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An American-style 15×15 crossword grid layout. A crossword (or crossword puzzle) is a word game consisting of a grid of black and white squares, into which solvers enter words or phrases ("entries") crossing each other horizontally ("across") and vertically ("down") according to a set of clues. Each white square is typically filled with one ...
There will be an intersection if 0 ≤ t ≤ 1 and 0 ≤ u ≤ 1. The intersection point falls within the first line segment if 0 ≤ t ≤ 1, and it falls within the second line segment if 0 ≤ u ≤ 1. These inequalities can be tested without the need for division, allowing rapid determination of the existence of any line segment ...
This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle C with center E. [5] This proves that the intersection of P and S is contained in C. Note that OE is the axis of the circle. Now consider a point D of the circle C. Since C lies in ...
Taking this one stage further, the clue word can hint at the word or words to be abbreviated rather than giving the word itself. For example: "About" for C or CA (for "circa"), or RE. "Say" for EG, used to mean "for example". More obscure clue words of this variety include: "Model" for T, referring to the Model T.
The intersection (red) of two disks (white and red with black boundaries). The circle (black) intersects the line (purple) in two points (red). The disk (yellow) intersects the line in the line segment between the two red points. The intersection of D and E is shown in grayish purple. The intersection of A with any of B, C, D, or E is the empty ...
The book is organized into three sections. [2] [3] The first section provides introductory material, describing different mathematical situations in which multiple curves might meet, and providing different possible explanations for this phenomenon, including symmetry, geometric transformations, and membership of the curves in a pencil of curves. [4]
Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external ...
The sum of the squared lengths of any two perpendicular chords intersecting at a given point is the same as that of any other two perpendicular chords intersecting at the same point, and is given by 8r 2 – 4p 2 (where r is the circle's radius and p is the distance from the center point to the point of intersection). [5]