orthogonal

## 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.

## 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.

## Synonyms

## Quiz categories containing **orthogonal**

https://static.wixstatic.com/media/eb68db_0f82c81bc9d541c28e60a7e86b19098f~mv2.jpg, https://static.wixstatic.com/media/eb68db_3d0b76aa2c5f4988a3b79c60fd01ccd3~mv2.jpg, https://static.wixstatic.com/media/eb68db_17dcd098d2cd40cd931a70f28c947ca6~mv2.jpg

SAT 14 (Scholastic Assessment Test), High School 5, Science and Technology

level,perpendicular,upright,vertical

perpendicular, parallel, aligned, convergent

eb68db_7c1fe0e175794e8192f56acf1b6d4850.mp3

foursquare,plumb,quadrate,quadratic,rectangular,rectilinear,right,square,squared,straight