geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the...

trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third...

compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these constructions is...

a surface plate must be used. An idealized straightedge is used in compass-and-straightedge constructions in plane geometry. It may be used: Given two...

Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional...

be constructed with compass and straightedge in a finite number of steps. Equivalently, r {\displaystyle r} is constructible if and only if there is a...

of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified...

sometimes used as a way of obtaining a position line using a sextant when no compass is available. The horizontal angle between two landmarks defines the circumcircle...

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...

compass and straightedge. The first girih patterns were made by copying a pattern template on a regular grid; the pattern was drawn with compass and straightedge...

use of straightedge and compass constructions, which simultaneously gave a geometric proof of the solution's correctness. Once a construction was completed...

property. This type of construction is called a neusis construction. It is also constructible with compass, straightedge and angle trisector. The impossibility...

included spherical ruler and compass support synthetic straightedge and compass construction on the sphere. The Lénárt sphere and accessories are produced...

can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon...

Geometric Constructions has ten chapters. The first two discuss straightedge and compass constructions, including many of the constructions from Euclid's...

mathematical impossibility of squaring the circle using only straightedge and compass constructions, suspected since ancient times, had been rigorously proven...

mathematician Oenopides (ca. 440 BC) was the first to put compass-and-straightedge constructions above neuseis. The principle to avoid neuseis whenever possible...

only instruments used in most geometric constructions are the compass and straightedge. Also, every construction had to be complete in a finite number of...

perpendicular to the line AB through the point P using compass-and-straightedge construction, proceed as follows (see figure left): Step 1 (red): construct...

many compass-and-straightedge constructions resulting in circles. The simplest and most basic is the construction given the centre of the circle and a point...

including the traditional straightedge and compass construction; the construction of a grid of polygons; and the use of a set of girih tiles with lines...

Copying a line segment with compass and straightedge Dividing a line segment into N equal parts with compass and straightedge Animated demonstration This...

and Gauss knew of these. Nobody has been able to prove whether there are any more. Thus, a regular n-gon has a straightedge-and-compass construction if...

using only a compass and straightedge, but even in ancient times solutions were known that employed other methods. The Egyptians, Indians, and particularly...

1988, pp. 180–184 Heath 1956, p. 194 Only the third is a straightedge and compass construction, the first two are infinitary processes (they require an...

on a 1 {\displaystyle a_{1}} and N {\displaystyle N} on a 2 {\displaystyle a_{2}} . Straightedge and compass construction: A system of orthogonal circles...

proportionals between one line and another of twice its length, but could not solve this with a compass and straightedge construction, a task which is now known...

A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or...

calculated. Compasses-and-straightedge constructions are used to illustrate principles of plane geometry. Although a real pair of compasses is used to draft visible...

Alexander's empire. Ptolemy began a process of hellenization and commissioned numerous constructions, building the massive Musaeum institution, which was a...