Al-Kashi (d. 1429) was one of the greatest Islamic scientists. One of his achievements was to develop five ways of modeling architectural arches, vaults, and domes using only a compass and straightedge. These models allow one to perform calculations, such as finding the surface area or volume of domes, which can be useful in preparing estimates of construction costs.
This 16-minute videotape describes these models for five different types of arches. These arches might form portals or windows or be rotated around a central axis to form a dome. The mathematical constructions are clearly demonstrated on the video through computer animation and are compared to photographs of existing domes in Buchara and Samarkand, where al-Kashi worked. The constructions are also used to create a computer-generated model of a qubba, or mausoleum, in honor of al-Kashi. In addition, the video shows a computer-generated recreation of an observatory of which al-Kashi was one of the founders. Explanations are provided in a voice-over on the videotape and in an accompanying booklet.