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The farthest this end of the needle can move away from this line horizontally in its region is t. The probability that the farthest end of the needle is located no more than a distance l cos θ away from the line (and thus that the needle crosses the line) out of the total distance t it can move in its region for 0 ≤ θ ≤ π / 2 is ...
Let AC be the base of a triangle ABC. Let ladder (line) AD have its foot at A and intersect BC at D; likewise, let ladder CE have its foot at C and intersect AB at E. Let AD intersect CE at F. Extend parallel lines from the points E, B, F, and D, intersecting AC at the points I, G, J, and H, respectively. Then
The corresponding concept to hyperbolic line arrangements for pseudolines is a weak pseudoline arrangement, [52] a family of curves having the same topological properties as lines [53] such that any two curves in the family either meet in a single crossing point or have no intersection.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.