Definition of diagonal in English:

diagonal

adjective dʌɪˈaɡ(ə)n(ə)ldaɪˈæɡənl

1(of a straight line) joining two opposite corners of a square, rectangle, or other straight-sided shape.
Example sentencesExamples
- This study consisted of a grid of 15 squares, each inscribed with one or more horizontal, vertical, and diagonal lines in different orientations.
- The other diagonal lines specify points with this ratio above 10, 100, and 1000.
- Symbols occurring close to the diagonal line represent a perfect match between simulated and measured data.
- In the grid numerous long diagonal white lines can clearly be seen.
- The thin diagonal line is the 1: 1 relationship.
- One option is to draw a diagonal line between two opposite points to represent movement between here and there.
- The design was very nice, with diagonal lines forming a grid, each square filled with a snapshot of the movie in rich, warm tones.
- Draw two diagonal lines dividing the square and the rectangle into triangles.
- The diagonal line connecting these two points must equal 5 feet.
- The points 11 to 13, outside the common ancestor 3 of the probes 7 and 9, lie on the diagonal line A.
- They form a diagonal shape at the bottom of the torso, and can be divided into the front triangle and the back triangle.
- The diagonal line indicates where the data points would be if the measurements obtained with the 2 techniques were identical.
- If each successive 10% of households held 10% of total income, then the curve would be a diagonal line at 45°.
- The diagonal line indicates d N = d S, meaning neutral selection.
- The starting positions of the first instance of the repeat on the upper strand and the starting position of the second instance of the repeat on the lower strand are connected by a diagonal line.
- A diagonal line separated a triangle of white and another of blue that together formed a rectangle.
- He imagined how a diagonal line cutting across a square would divide the square into two right triangles.
- In principle, with perfect agreement between the two sequences, all points will lie on the diagonal line, while large deviations indicate large branch length differences.
- This is accomplished by avoiding vertical, horizontal or diagonal lines, and checker-board patterns of pixels for which the color level is decremented.
- Fibonacci fans are composed of diagonal lines.
1. 1.1 (of a line) straight and at an angle; slanting.
  a tie with diagonal stripes
  Example sentencesExamples
  The scabs had faded, so there were only two faint pink diagonal lines.
  Towards the west end is the main staircase, its bottom flight skewed to the angle of the south wing in response to the diagonal thrust of the approach.
  Press your heels down onto the ball, pull your abs inward, and raise your hips and torso off the floor until your ankles, hips and shoulders are in a straight, diagonal line.
  At one point the dancer stamped nimbly in a diagonal line across the stage and stopped in the front corner.
  In the second half Windermere had the advantage of the diagonal crosswind and continued to apply pressure to the Gosforth line without turning it into points.
  These rays are also useful artistically for breaking up the shapes of the mountains with diagonal lines.
  I bought a black sleeveless Lycra shirt with yellow and white diagonal stripes across the chest.
  Score the squid by holding the knife at an angle and making diagonal cuts, taking care not to cut right through.
  Double diagonal lines indicate an area not drawn to scale.
  The film, with the exception of one shot, is composed of precisely two camera angles: a diagonal shot from the dashboard towards the passenger seat, and another, similar shot towards the driver seat.
  The diagonal passes that are fed in are very difficult to defend against.
  If scaffolds are not set away, mortar may lodge on diagonal bracing and adhere to wall.
  We can see that as we increase resolution, drawing a straight, diagonal line looks better.
  As for color, choose a gold and black regimental tie with alternating diagonal stripes.
  The solid diagonal line represents the situation when the two estimated distributions were identical.
  One end of the upper stone was fixed to a pivot and both stones were ‘dressed’ with small diagonal grooves which crossed each other at an angle as the upper stone swept across the lower in an arc.
  A reflective road sign with diagonal stripes of black and white thrusts itself upward through the picture plane.
  Pencil-thin diagonal blues and greens angle across the surface like tracer-bullet tracks streaking across a movie screen.
  The column spacing makes for a complex, overlapping matrix when viewed from a diagonal angle.
  Synonyms
  crossways, crosswise, from corner to corner, slanting, slanted, aslant, slant, slantwise, sloping, oblique, inclined, inclining, tilted, tilting, angled, at an angle, cornerwise
  Scottish squint
  North American cater-cornered, cater-corner, catty-cornered, kitty-corner

