Definition

1. Adjective:

   • Having a slanted direction: Describes something that is neither horizontal nor vertical, but runs at an angle between them.
   • Connecting nonadjacent corners: In geometry, describes a line connecting two corners of a shape that are not next to each other.

2. Noun:

   • A slanted line: A straight line that joins two opposite corners of a square, rectangle, or other polygon.
   • A chessboard pattern: In chess, a line of squares of the same color running obliquely across the board.
   • A punctuation mark: The slash (/) character.
   • A mathematical set: In a matrix, a set of entries arranged from one corner to the opposite corner.

Usage Examples

• Adjective:

  • She drew a diagonal line from the top left to the bottom right of the paper.
  • The path cut a diagonal route across the field.

• Noun:

  • The diagonal of a square is longer than any of its sides.
  • The bishop in chess moves along the diagonal.
  • Use a diagonal (/) to separate the day and month in the date.

Advanced Usage

• "On the diagonal": Moving or oriented in a slanted direction.
  • The stripes on the shirt run on the diagonal.
• "Diagonal relationship": In chemistry, a similarity in properties between elements that are diagonally adjacent in the periodic table.
  • Lithium and magnesium show a diagonal relationship.

Variants and Related Words

• Diagonally (adverb): In a diagonal direction or manner.
  • The street runs diagonally through the city center.
• Diagonalization (noun): In mathematics, the process of converting a matrix into a diagonal form.

Synonyms

• Slanted
• Oblique
• Crosswise

Related Phrases

• Main diagonal: In a square matrix, the diagonal from the top left to the bottom right.
• Off-diagonal: Referring to elements in a matrix that are not on the main diagonal.
• Diagonal matrix: A matrix in which all entries outside the main diagonal are zero.

Adjective

1. having an oblique or slanted direction
2. connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face
   • a diagonal line across the page

Noun

1. a punctuation mark (/) used to separate related items of information
2. (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry
3. an oblique line of squares of the same color on a checkerboard
   • the bishop moves on the diagonals
4. a line or cut across a fabric that is not at right angles to a side of the fabric
5. (geometry) a straight line connecting any two vertices of a polygon that are not adjacent