octant

/'ɔktənt/

Thân thiện

A sailor uses an octant to measure the sun's angle above the horizon.

Definition

1. Noun:
   • A measuring instrument for navigation and astronomy: An octant is a historical navigational instrument used to measure the angle between a celestial body (like the sun or a star) and the horizon. It is similar to a sextant but has a calibrated arc of 45 degrees (one-eighth of a circle), allowing for angle measurements up to 90 degrees.
   • One-eighth of a circle: In geometry, an octant refers to any of the eight equal parts into which a circle can be divided, corresponding to a 45-degree angle or arc.
   • A region in three-dimensional space: In mathematics and coordinate geometry, an octant is any of the eight divisions of a three-dimensional Cartesian coordinate system, defined by the signs of the x, y, and z coordinates (e.g., the region where x, y, and z are all positive).

Usage Examples

• Noun (Navigational Instrument):
  • The sailor used an octant to determine the ship's latitude by measuring the sun's altitude at noon.
  • Before the sextant was invented, the octant was a crucial tool for celestial navigation.
• Noun (Geometry):
  • A full circle of 360 degrees is divided into eight octants of 45 degrees each.
  • The pie chart was split into octants to represent the eight different categories.
• Noun (Coordinate Geometry):
  • In 3D graphics, the object was located in the first octant, where all coordinates are positive.
  • The function's value was analyzed in each octant of the coordinate system.

Advanced Usage

• Historical Context: The octant, invented in the 18th century, was a precursor to the modern sextant. Its 45-degree arc (one-eighth of a full circle) gave it its name and limited its measuring range compared to later instruments.
• "Octant of a sphere": In spherical geometry, an octant can refer to one-eighth of the surface of a sphere, bounded by three great circles at right angles to each other.

Variants and Related Words

• Sextant (noun): A later navigational instrument with a 60-degree arc (one-sixth of a circle), allowing for angle measurements up to 120 degrees. It largely replaced the octant.
• Quadrant (noun): An earlier instrument with a 90-degree arc (one-quarter of a circle).

Synonyms

• Navigational instrument: Reflecting tool, angle-measuring device.
• Eighth (of a circle): 45-degree sector (in the context of geometry).

Related Phrases

• "To take an octant observation": (Historical phrase) To use an octant to measure the altitude of a celestial body for navigation.
  • The captain ordered the mate to take an octant observation at dusk.

Học thuật

Noun

1. a measuring instrument for measuring angles to a celestial body; similar to a sextant but with 45 degree calibration