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What is an octant?

What is an octant? Here are some definitions.

Noun
  1. The eighth part of a circle; an arc of 45 degrees.
  2. (astrology) The aspect of two planets that are 45°, or one-eighth of a circle, apart.
  3. (geometry) The eighth part of a disc; a sector of 45 degrees; half a quadrant.
  4. (nautical) An instrument for measuring angles, particularly of elevation.
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Examples
The model put forward for the action of BDL suggests that auxin is involved in determining hypophyseal cell fate at the octant stage.
The arc was extended from an octant to a sextant and a stout handle was added at the back of the instrument.
Thus fig. 59 conveniently represents an octant of the wave surface, which cuts each coordinate plane in a circle and an ellipse.
The scutellum arises from octant cells, which also contribute to the cotyledon.
William Logan won an octant, a less advanced version of a sextant, as a mathematics prize in university.
The partition of the quadrant cells in a transverse plane then produces an octant stage.

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