noun dʌɪˈaɡ(ə)n(ə)ldaɪˈæɡənl

1A straight line joining two opposite corners of a square, rectangle, or other straight-sided shape.
Example sentencesExamples
- The diagonal of a square of side 30 is found by multiplying 30 by the approximation to 2.
- We can find the length of the other side of the triangle, the diagonal AT, by using Pythagoras' Theorem.
- For example, the Pythagoreans did not expect to uncover irrational numbers in the diagonal of a square.
- He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point.
- How would you get the number of diagonals in a polygon?
- After everything is nailed together, check the wall for squareness first by measuring across diagonally from one corner to the other, then measuring the opposite diagonal.
- If you turn the squares on the diagonal, creating a diamond shape, the measurement is less obvious.
- A mathematical theorem about diagonals of rectangles might mention two equal and similar triangles which are, nonetheless, distinct.
- Do this at a diagonal, from one corner of the square to the opposite corner.
- The five-pointed stars on many flags of the world (for example, the European flag) are made by cutting the diagonals of a pentagon according to the Golden Ratio.
- Observe that opposite sides of these hexagons are parallel, because the equal-area condition requires them to be parallel to a common diagonal.
- It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles.
- Complete the parallelogram CABD and draw in the diagonal AD which is then easily seen to bisect the angle CAB.
- Let d be the length of the diagonal of a square and s the length of its sides.
- When you can't draw any more without intersecting existing diagonals, count their total number.
- Similarly, we only know that a diagonal of a square is incommensurable with its side if we know that there are squares and that squares have diagonals.
- The particular tablet which concerns us is not one relating to administration but one which presents a geometrical problem which asks for the dimensions of a rectangle whose area and diagonal are known.
- Cut into squares and then cut the squares along the diagonal.
- Third, show that every simple lattice polygon may be dissected into a union of lattice triangles (e.g., by its diagonals.)
1. 1.1Mathematics The set of elements of a matrix that lie on a line joining two opposite corners.
  Example sentencesExamples
  If we restrict ourselves to the 2x2 arrays whose diagonals lie on the main diagonal of the table, then the sum of four numbers in the array is always a perfect square.
  The diagonal of the rate matrix is specified such that the row sums are equal to zero.
  The alpha values and the mean interitem correlations are presented in the diagonals of the matrices in Table 2.
  If we let D denote the diagonal matrix with the entries of along its diagonal, then reversibility is equivalent to the detailed balance condition
2. 1.2 A slanting straight line.
  the bars of light made diagonals across the entrance
  tiles can be laid on the diagonal
  Example sentencesExamples
  The paintings are thick with diagonals; light is pure color, color is pure stroke.
  His perspectives, building across the paper horizontally, were slightly tilted and cut by occasional diagonals, almost as if caught by an amateur's camera.
  These lines also work best when they follow a diagonal, rather than a straight horizontal or vertical.
  The paved walkway I follow runs at a diagonal across the slope toward the beach.
  The quartet begins with the dancers - dressed in everyday clothes, but colorful so as not to be dull under stage lights - standing in a square formation along a slight diagonal.
  The positioning of the diving board - coming at a diagonal out of the corner - gives perspective as well as cutting across the predominant horizontals.
  He shaped for a diagonal into the box, before cutting through a low drive that swerved slightly away from the goalkeeper.
  Take cuttings from last seasons growth, cut just below the bud and trim the top on the diagonal.
  Set against the rectangular everyday norm, it is the zigzags and clashing diagonals of the interior that provide the most convincing symbols of conflict, giving real identity to the purpose of the building.
  They can be disturbing unless supported by verticals or opposing diagonals.
  Nothing is in a predictable relationship; the beams are not the same sizes, and although they pass through each other in fairly straight diagonals, the effect is entanglement, not movement.
  Let stand ten minutes, then slice very thin and on the diagonal.
  Spanning the entire adjacent wall, an ascending diagonal was joined by a rippled line.
  Arrange in a circle, in corners or in a diagonal.
  The truncated shapes often incorporate diagonals, and these shapes, in turn, recur in the artist's paintings.
  Circles, rounded shapes and curves have become prominent in Ross's work, whether in terse, varicolored, concentric bands or in combination with diagonals, pentagons and trapezoids.
  It wasn't the fact that she was unused to the size of the car, or that little Billy was throwing a fit on the back seat that meant she ended up forming a diagonal between the white lines, oh no.
  A wood sculpture from 2002 bunches several small rectangular forms beneath two lengthy diagonals that meet at the top like the tips of fingers joined in prayer.
  There is nothing static in Strand's New York: It is a city built of passing glances, a streetscape of dashing diagonals and unexpected angles.
  Miller photographs buildings from high angles to get repeating diagonals and pyramidlike forms, then manipulates this imagery so that it draws the eye inward or seems to project from the surface of the picture.
3. 1.3Chess A slanting row of squares whose colour is the same.
  Example sentencesExamples
  Her king was safe on h8, protected on the long diagonal by her bishop on e5.
  After a queen pawn opening, Hort threatened mate on the long diagonal.
  As frequently happens in such a situation, White does not have a diagonal for his dark Bishop, nor does he have any other diagonals from which to aim at his opponent's King.
  Black decides that he has to get White's Bishop off that laser a2-g8 diagonal!
  If you move a pawn to open up a diagonal for a bishop, then should you usually NOT move up another pawn to develop the bishop on the other diagonal.

