For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

* The knight moves to any of the closest squares that are not on the same rank, file, or diagonal, thus the move forms an " L "- shape: two squares vertically and one square horizontally, or two squares horizontally and one square vertically.

Therefore, the diagonal of a 4 x 9 lattice does not intersect any other square lattice | lattice points

Baudhayana ( c. 8th century BCE ) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as:,,,, and as well as a statement of the Pythagorean theorem for the sides of a square: " The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection ( YBC 7289 ), which gives a sexagesimal numerical approximation of, the length of the diagonal in a unit square.

For other examples, see proof that the square root of 2 is not rational and Cantor's diagonal argument.

If either the 2nd player chooses to move to the square diagonal to the first player or the first player's 2nd move is not to this square given the choice, then a starting position before flipping moves commence that differs from the standard Othello position arises.

For the specific game of Othello ( as technically differing from Reversi ), the rules state that the game begins with four disks placed in a square in the middle of the grid, two facing light-up, two pieces with the dark side up, with same-colored disks on a diagonal with each other.

It is exactly the length of the diagonal of a square with side length 1.

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal ( the diagonal from the upper left to the lower right ) of A, i. e.,

This follows immediately from the fact that transposing a square matrix does not affect elements along the main diagonal.

Large structures can be built with a combination of square and diagonal lashing, with square lashing generally used on load bearing members and diagonal lashing usually applied to cross bracing.

Large, semipermanent structures may be built with a combination of square lashing, which is stronger, and diagonal lashing.

To reduce travel times, two diagonal streets crossed the square grid, passing through the central square.

Each point on C, as a vertex, may possess a finite number of corresponding diagonal points by the above construction.

We must now show that on some component of the graph there exist two points for which the corresponding diagonal points in the C-plane are on opposite sides of C.

Each grid point has eight neighbouring grid points: Up, down, left, right, and the four diagonal directions.

Better yet, the geometry of the attachment points meant the heel strap was mechanically attached below that of the toe strap, which provided a constant " diagonal downpull " that naturally returned the heel to the ski.

Specifically, draw a diagonal line connecting two points on the diagram so that every other point is either on or to the right and above it.

Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal.

One of the basic positions of the body in which the dancer assumes a position with the body facing downstage on a diagonal and points the downstage leg in second position, along the other diagonal, either touching the floor or en l ' air.

The diagonal terms in the matrix are the direct-related stiffnesses ( or simply stiffnesses ) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom ( either at the same or different points ) or the same degree of freedom at two different points.

The aft attachment points consist of three separate struts: upper, diagonal and lower.

Tactical play would lead to the contestant building up lines of noughts or crosses, for which points were awarded ( 10 points per horizontal, vertical or diagonal line ).

* 50 points for a three-block vertical Klax, 1, 000 points for a three-block horizontal Klax, and 5, 000 points for a three-block diagonal Klax.

To prevent the beams from tipping over onto their side, blocking is used at each end, and for additional stiffness, blocking or diagonal wood or metal bracing may be placed between beams at one or more points in their spans.

* In a matrix of 9 points ( as in the picture and description above ), if the first two rows and the six " diagonal " triads are collinear, then the third row is collinear.

The next measure is the percentage of recurrence points which diagonal lines in the recurrence plot of minimal length:

The badge of the Order is a blue enamelled gold Maltese cross with white enamelled borders with small gold balls on the points and blue diagonal lozenges between the arms also with white enamelled borders.

Oblique asymptotes are diagonal lines so that the difference between the curve and the line approaches 0 as x tends to +∞ or −∞.

Using the diagonal argument, it is possible to define a real number x, which is not equal to G ( n ) for any n. This means that there is a language L ' that defines x, which is undefinable in L.

Recall that all the terms in a diagonal going from the upper-left to the lower-right correspond to the same power of x, and that the a-terms are the coefficients of the polynomial ( x + 1 )< sup > n </ sup >, and we are determining the coefficients of ( x + 1 )< sup > n + 1 </ sup >.

Now, for any given i not 0 or n + 1, the coefficient of the x < sup > i </ sup > term in the polynomial ( x + 1 )< sup > n + 1 </ sup > is equal to a < sub > i </ sub > ( the figure above and to the left of the figure to be determined, since it is on the same diagonal ) + a < sub > i − 1 </ sub > ( the figure to the immediate right of the first figure ).

The Eixample grid introduced innovative design elements that made it exceptional at the time and even unique among subsequent grid plans: a ) a very large block measuring 113m by 113m ( 370 x 370 feet ) far larger than the old city blocks and larger than any Roman, Greek blocks and their mutations ( see drawing below ); b ) a 20 m ( 66 feet ) road width ( right of way ) compared to mostly 3 m in the old city c ) square blocks with truncated corners and d ) major roads perpendicular and diagonal measuring 50 m ( 164 feet ) in width.

A saltire, or Saint Andrew's Cross, is a heraldic symbol in the form of a diagonal cross ☓ or letter x. Saint Andrew is said to have been martyred on such a cross.

On the flat drawing, two axes, x and z on the figure, are perpendicular and the length on these axes are drawn with a 1: 1 scale ; it is thus similar to the dimetric projections, although it is not an orthographic projection, as the third axis, here y, is drawn in diagonal, making an arbitrary angle with the x " axis, usually 30 or 45 °.

The diagonal basis for the split-complex number plane can be invoked by using an ordered pair ( x, y ) for and making the mapping

The stitch is done by creating a line of diagonal stitches going in one direction, usually using the warp and weft of the fabric as a guide, then on the return journey crossing the diagonal in the other direction, creating an " x ".

with one vertex at the origin, base on the diagonal ray y = x, and third vertex on the hyperbola

For a given iterated function f: R → R, the plot consists of a diagonal ( x

It follows from the definition of a fixed point that these spirals will center at a point where the diagonal y = x line crosses the function graph.

( The 1968 AOPA Directory shows DAB's longest runway as 5700 ft, but maybe it wasn't up to date -- the 1969 Directory shows 7500 ft .) Runways 6 and 16 were 150 ' wide, the two diagonal runways were closed, and a 3100 ' x 75 ' flight training runway was built parallel to the main runway, on the south side of the field.