Kaitrigons

A kaitrigon is a hypothetical type of polygon characterized by a specific geometric property. In Euclidean geometry, a regular n-gon has n equal sides and n equal interior angles. A kaitrigon, however, is defined by having its sides form a sequence where each side's length is a multiple of the previous side's length by a constant ratio. This means if the sides are $s_1, s_2, s_3, ..., s_n$, then $s_2 = r \cdot s_1$, $s_3 = r \cdot s_2 = r^2 \cdot s_1$, and so on, where $r$ is the constant ratio.

The angles of a kaitrigon are not necessarily equal. The construction of a kaitrigon is possible for various numbers of sides, though specific arrangements and closure conditions can limit the possible values of the ratio $r$ and the angles. For instance, a triangle with sides in geometric progression, if it can be formed, would be a kaitrigon with n=3. Similarly, a quadrilateral with sides $s, sr, sr^2, sr^3$ would also be considered a kaitrigon. The study of such polygons often involves exploring the geometric constraints required for them to exist in a closed planar form. The term "kaitrigon" is not a standard term in mainstream geometry literature and may appear in specific academic contexts or theoretical explorations.