Origin

Mid 16th century: from Latin diagonalis, from Greek diagōnios 'from angle to angle', from dia 'through' + gōnia 'angle'.

pentagon from late 16th century:
The Greek expertise in geometry means that many geometrical forms have Greek names. The five-sided pentagon is formed from penta ‘five’ and gonia ‘angle’, just as polygon (late 16th century) is formed from the word for ‘many’ plus -gon and diagonal (mid 16th century) with dia ‘through’. Penta is also found in words such as the mystic figures of the pentangle (Late Middle English), pentacle (late 16th century), and pentagram (mid 19th century), and in the pentathlon (early 17th century), once the original five events of leaping, running, discus-throwing, spear-throwing, and wrestling of ancient Greek and Roman games. Fifty is found in Pentecost (Old English) which came via ecclesiastical Latin from Greek pentēkostē (hēmera) ‘fiftieth (day)’. The Jewish festival of Shavuoth is held on the fiftieth day after the second day of Passover. The Christian festival is held on the seventh Sunday after Easter commemorating the descent of the Holy Spirit on the disciples as recorded in Acts 2.

Rhymes

heptagonal, hexagonal, octagonal, tetragonal

Definition of diagonal in US English:

diagonal

(also diag.)

adjectivedīˈaɡənldaɪˈæɡənl

1(of a straight line) joining two opposite corners of a square, rectangle, or other straight-sided shape.
Example sentencesExamples
- The diagonal line indicates d N = d S, meaning neutral selection.
- This study consisted of a grid of 15 squares, each inscribed with one or more horizontal, vertical, and diagonal lines in different orientations.
- The points 11 to 13, outside the common ancestor 3 of the probes 7 and 9, lie on the diagonal line A.
- They form a diagonal shape at the bottom of the torso, and can be divided into the front triangle and the back triangle.
- A diagonal line separated a triangle of white and another of blue that together formed a rectangle.
- In principle, with perfect agreement between the two sequences, all points will lie on the diagonal line, while large deviations indicate large branch length differences.
- This is accomplished by avoiding vertical, horizontal or diagonal lines, and checker-board patterns of pixels for which the color level is decremented.
- Draw two diagonal lines dividing the square and the rectangle into triangles.
- The design was very nice, with diagonal lines forming a grid, each square filled with a snapshot of the movie in rich, warm tones.
- The other diagonal lines specify points with this ratio above 10, 100, and 1000.
- Fibonacci fans are composed of diagonal lines.
- The thin diagonal line is the 1: 1 relationship.
- He imagined how a diagonal line cutting across a square would divide the square into two right triangles.
- One option is to draw a diagonal line between two opposite points to represent movement between here and there.
- The starting positions of the first instance of the repeat on the upper strand and the starting position of the second instance of the repeat on the lower strand are connected by a diagonal line.
- In the grid numerous long diagonal white lines can clearly be seen.
- The diagonal line connecting these two points must equal 5 feet.
- The diagonal line indicates where the data points would be if the measurements obtained with the 2 techniques were identical.
- Symbols occurring close to the diagonal line represent a perfect match between simulated and measured data.
- If each successive 10% of households held 10% of total income, then the curve would be a diagonal line at 45°.
1. 1.1 (of a line) straight and at an angle; slanting.
  a tie with diagonal stripes
  Example sentencesExamples
  The diagonal passes that are fed in are very difficult to defend against.
  The solid diagonal line represents the situation when the two estimated distributions were identical.
  At one point the dancer stamped nimbly in a diagonal line across the stage and stopped in the front corner.
  A reflective road sign with diagonal stripes of black and white thrusts itself upward through the picture plane.
  Score the squid by holding the knife at an angle and making diagonal cuts, taking care not to cut right through.
  We can see that as we increase resolution, drawing a straight, diagonal line looks better.
  The film, with the exception of one shot, is composed of precisely two camera angles: a diagonal shot from the dashboard towards the passenger seat, and another, similar shot towards the driver seat.
  These rays are also useful artistically for breaking up the shapes of the mountains with diagonal lines.
  Towards the west end is the main staircase, its bottom flight skewed to the angle of the south wing in response to the diagonal thrust of the approach.
  Press your heels down onto the ball, pull your abs inward, and raise your hips and torso off the floor until your ankles, hips and shoulders are in a straight, diagonal line.
  I bought a black sleeveless Lycra shirt with yellow and white diagonal stripes across the chest.
  The column spacing makes for a complex, overlapping matrix when viewed from a diagonal angle.
  If scaffolds are not set away, mortar may lodge on diagonal bracing and adhere to wall.
  The scabs had faded, so there were only two faint pink diagonal lines.
  Double diagonal lines indicate an area not drawn to scale.
  As for color, choose a gold and black regimental tie with alternating diagonal stripes.
  Pencil-thin diagonal blues and greens angle across the surface like tracer-bullet tracks streaking across a movie screen.
  In the second half Windermere had the advantage of the diagonal crosswind and continued to apply pressure to the Gosforth line without turning it into points.
  One end of the upper stone was fixed to a pivot and both stones were ‘dressed’ with small diagonal grooves which crossed each other at an angle as the upper stone swept across the lower in an arc.
  Synonyms
  crossways, crosswise, from corner to corner, slanting, slanted, aslant, slant, slantwise, sloping, oblique, inclined, inclining, tilted, tilting, angled, at an angle, cornerwise

