In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.
A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation. The estimation of this angle, the altitude, is known as sighting or shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart—for example, sighting the Sun at noon or Polaris at night to estimate latitude. Sighting the height of a landmark can give a measure of distance off and, held horizontally, a sextant can measure angles between objects for a position on a chart. A sextant can also be used to measure the lunar distance between the moon and another celestial object in order to determine Greenwich Mean Time and hence longitude. The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749), but it was also found later in the unpublished writings of Isaac Newton (1643–1727). Additional links can be found to Bartholomew Gosnold (1571–1607) indicating that the use of a sextant for nautical navigation predates Hadley's implementation. In 1922, it was modified for aeronautical navigation by Portuguese navigator and naval officer Gago Coutinho.
A drawing board is, in its antique form, a kind of multipurpose desk which can be used for any kind of drawing, writing or impromptu sketching on a large sheet of paper or for reading a large format book or other oversized document or for drafting precise technical illustrations. The drawing table used to be a frequent companion to a pedestal desk in a gentleman's study or private library, during the pre-industrial and early industrial era.
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects.
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the segment bisector and the angle bisector.
In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
A French curve is a template usually made from metal, wood or plastic composed of many different curves. It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The shapes are segments of the Euler spiral or clothoid curve. The curve is placed on the drawing material, and a pencil, knife or other implement is traced around its curves to produce the desired result.
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. The central angle is also known as the arc's angular distance.
A pair of compasses, also known as a compass, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
In mathematics, a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180°. It has only one line of symmetry. In non-technical usage, the term "semicircle" is sometimes used to refer to a half-disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as all the interior points.
The triquetrum was the medieval name for an ancient astronomical instrument first described by Ptolemy in the Almagest. Also known as Parallactic Rulers, it was used for determining altitudes of heavenly bodies. Ptolemy calls it a "parallactic instrument" and seems to have used it to determine the zenith distance and parallax of the Moon.
Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.
Reflecting instruments are those that use mirrors to enhance their ability to make measurements. In particular, the use of mirrors permits one to observe two objects simultaneously while measuring the angular distance between the objects. While reflecting instruments are used in many professions, they are primarily associated with celestial navigation as the need to solve navigation problems, in particular the problem of the longitude, was the primary motivation in their development.
In geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
Technical drawing tools include and are not limited to: pens, rulers, compasses, protractors and drawing utilities. Drafting tools may be used for measurement and layout of drawings, or to improve the consistency and speed of creation of standard drawing elements. The tools used for manual technical drawing have been displaced by the advent of the personal computer and its common utilization as the main tool in computer-aided drawing, draughting and design (CADD).
A schema for horizontal dials is a set of instructions used to construct horizontal sundials using compass and straightedge construction techniques, which were widely used in Europe from the late fifteenth century to the late nineteenth century. The common horizontal sundial is a geometric projection of an equatorial sundial onto a horizontal plane.
