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Orthogonal Meaning: Definition, Examples, and Translations

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orthogonal

[ɔːˈθɒɡən(ə)l ]

Definitions

Context #1 | Adjective

mathematics

Of or involving right angles; at right angles.

Synonyms

90-degree, perpendicular, right-angled.

Which Synonym Should You Choose?

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Word Description / Examples
orthogonal

Typically used in mathematical, statistical, or more technical contexts to denote things that are independent or at right angles to each other in multiple dimensions.

  • In data analysis, the axes of a graph should be orthogonal to clearly show the relationships between variables
perpendicular

Often used in both everyday language and academic settings to describe lines that intersect to form right angles, especially in the context of physics, engineering, and geometry.

  • He placed the book perpendicular to the shelf for better stability
right-angled

Mainly used in geometric contexts to describe triangles or other shapes that have at least one 90-degree angle.

  • The right-angled triangle is a fundamental shape in trigonometry
90-degree

Commonly used in everyday language and basic geometry to describe a quarter turn or an angle that forms a perfect square corner.

  • The carpenter cut the wood at a 90-degree angle to ensure the frame would be square

Examples of usage

  • The vectors are orthogonal to each other.
  • The lines are orthogonal.
Context #2 | Adjective

physics

Unrelated; independent in terms of variables or factors.

Synonyms

independent, uncorrelated, unrelated.

Which Synonym Should You Choose?

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Word Description / Examples
orthogonal

Used in mathematics or statistics to describe two lines or vectors that are at right angles to each other. Can also be used more figuratively to describe concepts or problems that are completely separate and do not overlap.

  • The two principal components are orthogonal to each other, ensuring no redundancy in information.
  • The tasks assigned to the team were orthogonal, meaning they could be handled independently.
independent

Commonly used in general English to describe a person, country, or variable that is free from control or influence by others. In statistics, it refers to variables that do not affect one another.

  • She has always been an independent thinker, making decisions based on her own values.
  • In the experiment, the variables were considered independent, meaning changes in one did not impact the other.
unrelated

Commonly used to describe things that have no connection or relationship to each other. Often used in everyday language and general contexts.

  • Her comment was entirely unrelated to the topic we were discussing.
  • The two incidents were unrelated, happening in different locations and times.
uncorrelated

Used in statistics to describe two variables that do not show any linear relationship with each other. Often used in risk management and investment portfolio contexts.

  • The returns on these two assets are uncorrelated, reducing overall portfolio risk.
  • We observed that the data points were uncorrelated, implying no discernible pattern.

Examples of usage

  • The two variables are orthogonal to each other.

Translations

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

  • In geometry, orthogonal lines are often used in coordinate systems, such as the Cartesian plane.
  • Two vectors are called orthogonal if their dot product equals zero, indicating they are at a right angle to each other.
  • Orthogonality is important in statistics as well, ensuring that data objects are independent of each other.

Computer Science

  • In programming, orthogonality refers to features that can be used independently without affecting one another, improving code efficiency.
  • Orthogonal data structures allow for modularity and easier debugging, which are key in software development.
  • System design that emphasizes orthogonality leads to simpler interfaces and cleaner architecture.

Art and Design

  • In visual art, orthogonal lines can create perspective, guiding the viewer's eye toward a vanishing point.
  • Architectural designs often use orthogonal principles, leading to structured forms that maintain harmony and balance.
  • Graphic design uses orthogonal grids to ensure elements are aligned neatly, conveying clarity and professionalism.

Physics

  • In physics, orthogonal systems, such as Cartesian coordinates, simplify the description of motion in multiple dimensions.
  • The principles of orthogonality are applied in quantum mechanics to describe states that are independent of one another.
  • Orthogonality in wave mechanics indicates that two waves can coexist without interfering with each other’s properties.

Origin of 'orthogonal'

Main points about word origin

  • The term comes from Greek roots: 'ortho' meaning right or straight, and 'gonal' meaning angle.
  • It was first used in English in the early 19th century to describe mathematical properties related to angles.
  • The prefix 'ortho' is also found in other words that suggest straightness, like 'orthopedics' which deals with straightening bones.

The word 'orthogonal' originated from the Greek word 'orthogōnios', which is a combination of 'orthos' meaning 'straight' or 'right' and 'gōnia' meaning 'angle'. The term was first used in mathematics to describe perpendicular lines or vectors. Over time, the concept of orthogonality has been extended to various fields such as physics, engineering, and computer science, where it denotes independence or lack of correlation. The notion of orthogonality plays a crucial role in many mathematical and scientific disciplines.

See also: orthogonality, orthogonally.

Word Frequency Rank

Ranked #11,402, this word falls into high-advanced vocabulary. It appears less frequently but is valuable for expressing precise meanings in specific contexts.