noundīˈaɡənldaɪˈæɡənl

1A straight line joining two opposite corners of a square, rectangle, or other straight-sided shape.
Example sentencesExamples
- Let d be the length of the diagonal of a square and s the length of its sides.
- We can find the length of the other side of the triangle, the diagonal AT, by using Pythagoras' Theorem.
- Observe that opposite sides of these hexagons are parallel, because the equal-area condition requires them to be parallel to a common diagonal.
- Do this at a diagonal, from one corner of the square to the opposite corner.
- He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point.
- For example, the Pythagoreans did not expect to uncover irrational numbers in the diagonal of a square.
- Third, show that every simple lattice polygon may be dissected into a union of lattice triangles (e.g., by its diagonals.)
- How would you get the number of diagonals in a polygon?
- The diagonal of a square of side 30 is found by multiplying 30 by the approximation to 2.
- It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles.
- A mathematical theorem about diagonals of rectangles might mention two equal and similar triangles which are, nonetheless, distinct.
- The five-pointed stars on many flags of the world (for example, the European flag) are made by cutting the diagonals of a pentagon according to the Golden Ratio.
- When you can't draw any more without intersecting existing diagonals, count their total number.
- After everything is nailed together, check the wall for squareness first by measuring across diagonally from one corner to the other, then measuring the opposite diagonal.
- If you turn the squares on the diagonal, creating a diamond shape, the measurement is less obvious.
- Similarly, we only know that a diagonal of a square is incommensurable with its side if we know that there are squares and that squares have diagonals.
- Cut into squares and then cut the squares along the diagonal.
- Complete the parallelogram CABD and draw in the diagonal AD which is then easily seen to bisect the angle CAB.
- The particular tablet which concerns us is not one relating to administration but one which presents a geometrical problem which asks for the dimensions of a rectangle whose area and diagonal are known.
1. 1.1Mathematics The set of elements of a matrix that lie on a line joining two opposite corners.
  Example sentencesExamples
  If we let D denote the diagonal matrix with the entries of along its diagonal, then reversibility is equivalent to the detailed balance condition
  The diagonal of the rate matrix is specified such that the row sums are equal to zero.
  If we restrict ourselves to the 2x2 arrays whose diagonals lie on the main diagonal of the table, then the sum of four numbers in the array is always a perfect square.
  The alpha values and the mean interitem correlations are presented in the diagonals of the matrices in Table 2.
2. 1.2 A slanting straight pattern or line.
  the bars of light made diagonals across the entrance
  tiles can be laid on the diagonal
  Example sentencesExamples
  Circles, rounded shapes and curves have become prominent in Ross's work, whether in terse, varicolored, concentric bands or in combination with diagonals, pentagons and trapezoids.
  Set against the rectangular everyday norm, it is the zigzags and clashing diagonals of the interior that provide the most convincing symbols of conflict, giving real identity to the purpose of the building.
  The truncated shapes often incorporate diagonals, and these shapes, in turn, recur in the artist's paintings.
  The paintings are thick with diagonals; light is pure color, color is pure stroke.
  The paved walkway I follow runs at a diagonal across the slope toward the beach.
  His perspectives, building across the paper horizontally, were slightly tilted and cut by occasional diagonals, almost as if caught by an amateur's camera.
  It wasn't the fact that she was unused to the size of the car, or that little Billy was throwing a fit on the back seat that meant she ended up forming a diagonal between the white lines, oh no.
  Spanning the entire adjacent wall, an ascending diagonal was joined by a rippled line.
  The quartet begins with the dancers - dressed in everyday clothes, but colorful so as not to be dull under stage lights - standing in a square formation along a slight diagonal.
  Nothing is in a predictable relationship; the beams are not the same sizes, and although they pass through each other in fairly straight diagonals, the effect is entanglement, not movement.
  Miller photographs buildings from high angles to get repeating diagonals and pyramidlike forms, then manipulates this imagery so that it draws the eye inward or seems to project from the surface of the picture.
  A wood sculpture from 2002 bunches several small rectangular forms beneath two lengthy diagonals that meet at the top like the tips of fingers joined in prayer.
  Arrange in a circle, in corners or in a diagonal.
  The positioning of the diving board - coming at a diagonal out of the corner - gives perspective as well as cutting across the predominant horizontals.
  He shaped for a diagonal into the box, before cutting through a low drive that swerved slightly away from the goalkeeper.
  Take cuttings from last seasons growth, cut just below the bud and trim the top on the diagonal.
  These lines also work best when they follow a diagonal, rather than a straight horizontal or vertical.
  They can be disturbing unless supported by verticals or opposing diagonals.
  Let stand ten minutes, then slice very thin and on the diagonal.
  There is nothing static in Strand's New York: It is a city built of passing glances, a streetscape of dashing diagonals and unexpected angles.
3. 1.3Chess A slanting row of squares whose color is the same.
  Example sentencesExamples
  Black decides that he has to get White's Bishop off that laser a2-g8 diagonal!
  After a queen pawn opening, Hort threatened mate on the long diagonal.
  As frequently happens in such a situation, White does not have a diagonal for his dark Bishop, nor does he have any other diagonals from which to aim at his opponent's King.
  If you move a pawn to open up a diagonal for a bishop, then should you usually NOT move up another pawn to develop the bishop on the other diagonal.
  Her king was safe on h8, protected on the long diagonal by her bishop on e5.

