egységdiagonálú

In geometry, an egységdiagonálú, which translates from Hungarian as "unit diagonal," refers to a special type of polygon where the length of its diagonal is equal to one unit. This concept is most commonly applied to quadrilaterals, but can theoretically extend to polygons with more sides.

The most straightforward example of an egységdiagonálú is a square with sides of length $1/\sqrt{2}$. In this case, the diagonal, calculated using the Pythagorean theorem, would be $\sqrt{(1/\sqrt{2})^2 + (1/\sqrt{2})^2} = \sqrt{1/2 + 1/2} = \sqrt{1} = 1$. Therefore, this specific square is an egységdiagonálú.

However, the term is not exclusive to squares. Any quadrilateral that possesses a diagonal measuring exactly one unit could be classified as an egységdiagonálú. This could include various rectangles, rhombuses, or even irregular quadrilaterals, provided their geometric properties result in a diagonal of length one. The implications of a polygon being an egységdiagonálú often relate to its area or its relationship with inscribed or circumscribed circles, where a unit diagonal can simplify calculations or impose specific constraints. The term is less frequently encountered in general mathematical discourse and is more specific to certain problem sets or areas of study.