The flag of Turkey consists of a red background (color code: Pantone 186 C) with a white star and crescent symbol. The aspect ratio is 2:3.

Geometric properties and measurements:

1. Crescent: The center of the circle forming the outer arc of the crescent is located at the point (1/2, 1/2) of the flag's width and height. The radius of this circle is 1/4 of the flag's width. The inner arc of the crescent is formed by a circle with a radius of 1/5 of the flag's width, concentric to the outer circle.
2. Star: The five-pointed star is situated to the right of the crescent. The distance between the center of the star and the center of the circles forming the crescent is equal to 1/3 of the flag's width. The star's diameter is 1/4 of the flag's width.
3. Star angles: Each angle between the star's points is 36 degrees, and the angle from the star's center to its points is 72 degrees.

These geometric properties and measurements are based on the Turkish flag regulation law No. 2994 dated May 29, 1936.