Origin

Mid 16th century: from Latin diagonalis, from Greek diagōnios ‘from angle to angle’, from dia ‘through’ + gōnia ‘angle’.

单词	diagonal
释义	Definition of diagonal in English: diagonal adjective dʌɪˈaɡ(ə)n(ə)ldaɪˈæɡənl 1(of a straight line) joining two opposite corners of a square, rectangle, or other straight-sided shape. Example sentencesExamples This study consisted of a grid of 15 squares, each inscribed with one or more horizontal, vertical, and diagonal lines in different orientations. The other diagonal lines specify points with this ratio above 10, 100, and 1000. Symbols occurring close to the diagonal line represent a perfect match between simulated and measured data. In the grid numerous long diagonal white lines can clearly be seen. The thin diagonal line is the 1: 1 relationship. One option is to draw a diagonal line between two opposite points to represent movement between here and there. The design was very nice, with diagonal lines forming a grid, each square filled with a snapshot of the movie in rich, warm tones. Draw two diagonal lines dividing the square and the rectangle into triangles. The diagonal line connecting these two points must equal 5 feet. The points 11 to 13, outside the common ancestor 3 of the probes 7 and 9, lie on the diagonal line A. They form a diagonal shape at the bottom of the torso, and can be divided into the front triangle and the back triangle. The diagonal line indicates where the data points would be if the measurements obtained with the 2 techniques were identical. If each successive 10% of households held 10% of total income, then the curve would be a diagonal line at 45°. The diagonal line indicates d N = d S, meaning neutral selection. The starting positions of the first instance of the repeat on the upper strand and the starting position of the second instance of the repeat on the lower strand are connected by a diagonal line. A diagonal line separated a triangle of white and another of blue that together formed a rectangle. He imagined how a diagonal line cutting across a square would divide the square into two right triangles. In principle, with perfect agreement between the two sequences, all points will lie on the diagonal line, while large deviations indicate large branch length differences. This is accomplished by avoiding vertical, horizontal or diagonal lines, and checker-board patterns of pixels for which the color level is decremented. Fibonacci fans are composed of diagonal lines. 1.1 (of a line) straight and at an angle; slanting. a tie with diagonal stripes Example sentencesExamples The scabs had faded, so there were only two faint pink diagonal lines. Towards the west end is the main staircase, its bottom flight skewed to the angle of the south wing in response to the diagonal thrust of the approach. Press your heels down onto the ball, pull your abs inward, and raise your hips and torso off the floor until your ankles, hips and shoulders are in a straight, diagonal line. At one point the dancer stamped nimbly in a diagonal line across the stage and stopped in the front corner. In the second half Windermere had the advantage of the diagonal crosswind and continued to apply pressure to the Gosforth line without turning it into points. These rays are also useful artistically for breaking up the shapes of the mountains with diagonal lines. I bought a black sleeveless Lycra shirt with yellow and white diagonal stripes across the chest. Score the squid by holding the knife at an angle and making diagonal cuts, taking care not to cut right through. Double diagonal lines indicate an area not drawn to scale. The film, with the exception of one shot, is composed of precisely two camera angles: a diagonal shot from the dashboard towards the passenger seat, and another, similar shot towards the driver seat. The diagonal passes that are fed in are very difficult to defend against. If scaffolds are not set away, mortar may lodge on diagonal bracing and adhere to wall. We can see that as we increase resolution, drawing a straight, diagonal line looks better. As for color, choose a gold and black regimental tie with alternating diagonal stripes. The solid diagonal line represents the situation when the two estimated distributions were identical. One end of the upper stone was fixed to a pivot and both stones were ‘dressed’ with small diagonal grooves which crossed each other at an angle as the upper stone swept across the lower in an arc. A reflective road sign with diagonal stripes of black and white thrusts itself upward through the picture plane. Pencil-thin diagonal blues and greens angle across the surface like tracer-bullet tracks streaking across a movie screen. The column spacing makes for a complex, overlapping matrix when viewed from a diagonal angle. Synonyms crossways, crosswise, from corner to corner, slanting, slanted, aslant, slant, slantwise, sloping, oblique, inclined, inclining, tilted, tilting, angled, at an angle, cornerwise Scottish squint North American cater-cornered, cater-corner, catty-cornered, kitty-corner noun dʌɪˈaɡ(ə)n(ə)ldaɪˈæɡənl 1A straight line joining two opposite corners of a square, rectangle, or other straight-sided shape. Example sentencesExamples The diagonal of a square of side 30 is found by multiplying 30 by the approximation to 2. We can find the length of the other side of the triangle, the diagonal AT, by using Pythagoras' Theorem. For example, the Pythagoreans did not expect to uncover irrational numbers in the diagonal of a square. He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. How would you get the number of diagonals in a polygon? After everything is nailed together, check the wall for squareness first by measuring across diagonally from one corner to the other, then measuring the opposite diagonal. If you turn the squares on the diagonal, creating a diamond shape, the measurement is less obvious. A mathematical theorem about diagonals of rectangles might mention