How much of an impact did Persian culture have on Islamic and/or Arabic art?

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Some major persian achievements: Mathematics: Foundation of all modern math in the Arab-Islamic fusion of Greek
theory with Hindu-Muslim decimal numbers

1. Systematize: Algebra

2. Origin: Trigonometry; heliocentric theory (astronomy)

3. Introduce to West: Zero; decimal counting

Medicine: Medical scholars also practice medicine

1. Origin: Alcohol (for medicinal purposes)

2. Teaching hospital (the hospital itself was actually invented by Christianity) •

Art: Persian art has very limited representation of humans, animals. Instead:

1. Calligraphy - writing (script)

2. Geometric designs, patterns

3. "Arabesque" - intertwined flowers, plants

NOTE: Islamic values and cultural exchanges between Arab and Persian society was frequent, resulting in the formation of an Islamic cultural tradition. Formost of these is the Quran and sharia law were main sources to formulate moral guidelines. Values were promoted by  Ulama (Muslim scholars), qadis (Muslim judges), and missionaries were main agents.  Education also promoted Islamic values, as every male was supposed to memorize the Quran.

3. Sufis, or Islamic mystics like the Persian Sufi Al-Hasan al-Basri. Also, there is Persian influence on Islam notable in literary works and ideas of kingship as wise, benevolent, absolute 

Often mistaken is the Indian influences which were adopted "Hindi numerals," which Europeans later called "Arabic numerals"

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