What is an orthogonal?

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Orthogonal or orthogonality are terms from mathematics. You won't be confronted with it in the first few years of school, but you can no longer avoid the term in upper school. It is also beneficial for general education if you know what the term means

Two straight lines or planes can be said to be orthogonal.
Two straight lines or planes can be said to be orthogonal.

Orthogonal - this is a term you will find in the mathematics will hear. He is the sub-area of geometry, but in some cases also assigned to Analysis. Orthogonality denotes a geometric relationship that, for example Straight lines, but can also have planes: They are perpendicular to one another.

The origin of the term can be traced back to ancient Greek. It is made up of ὀρθός and γωνία, which means "right" and "corner". Orthogonal mathematical elements are therefore in the right angle to each other.

An orthogonal is a perpendicular

  • An orthogonal is a straight line that is perpendicular to another straight line, but also to a plane, i.e. forms a right angle (90 °).
  • There are numerous examples throughout the field of mathematics. Two straight lines can be perpendicular to one another, i.e. orthogonal, both in the two-dimensional and in the three-dimensional. A straight line that is perpendicular to a plane in three-dimensional space is also called an orthogonal.
  • In addition, it is also possible for two adjacent sides to form the required right angle, for example in the case of a rectangle. Base and height in a triangle are always perpendicular to one another, as are the opposite and adjacent sides in a right-angled triangle.
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There are different calculation variants

  • Whether two straight lines are orthogonal in two-dimensional space (coordinate system) can easily be checked on the basis of their gradients. The following applies: m1 * m2 = -1.
  • It is more difficult to check orthogonality in three-dimensional space, in which you work with points and direction vectors, for example in analytical geometry. The scalar product is available here, which results in the value zero in the case of the orthogonality of two direction vectors of straight lines or planes.

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