two equal and similar triangles which are, nonetheless, distinct. Do this at a diagonal, from one corner of the square to the opposite corner. The five-pointed stars on many flags of the world (for example, the European flag) are made by cutting the diagonals of a pentagon according to the Golden Ratio. Observe that opposite sides of these hexagons are parallel, because the equal-area condition requires them to be parallel to a common diagonal. It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles. Complete the parallelogram CABD and draw in the diagonal AD which is then easily seen to bisect the angle CAB. Let d be the length of the diagonal of a square and s the length of its sides. When you can't draw any more without intersecting existing diagonals, count their total number. Similarly, we only know that a diagonal of a square is incommensurable with its side if we know that there are squares and that squares have diagonals. The particular tablet which concerns us is not one relating to administration but one which presents a geometrical problem which asks for the dimensions of a rectangle whose area and diagonal are known. Cut into squares and then cut the squares along the diagonal. Third, show that every simple lattice polygon may be dissected into a union of lattice triangles (e.g., by its diagonals.) 1.1Mathematics The set of elements of a matrix that lie on a line joining two opposite corners. Example sentencesExamples If we restrict ourselves to the 2x2 arrays whose diagonals lie on the main diagonal of the table, then the sum of four numbers in the array is always a perfect square. The diagonal of the rate matrix is specified such that the row sums are equal to zero. The alpha values and the mean interitem correlations are presented in the diagonals of the matrices in Table 2. If we let D denote the diagonal matrix with the entries of along its diagonal, then reversibility is equivalent to the detailed balance condition 1.2 A slanting straight line. the bars of light made diagonals across the entrance tiles can be laid on the diagonal Example sentencesExamples The paintings are thick with diagonals; light is pure color, color is pure stroke. His perspectives, building across the paper horizontally, were slightly tilted and cut by occasional diagonals, almost as if caught by an amateur's camera. These lines also work best when they follow a diagonal, rather than a straight horizontal or vertical. The paved walkway I follow runs at a diagonal across the slope toward the beach. The quartet begins with the dancers - dressed in everyday clothes, but colorful so as not to be dull under stage lights - standing in a square formation along a slight diagonal. The positioning of the diving board - coming at a diagonal out of the corner - gives perspective as well as cutting across the predominant horizontals. He shaped for a diagonal into the box, before cutting through a low drive that swerved slightly away from the goalkeeper. Take cuttings from last seasons growth, cut just below the bud and trim the top on the diagonal. Set against the rectangular everyday norm, it is the zigzags and clashing diagonals of the interior that provide the most convincing symbols of conflict, giving real identity to the purpose of the building. They can be disturbing unless supported by verticals or opposing diagonals. Nothing is in a predictable relationship; the beams are not the same sizes, and although they pass through each other in fairly straight diagonals, the effect is entanglement, not movement. Let stand ten minutes, then slice very thin and on the diagonal. Spanning the entire adjacent wall, an ascending diagonal was joined by a rippled line. Arrange in a circle, in corners or in a diagonal. The truncated shapes often incorporate diagonals, and these shapes, in turn, recur in the artist's paintings. Circles, rounded shapes and curves have become prominent in Ross's work, whether in terse, varicolored, concentric bands or in combination with diagonals, pentagons and trapezoids. It wasn't the fact that she was unused to the size of the car, or that little Billy was throwing a fit on the back seat that meant she ended up forming a diagonal between the white lines, oh no. A wood sculpture from 2002 bunches several small rectangular forms beneath two lengthy diagonals that meet at the top like the tips of fingers joined in prayer. There is nothing static in Strand's New York: It is a city built of passing glances, a streetscape of dashing diagonals and unexpected angles. Miller photographs buildings from high angles to get repeating diagonals and pyramidlike forms, then manipulates this imagery so that it draws the eye inward or seems to project from the surface of the picture. 1.3Chess A slanting row of squares whose colour is the same. Example sentencesExamples Her king was safe on h8, protected on the long diagonal by her bishop on e5. After a queen pawn opening, Hort threatened mate on the long diagonal. As frequently happens in such a situation, White does not have a diagonal for his dark Bishop, nor does he have any other diagonals from which to aim at his opponent's King. Black decides that he has to get White's Bishop off that laser a2-g8 diagonal! If you move a pawn to open up a diagonal for a bishop, then should you usually NOT move up another pawn to develop the bishop on the other diagonal. Origin Mid 16th century: from Latin diagonalis, from Greek diagōnios 'from angle to angle', from dia 'through' + gōnia 'angle'. pentagon from late 16th century: The Greek expertise in geometry means that many geometrical forms have Greek names. The five-sided pentagon is formed from penta ‘five’ and gonia ‘angle’, just as polygon (late 16th century) is formed from the word for ‘many’ plus -gon and diagonal (mid 16th century) with dia ‘through’. Penta is also found in words such as the mystic figures of the pentangle (Late Middle English), pentacle (late 16th century), and