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2. Compass (drawing tool) - Wikipedia

   en.wikipedia.org/wiki/Compass_(drawing_tool)

   A beam compass and a regular compass Using a compass A compass with an extension accessory for larger circles A bow compass capable of drawing the smallest possible circles. A compass, also commonly known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs.

3. Straightedge and compass construction - Wikipedia

   en.wikipedia.org/wiki/Straightedge_and_compass...

   Angle trisection is the construction, using only a straightedge and a compass, of an angle that is one-third of a given arbitrary angle. This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8]

4. Elementary mathematics - Wikipedia

   en.wikipedia.org/wiki/Elementary_mathematics

   Compass-and-straightedge, also known as ruler-and-compass construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse ...

5. Mathematical instrument - Wikipedia

   en.wikipedia.org/wiki/Mathematical_instrument

   Animation of construction of a pentagon using a compass and straightedge. A mathematical instrument is a tool or device used in the study or practice of mathematics.In geometry, construction of various proofs was done using only a compass and straightedge; arguments in these proofs relied only on idealized properties of these instruments and literal construction was regarded as only an ...

6. Inversive geometry - Wikipedia

   en.wikipedia.org/wiki/Inversive_geometry

   The circle inversion map is anticonformal, which means that at every point it preserves angles and reverses orientation (a map is called conformal if it preserves oriented angles). Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian ...

7. Napoleon's problem - Wikipedia

   en.wikipedia.org/wiki/Napoleon's_problem

   Napoleon's problem is a compass construction problem. In it, a circle and its center are given. The challenge is to divide the circle into four equal arcs using only a compass. [1] [2] Napoleon was known to be an amateur mathematician, but it is not known if he either created or solved the problem.

8. Cardinal direction - Wikipedia

   en.wikipedia.org/wiki/Cardinal_direction

   Direction determination refers to the ways in which a cardinal direction or compass point can be determined in navigation and wayfinding.The most direct method is using a compass (magnetic compass or gyrocompass), but indirect methods exist, based on the Sun path (unaided or by using a watch or sundial), the stars, and satellite navigation.

9. Angle trisection - Wikipedia

   en.wikipedia.org/wiki/Angle_trisection

   The triple-angle formula gives an expression relating the cosines of the original angle and its trisection: cos θ = 4 cos 3 ⁠ θ / 3 ⁠ − 3 cos ⁠ θ / 3 ⁠. It follows that, given a segment that is defined to have unit length, the problem of angle trisection is equivalent to constructing a segment whose length is the root of a cubic ...