Perpendicularité

Perpendicularité is a fundamental geometric concept describing the relationship between two lines, planes, or other geometric objects that intersect at a right angle. In Euclidean geometry, two lines are considered perpendicular if they meet at an angle of 90 degrees. This relationship is crucial for defining concepts like orthogonality and is often represented by the symbol '⊥'.

In two-dimensional space, two lines are perpendicular if the product of their slopes is -1. For example, a line with a slope of 2 is perpendicular to a line with a slope of -1/2. Vertical and horizontal lines are also perpendicular to each other. In three-dimensional space, the concept extends to lines and planes. A line can be perpendicular to a plane if it is perpendicular to every line in that plane passing through the point of intersection. Similarly, two planes are perpendicular if the dihedral angle between them is 90 degrees.

The concept of perpendicularity has wide-ranging applications in various fields. In physics, it's used to describe forces acting at right angles, such as in vector analysis. In engineering and architecture, perpendicularity is essential for constructing stable and functional structures. In computer graphics, it plays a role in defining coordinate systems and rendering algorithms. The precise definition and properties of perpendicularity are foundational to understanding more complex geometric structures and mathematical relationships.