pentagram (mid 19th century), and in the pentathlon (early 17th century), once the original five events of leaping, running, discus-throwing, spear-throwing, and wrestling of ancient Greek and Roman games. Fifty is found in Pentecost (Old English) which came via ecclesiastical Latin from Greek pentēkostē (hēmera) ‘fiftieth (day)’. The Jewish festival of Shavuoth is held on the fiftieth day after the second day of Passover. The Christian festival is held on the seventh Sunday after Easter commemorating the descent of the Holy Spirit on the disciples as recorded in Acts 2. Rhymes heptagonal, hexagonal, octagonal, tetragonal Definition of diagonal in US English: diagonal (also diag.) adjectivedīˈaɡənldaɪˈæɡənl 1(of a straight line) joining two opposite corners of a square, rectangle, or other straight-sided shape. Example sentencesExamples The diagonal line indicates d N = d S, meaning neutral selection. This study consisted of a grid of 15 squares, each inscribed with one or more horizontal, vertical, and diagonal lines in different orientations. The points 11 to 13, outside the common ancestor 3 of the probes 7 and 9, lie on the diagonal line A. They form a diagonal shape at the bottom of the torso, and can be divided into the front triangle and the back triangle. A diagonal line separated a triangle of white and another of blue that together formed a rectangle. In principle, with perfect agreement between the two sequences, all points will lie on the diagonal line, while large deviations indicate large branch length differences. This is accomplished by avoiding vertical, horizontal or diagonal lines, and checker-board patterns of pixels for which the color level is decremented. Draw two diagonal lines dividing the square and the rectangle into triangles. The design was very nice, with diagonal lines forming a grid, each square filled with a snapshot of the movie in rich, warm tones. The other diagonal lines specify points with this ratio above 10, 100, and 1000. Fibonacci fans are composed of diagonal lines. The thin diagonal line is the 1: 1 relationship. He imagined how a diagonal line cutting across a square would divide the square into two right triangles. One option is to draw a diagonal line between two opposite points to represent movement between here and there. The starting positions of the first instance of the repeat on the upper strand and the starting position of the second instance of the repeat on the lower strand are connected by a diagonal line. In the grid numerous long diagonal white lines can clearly be seen. The diagonal line connecting these two points must equal 5 feet. The diagonal line indicates where the data points would be if the measurements obtained with the 2 techniques were identical. Symbols occurring close to the diagonal line represent a perfect match between simulated and measured data. If each successive 10% of households held 10% of total income, then the curve would be a diagonal line at 45°. 1.1 (of a line) straight and at an angle; slanting. a tie with diagonal stripes Example sentencesExamples The diagonal passes that are fed in are very difficult to defend against. The solid diagonal line represents the situation when the two estimated distributions were identical. At one point the dancer stamped nimbly in a diagonal line across the stage and stopped in the front corner. A reflective road sign with diagonal stripes of black and white thrusts itself upward through the picture plane. Score the squid by holding the knife at an angle and making diagonal cuts, taking care not to cut right through. We can see that as we increase resolution, drawing a straight, diagonal line looks better. The film, with the exception of one shot, is composed of precisely two camera angles: a diagonal shot from the dashboard towards the passenger seat, and another, similar shot towards the driver seat. These rays are also useful artistically for breaking up the shapes of the mountains with diagonal lines. Towards the west end is the main staircase, its bottom flight skewed to the angle of the south wing in response to the diagonal thrust of the approach. Press your heels down onto the ball, pull your abs inward, and raise your hips and torso off the floor until your ankles, hips and shoulders are in a straight, diagonal line. I bought a black sleeveless Lycra shirt with yellow and white diagonal stripes across the chest. The column spacing makes for a complex, overlapping matrix when viewed from a diagonal angle. If scaffolds are not set away, mortar may lodge on diagonal bracing and adhere to wall. The scabs had faded, so there were only two faint pink diagonal lines. Double diagonal lines indicate an area not drawn to scale. As for color, choose a gold and black regimental tie with alternating diagonal stripes. Pencil-thin diagonal blues and greens angle across the surface like tracer-bullet tracks streaking across a movie screen. In the second half Windermere had the advantage of the diagonal crosswind and continued to apply pressure to the Gosforth line without turning it into points. One end of the upper stone was fixed to a pivot and both stones were ‘dressed’ with small diagonal grooves which crossed each other at an angle as the upper stone swept across the lower in an arc. Synonyms crossways, crosswise, from corner to corner, slanting, slanted, aslant, slant, slantwise, sloping, oblique, inclined, inclining, tilted, tilting, angled, at an angle, cornerwise noundīˈaɡənldaɪˈæɡənl 1A straight line joining two opposite corners of a square, rectangle, or other straight-sided shape. Example sentencesExamples Let d be the length of the diagonal of a square and s the length of its sides. We can find the length of the other side of the triangle, the diagonal AT, by using Pythagoras' Theorem. Observe that opposite sides of these hexagons are parallel, because the equal-area condition requires them to be parallel to a common diagonal. Do this at a diagonal, from