Final answer:
Islamic achievements include Al-Khwarizmi's development of algebra, Ibn Sina's contributions to medicine and philosophy, and the advancement of Islamic art through quasi-crystalline geometry.
Step-by-step explanation:
The achievements of Islamic thinkers, scientists, and artists have been significant and varied. One key achievement was the development of algebra by Al-Khwarizmi, which laid the groundwork for modern mathematics. Another was the influential work of Ibn Sina (Avicenna), who made critical contributions to medicine and philosophy. Additionally, Islamic art was greatly enhanced by the use of quasi-crystalline geometry to create intricate and infinitely repeating patterns without repeating the actual pattern, reflecting a deep understanding of symmetry and geometry.