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In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
Construction of a regular pentagon. In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not.
In addition, the sutras describe procedures for constructing a square with area equal either to the sum or to the difference of two given squares. Both constructions proceed by letting the largest of the squares be the square on the diagonal of a rectangle, and letting the two smaller squares be the squares on the sides of that rectangle.
In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that "any geometric construction" refers to figures that contain no straight lines, as it is clearly impossible to draw a straight line without a ...
Geometric drawing made with ruler and compass. Geometric drawing consists of a set of processes for constructing geometric shapes and solving problems with the use of a ruler without graduation and the compass (drawing tool). [1] [2] Modernly, such studies can be done with the aid of software, which simulates the strokes performed by these ...
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed.The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P that are parallel to L. [1]
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 following construction is a variation of H. W. Richmond's construction. The differences to the original: The circle k 2 determines the point H instead of the bisector w 3. The circle k 4 around the point G' (reflection of the point G at m) yields the point N, which is no longer so close to M, for the construction of the tangent.
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