one corner of the square to the opposite corner. He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. For example, the Pythagoreans did not expect to uncover irrational numbers in the diagonal of a square. Third, show that every simple lattice polygon may be dissected into a union of lattice triangles (e.g., by its diagonals.) How would you get the number of diagonals in a polygon? The diagonal of a square of side 30 is found by multiplying 30 by the approximation to 2. It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles. A mathematical theorem about diagonals of rectangles might mention two equal and similar triangles which are, nonetheless, distinct. The five-pointed stars on many flags of the world (for example, the European flag) are made by cutting the diagonals of a pentagon according to the Golden Ratio. When you can't draw any more without intersecting existing diagonals, count their total number. After everything is nailed together, check the wall for squareness first by measuring across diagonally from one corner to the other, then measuring the opposite diagonal. If you turn the squares on the diagonal, creating a diamond shape, the measurement is less obvious. Similarly, we only know that a diagonal of a square is incommensurable with its side if we know that there are squares and that squares have diagonals. Cut into squares and then cut the squares along the diagonal. Complete the parallelogram CABD and draw in the diagonal AD which is then easily seen to bisect the angle CAB. The particular tablet which concerns us is not one relating to administration but one which presents a geometrical problem which asks for the dimensions of a rectangle whose area and diagonal are known. 1.1Mathematics The set of elements of a matrix that lie on a line joining two opposite corners. Example sentencesExamples If we let D denote the diagonal matrix with the entries of along its diagonal, then reversibility is equivalent to the detailed balance condition The diagonal of the rate matrix is specified such that the row sums are equal to zero. If we restrict ourselves to the 2x2 arrays whose diagonals lie on the main diagonal of the table, then the sum of four numbers in the array is always a perfect square. The alpha values and the mean interitem correlations are presented in the diagonals of the matrices in Table 2. 1.2 A slanting straight pattern or line. the bars of light made diagonals across the entrance tiles can be laid on the diagonal Example sentencesExamples Circles, rounded shapes and curves have become prominent in Ross's work, whether in terse, varicolored, concentric bands or in combination with diagonals, pentagons and trapezoids. Set against the rectangular everyday norm, it is the zigzags and clashing diagonals of the interior that provide the most convincing symbols of conflict, giving real identity to the purpose of the building. The truncated shapes often incorporate diagonals, and these shapes, in turn, recur in the artist's paintings. The paintings are thick with diagonals; light is pure color, color is pure stroke. The paved walkway I follow runs at a diagonal across the slope toward the beach. His perspectives, building across the paper horizontally, were slightly tilted and cut by occasional diagonals, almost as if caught by an amateur's camera. It wasn't the fact that she was unused to the size of the car, or that little Billy was throwing a fit on the back seat that meant she ended up forming a diagonal between the white lines, oh no. Spanning the entire adjacent wall, an ascending diagonal was joined by a rippled line. The quartet begins with the dancers - dressed in everyday clothes, but colorful so as not to be dull under stage lights - standing in a square formation along a slight diagonal. Nothing is in a predictable relationship; the beams are not the same sizes, and although they pass through each other in fairly straight diagonals, the effect is entanglement, not movement. Miller photographs buildings from high angles to get repeating diagonals and pyramidlike forms, then manipulates this imagery so that it draws the eye inward or seems to project from the surface of the picture. A wood sculpture from 2002 bunches several small rectangular forms beneath two lengthy diagonals that meet at the top like the tips of fingers joined in prayer. Arrange in a circle, in corners or in a diagonal. The positioning of the diving board - coming at a diagonal out of the corner - gives perspective as well as cutting across the predominant horizontals. He shaped for a diagonal into the box, before cutting through a low drive that swerved slightly away from the goalkeeper. Take cuttings from last seasons growth, cut just below the bud and trim the top on the diagonal. These lines also work best when they follow a diagonal, rather than a straight horizontal or vertical. They can be disturbing unless supported by verticals or opposing diagonals. Let stand ten minutes, then slice very thin and on the diagonal. There is nothing static in Strand's New York: It is a city built of passing glances, a streetscape of dashing diagonals and unexpected angles. 1.3Chess A slanting row of squares whose color is the same. Example sentencesExamples Black decides that he has to get White's Bishop off that laser a2-g8 diagonal! After a queen pawn opening, Hort threatened mate on the long diagonal. As frequently happens in such a situation, White does not have a diagonal for his dark Bishop, nor does he have any other diagonals from which to aim at his opponent's King. If you move a pawn to open up a diagonal for a bishop, then should you usually NOT move up another pawn to develop the bishop on the other diagonal. Her king was safe on h8, protected on the long diagonal by her bishop on e5. Origin Mid 16th century: from Latin diagonalis, from Greek diagōnios ‘from angle to angle’, from dia ‘through’ + gōnia ‘angle’.
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