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The most-used straightedge-and-compass constructions include: Constructing the perpendicular bisector from a segment; Finding the midpoint of a segment. Drawing a perpendicular line from a point to a line. Bisecting an angle; Mirroring a point in a line; Constructing a line through a point tangent to a circle; Constructing a circle through 3 ...
Draw lines AM and CM (both in light green), connecting the segment midpoint with each of the circle centers. Construct a line j (in purple) passing through point B, and perpendicular to AM. Line j is the radical axis between circle M(B) and circle A(B). Construct a line k (in dark green) passing through point D, and perpendicular to CM.
In hyperbolic geometry, one can use the standard ruler and compass that is often used in Euclidean plane geometry. However, there are a variety of compasses and rulers developed for hyperbolic constructions. A hypercompass can be used to construct a hypercycle given the central line and radius. [ 3 ] A horocompass can be used to construct a ...
Compass equivalence theorem. In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these constructions is a divider or collapsing compass, that is, a compass that "collapses" whenever it is lifted from a page, so that it may not be directly used to ...
In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both. The distance from a point to a line is the distance to the nearest point on that line. That is the point at which a segment from it to the given point is perpendicular to the line.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had ...
Constructible number. 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 ...
Angle trisection. Angles may be trisected via a neusis construction using tools beyond an unmarked straightedge and a compass. The example shows trisection of any angle θ > 3π 4 by a ruler with length equal to the radius of the circle, giving trisected angle φ = θ 3 . Angle trisection is a classical problem of straightedge and ...