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In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1 / 2 to 180 degrees by increments of 1 / 2 degree. Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the ...
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc. For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints. If an angle is subtended by a straight or curved segment, the segment is said to subtend the angle.
For tiny arcs, the chord is to the arc angle in degrees as π is to 3, or more precisely, the ratio can be made as close as desired to π / 3 ≈ 1.047 197 55 by making θ small enough. Thus, for the arc of 1 / 2 °, the chord length is slightly more than the arc angle in degrees. As the arc increases, the ratio of the chord to ...
Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic calculators became available. The 100 feet (30.48 m) is called a station, used to define length along a road or other alignment, annotated as stations plus feet 1+00, 2+00, etc. Metric ...