ornament around point C

Now create all radial segments of the ornament around point C and the shape of the star in the center.

Finally using exactly the same method, you will have to create the parts of the ornament around points A and B. Note, the star pattern around point A does not exactly match the segment AB. Therefore the side along AB stops before reaching point A. This will create strange holes near point A (see the next pic-ture)

Fig. 93 The repeat unit for the ornament from the minbar in the Şehzade Mosque

The repeat unit has a shape of a wedge with a 36° angle in the narrow side. It can be used to create a medallion shape but still, due to the known problems with regular decagons, it can-not be used to create an ornament covering the whole plane.

The next two figures show two versions of the ornament from the minbar

in the Şehzade Mosque.

S

RQ

P

D

C

A B

S

RQ

P

D

C

A B



Fig. 94 Two versions of the ornament from the medallion on the minbar in the Şehzade Mosque

The left image shows the ornament as it is on the minbar. The right image was created with fills and a gra-dient coloring available in many computer graphics programs.

There are still a few more interesting ornaments worth investigating in

the Şehzade Mosque, but there are also some other remarkable places in

Istanbul to visit and check what might be found there. Therefore, we leave

the remaining ornaments from the Şehzade Mosque for another time, and

now we will move to our next place to visit.

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 2015.

All sketches were created using Geometer’s Sketchpad®, a computer pro-

gram by KCP Technologies, now part of the McGraw-Hill Education. More

about Geometer’s Sketchpad can be found at Geometer’s Sketchpad Re-

source Center at http://www.dynamicgeometry.com/.

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 OF TECHNOLOGY,

COLLEGE OF ARTS & SCIENCES,

ABU DHABI CAMPUS,

UNITED ARAB EMIRATES

sketch 13 - wordpress.com · fig. 76 a simple geometric or-nament in the courtyard of the Şehzade...

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