Islamic mathematicians used various expressions to define the sphere, but they all essentially conveyed the same concept. Here are some explanations about the sphere from notable scholars:

• Al-Khwarizmi defined the sphere as: "A sphere is a round object formed by lines of equal length extending from a central point, called the center, to the surface."
• Al-Biruni described the sphere as: "A sphere is a round object bounded by a single surface. All lines drawn from this surface to the center are equal."
• Ali Qushji offered a detailed description of the sphere: "A sphere is a three-dimensional object enclosed by a round surface. From a central point within (the center), all lines drawn to this surface are equal. These lines are called radii. The line passing through the center and connecting two opposite points on the sphere is called the diameter. If the sphere rotates around this diameter, it becomes an axis, and its two ends are referred to as poles."

^{The Knowledge of Spheres in Islamic Astronomy}

The Sky and the Use of the Sphere

Islamic mathematicians derived their knowledge of the sphere from ancient Greek scientists such as Euclid and Archimedes. With this knowledge, they studied astronomy (the science of the sky) and spherical triangles (triangles drawn on a sphere). The sky was conceptualized as a sphere with the Earth at its center, and the stars were thought to be positioned on the surface of this celestial sphere.

^{Earth and Sky: Mathematics and Astronomy}

Celestial Spheres and Instruments

In the past, spherical instruments were created to understand the sky. Some of these include:

• Celestial Sphere (Gökküre): A model designed to show the positions of stars in the sky.
• Armillary Sphere (Halkalı Küre): An instrument used to examine celestial movements and perform various measurements.
• Astrolabe (Usturlap): A device used to determine the positions of stars in the sky. Famous scientists like Taqi al-Din in the Ottoman era constructed such tools.

^{Celestial Spheres and Astronomical Instruments}

Terrestrial Globes and Other Uses

Beyond astronomy, geographers also used spheres. Terrestrial globes served as models representing Earth's map. Additionally, opticians used glass spheres called "burning spheres" to concentrate sunlight onto a single point.

^{Science and the Sky: Astronomical Spheres}

Why the Sphere?

The sphere became an essential model for understanding both the heavens and the Earth. These instruments enabled a better comprehension of celestial movements, the positions of planets, and the structure of the Earth. Islamic mathematicians and scholars made significant strides in this area, paving the way for future scientists.

^{Celestial Sphere Models by Islamic Mathematicians}