Islamic Geometry.

Islamic Geometry are a type of geometric patterns that consist of Squares and circles,which are repeated to make a certain complex Pattern,these Islamic patterns were a product of Sasanian,Roman and pre-Islamic arabic patterns, which were fused together to make Islamic Designs and patterns,good examples are

The Shah Nematollah Vali Srine's dome.

Tiles in Alhambra.

And many more, The earliest variation of these designs can be traced back to the Great mosque of Kairouan,the first Islamic design which was used in around 8th century AD, were very simple and looked like this:

Once the Mosque of Kairouan was rebuilt in 9th century AD due to its foundations getting really old,then designed windows were used

From my knowledge I can see an evolution in the Islamic patterns
It seems the evolution's formula is like this:
The simple Rhombus-The overlapping Square and circles-the Seamless Islamic pattern we can see in the second image of this Post.

Then there are Islamic Arches,Islamic arches were very widely used in the North African Muslim communities and seem to be a mixture of Sasanian and Roman arches,

A Sasanian arch

Roman Arch.

So If we were to fuse these together we'd get these pattern of arches
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The similarities are clear of how the Islamic geometric patterns and Arches were designed,we can see each evolution in the geometry from the simple rhombus patterns to the seamless patterns in the tiles of Andalusia, and in the arches of Ancient Persia and Rome we can see the type of arches that have been made in Andalus,were derived from those arches It goes to show how the people of Al Andalus,or Islamic Andalusia, and The North african communities learned through this ancient architectury that can be found throughout Roman and Persian designs, the Islamic civilization studied old civilizations like The Romans and the Persian Sassanians, and from there they started to gather all this material to make types of Islamic geometry and designs which go from Simple to complex like the seamless patterns, it shows how these Patterns from Andalusia,spread onto the rest of the Muslim world due to how complex and satisfying to the eye,these geometric patterns are with these overlapping square and circles,and these triangular tiles which sorround a certain 6 pointed complex star or in this case,all kinds of stars that appear within Islamic geometry,and the complexity shows the hard work put in by each civilization to create these designs in proportion and perfection.