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orthogonal

adjective

/ɔːˈθɒɡənl/

IPA:

Dictionary definition of orthogonal

The relationship between two lines or vectors that are perpendicular to each other.
"The design of the building incorporated orthogonal lines for a modern aesthetic."

Detailed meaning of orthogonal

In this context, orthogonal is often used synonymously with perpendicular, meaning that the two lines or vectors intersect at a 90-degree angle. In a broader sense, however, orthogonal can be used to describe any two things that are completely unrelated or independent from one another. For example, in business, two different departments may have orthogonal goals or strategies, meaning that they are pursuing separate and unrelated objectives. Overall, the term orthogonal is used to describe a relationship or situation where two things have no direct or meaningful connection to each other.

Example sentences containing orthogonal

1. In geometry, two lines are orthogonal when they meet at a 90-degree angle.
2. The orthogonal vectors in the equation simplify the math.
3. An orthogonal approach to problem-solving can yield innovative solutions.
4. The architect designed the building with orthogonal lines for symmetry.
5. In computer graphics, orthogonal projections are used for accuracy.
6. An orthogonal matrix preserves the length and angles of vectors.

History and etymology of orthogonal

The adjective 'orthogonal' has its etymological roots in ancient Greek. It combines the Greek words 'orthos,' meaning 'straight' or 'right,' and 'gonia,' meaning 'angle.' In Greek geometry and mathematics, 'orthogonal' was used to describe a relationship between lines or vectors that are at right angles to each other, forming a perfect 90-degree angle. This term was later adopted into Latin as 'orthogonalis' and eventually made its way into English. 'Orthogonal' continues to describe the precise geometric relationship between objects that are perpendicular, emphasizing the concept of right angles and perpendicularity, which is integral in mathematics, engineering, and various fields where the perpendicular relationship is of significance.

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Further usage examples of orthogonal

1. The engineer employed orthogonal reinforcement for structural integrity.
2. The orthogonal layout of the garden created a sense of order.
3. In statistics, orthogonal variables are independent of each other.
4. The surveyor ensured the walls were orthogonal to the property lines.
5. The orthogonal axes on the graph facilitate precise measurement.
6. An orthogonal transformation can rotate coordinates in space.
7. The electrical engineers used orthogonal signals to avoid interference.
8. The artist employed orthogonal lines for a sense of depth.
9. In linear algebra, orthogonal matrices have unique properties.
10. The city streets formed an orthogonal grid for easy navigation.
11. Orthogonal design principles guided the software development.
12. The designer chose orthogonal patterns for the wallpaper.
13. The scientific method relies on orthogonal experimentation.
14. The mathematician proved the theorem using orthogonal vectors.
15. The two vectors are orthogonal, meaning they are at a 90-degree angle to each other.
16. The study analyzed the orthogonal properties of the material.
17. The researchers found that the two variables were orthogonal to each other.
18. The x and y axis are orthogonal in a Cartesian coordinate system.
19. The orthogonal projection of a vector onto a subspace is a common operation in linear algebra.
20. The orthogonal design of the experiment controlled for extraneous variables.
21. The orthogonal array was used to test all possible combinations of factors.
22. The two matrices were orthogonal, which made them particularly useful for certain calculations.
23. The orthogonal properties of a matrix can be determined by its eigenvectors.
24. The orthogonal cutting method is used in metalworking to remove material.
25. The orthogonal view of the object was helpful in understanding its three-dimensional structure.