Islam forbids the making of imitative art on the basis that it may lead to idolatry due to this, geometry starts to play a very important in Islamic art. Islamic artists did not seek geometry patterns to express themselves, but rather aimed to ennoble matter. It can be seen by works in the renaissance period for example “Ascension dome; Holy Women at the Sepulchre; and Pentecost dome. Mosaic, 12th century. San Marco, Venice.” whereby buildings surfaces/ ceilings were covered with figures; while Islamic artist chose to design complex geometric design in their art work. Building that still continues to remain popular among Islamic artists and designers all around the world today.

example of renaissance art in the dome

example of islamic art in the dome
Due to the fact that Islamic art focus mainly on their religion most geometry patterns there represents a (religious) meaning in it. For example the repeating patterns on their art represent the unchanging laws of God. Muslims are expected to observe certain rules as were originally set forth by the Prophet Muhammad, characterised by the "Pillars of Faith". In this way the rules of construction of geometric patterns provide a visual analogy to religious rules of behaviour. It was also being found out that, most Islamic art starts with a circle, which is believed that that’s the point at which all Islamic patterns begins and it represents an apt symbol of a religion and eternity (they are trying to emphasis on one god, role of Mecca and the centre of Islam).
From the research that I have done, I found out that the circle come three fundamental figures in Islamic art, the triangle, square and hexagon. The triangle by tradition is symbolic of human consciousness and the principle of harmony. Whereas the square, the symbol of physical experience and the physical world-or materiality-and the hexagon, of Heaven. Another symbol prevalent in Islamic art is the star and has been the chosen motif for many Islamic decorations.

In contemporary society, artist still uses geometry in their art work too. Geometry plays a huge part in cubist art. From an art history website, I found out that proportion, organic integrity and continuity of life samples and material objects are abandoned in cubist art. Cubist art usually resembles "a field of broken glass". The geometrically analytical approach to form and colour, and shattering of object in focus into geometrical sharp-edged angular pieces baptized the movement into 'Cubism'. A close look reveals very methodical destruction or rather deconstruction into angular 3-dymensional shaded facets, some of which are caving others convex. Cubism distrusts "whole" images perceived by the retina, considers them artificial and conventional, based on the influence of past art. It rejects these images and recognizes that perspective space is an illusory, rational invention, or a sign system inherited from works of art since the Renaissance. This is cubist art.
Therefore one usually will find out that in cubist artworks, objects seem to be broken up, analyzed, and re-assembled in an abstracted form—instead of depicting objects from one viewpoint, the artist depicts the subject from a multitude of viewpoints to represent the subject in a greater context. Often the surfaces intersect at seemingly random angles.

example of cubism art
One of the rather well- known artists (founder) for cubist art is Palo Picasso along with Georges Braque. For analytic cubism (1909–1912) which is a style of painting developed by both of them using monochrome brownish and neutral colors. Both artists took apart objects and “analyzed” them in terms of their shapes, resulting in both of their paintings at that time to have many similarities. Followed by, synthetic cubism (1912–1919) was a further development of the genre, in which cut paper fragments—often wallpaper or portions of newspaper pages—were pasted into compositions, marking the first use of collage in fine art
In summary:
Although both Islamic art and cubist art uses geometric pattern (shapes) as their main focus in every art pieces. However due to the fact that both Islamic and cubist art developed (founded) at different period of time, therefore then they are still different in terms of their purpose and the way they are being presented.
It was known that geometry pattern was being formed in Islamic art due to religious purpose by the fact that Islamic art pieces aren’t suppose to use human figures or animals in their art (except for special reasons) due to idolatry. This result in them using complex geometric patterns to represent things whereas for cubism art geometric patterns were used/ found out as artist would like to view things at a several point of view/ from different perspectives this can be seen by the emphasizing of the flat, two-dimensional surface of the picture plane, rejecting the traditional techniques of perspective, foreshortening, modelling, and chiaroscuro and refuting time-honoured theories of art as the imitation of nature. Cubist painters were unlikely to copy form, texture, colour, and space; instead, they presented a new reality in paintings that depicted radically fragmented objects, whose several sides were seen simultaneously.
In general, cubism and its legacy continue to inform the work of many contemporary artists. Not only is cubist imagery regularly used commercially but significant numbers of contemporary artists continue to draw upon it both stylistically and perhaps more importantly, theoretically. The latter contains the clue as to the reason for cubism's enduring fascination for artists. Whereas for geometry patterns in Islamic art, simple forms such as the circle and the square, were combined, duplicated, interlaced, and arranged in intricate combinations, that were found mostly in Islamic architecture today has becomes one of the most distinguishing features of Islamic art.

example of cubism sculpture today.
References:
http://www.salaam.co.uk/themeofthemonth/march02_index.php?l=3
http://www.huntfor.com/arthistory/C20th/cubism.htm
http://www.arthistoryarchive.com/arthistory/cubism
http://www.skyscrapercity.com/showthread.php?p=36161080
http://www.zoo-hoo.com/index.php?q=Islamic_architecture
http://www.vam.ac.uk/school_stdnts/schools_teach/teachers_resources/maths/index.html
http://blog.princeton.edu/wri152-3/fO5/fkherani/picassos_full_body_selfpotrait.html
http://fineartamerica.com/featured/rock-cube-jack-walsh.html