In Istanbul, almost each large mosque is full of interesting geometric ornaments. After visiting a few mosques we will find that some of the ornaments occur more frequently than some other. We will notice also that some geometric ornaments are quite unique and we can see them in one or two places only. There are numerous ornaments hidden in dark places and we do not notice them during a brief visit in a mosque. There are also so insignificant ornaments that we pass near them and we do not pay any attention to them. In this sketch we will look for such forgotten ornaments. We will start with a short visit to the Beyezid Mosque in Istanbul. Continue reading “Sketch 15: An octagonal beauty from the Beyezid Mosque”
Every time I visit Istanbul the Mahmut Paşa mosque is closed – no luck. So, I have no idea what we can find inside, but every time I am there I see a neglected cemetery next to the mosque and an octagonal tomb of Mahmut Paşa with interesting Moorish style decorations with small tiles in blue, black, green, yellow and turquoise. Continue reading “Sketch 14: Visiting the tomb of Mahmut Paşa”
In this sketch we will go to the Şehzade Mosque, also known as the Prince’s Mosque, another special mosque in Istanbul. This mosque, located 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 patterns. Continue reading “Sketch 13: The charming ornament from the Şehzade mosque”
Hagia 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 Holy 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. Continue reading “Sketch 12: Stars from the great Hagia Sophia”
The Sultan Ahmed Mosque is one of the treasures of Istanbul. It is probably the most frequently visited mosque in Turkey. It is also my favorite place. I can spend many hours in this Mosque and every time I am there I discover something new.
The Sultan Ahmed Mosque was built between 1609 and 1616 by the Ottoman architect Sedefkar Mehmet Agha, during the rule of Sultan Ahmed I (1590–1617). Its architecture is exceptional in many ways. This is the only mosque in the world with six minarets. Continue reading “Sketch 11: Geometric ornaments from the Sultan Ahmed Mosque”
In a small book on sacred geometry Miranda Lundy wrote a very short chapter entitled “Islamic designs – stars are born from subgrids.” In this chapter we can find two very meaningful sentences “Many beautiful ornaments are sitting in very simple subgrid, just waiting to be pulled out” and later “The subgrids themselves are rarely shown in traditional art. They are considered part of the underlying structure of reality, with the cosmos (‘cosmos’ means ‘adornment’) overlaid.” Continue reading “Sketch 10: Islamic art – in the labyrinth of grids and stars”
Islamic geometric ornaments, the main theme of this book, convey some aura of spirituality and connection with the other world. They do not have any earthly meaning. Geometric constructions, and very strict mathematical rigor, grant the craftsmen opportunity to demonstrate the highest possible skills. Continue reading “Sketch 9: Islamic art – a glimpse into the past”
We know quite a lot about mathematical art in the West. Hundreds of papers and books were written about Islamic art. Some researchers explored mathematical patterns in tribal art from both Americas as well as from Africa. However, we know very little about mathematical art in Chinese culture.
There are numerous examples of artistic creations in China that have very strong mathematical background. We can find them in geometric patterns on silk fabrics, on Chinese ceramic ware, in furniture as well as in windows and doors of Chinese buildings. Continue reading “Sketch 8: An introduction to the Chinese mathematical art”
For quite a while we are witnessing development of Hirotaka files. These are PDF documents with hundreds of geometry problems developed by a Japanese mathematician Hirotaka Ebisui (or Child of Frog). At the same time there are very few mathematicians, or even geometers, aware of existence of these files, and even less people who recognize their value. The objective of this sketch is to make a brief analysis of these files, examine roots of the geometry problems in the Hirotaka files, and point out their value. Continue reading “Sketch 7: The new temple geometry problems in Hirotaka files”