triangle

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The plane figure formed by connecting three points not in a straight line by straight line segments; a three-sided polygon.
2. n. Something shaped like such a figure: a triangle of land.
3. n. Any of various flat, three-sided drawing and drafting guides, used especially to draw straight lines at specific angles.
4. n. Music A percussion instrument consisting of a piece of metal in the shape of a triangle open at one angle.
5. n. A relationship involving three people, especially a ménage à trois.

Century Dictionary and Cyclopedia

1. n. A triangular box-fish, as Sectophrys trigonus, of the family Ostraciidæ of the West Indies.
2. n. In angling, an arrangement of three fish-hooks bound together with the points outward, forming a triangle.
3. Three-cornered; three-angled; triangular.
4. n. In geometry, a figure composed of three lines which meet two by two in three points, called the vertiees of the triangle; especially, a rectilinear figure of this description. The lines measured in the shortest way from vertex to vertex are called the sides of the triangle. The angles between the sides at the vertices measured so that each subtends a side are called the angles of the triangle.
5. n. Any three-cornered or three-sided figure, body, or arrangement; anything having a triangular form or bounding a three-sided space.
6. n. A musical instrument of percussion, made of a rod of polished steel bent into the form of triangle, and open at one of its angles. It is sounded by being struck with a small steel rod. It is frequently used in modern orchestral music for brilliant and sparkling effects.
7. n. [capitalized] In astron, same as Triangulum.
8. n. Eccles., a symbol of the Trinity. The equilateral triangle, as symbolizing the Trinity, is of frequent occurrence, in various combinations, in Christian ornament.
9. n. A chest made in triangular form to hold a priest's cope.
10. n. A three-cornered straight-edge, with one right angle and the other angles more or less acute, used in conjunction with the T-square for drawing parallel, perpendicular, or diagonal lines.
11. n. A kind of gin for raising heavy weights, formed by three spars joined at top. See gin, 2 .
12. n. Milit., formerly, in the British army, a sort of frame formed of three halberds stuck in the ground and united at the top, to which soldiers were bound to be flogged: generally in the plural.
13. n. In ceramics, a form of stilt consisting of three metal pins held together in the form of triangle. See stilt, 5.
14. n. One of certain tortricid moths: an English collectors' name. Tortrix rufana is the red triangle.
15. n. In entomology, a large three-sided cell found in the wings of many dragon-flies. It lies near the middle of the basal half of the wing, and its form and relations to the other cells, both of the anterior and posterior wings, are of much value in classification. It is often called the discoidal triangle, to distinguish it from the internal triangle, which adjoins it on the inner side, and the anal triangle, which lies close to the anal border of the wing.
16. n. See conjugate triangles, under conjugate.
17. n. A triangle whose sides are rectilinear.
18. n. the circumscribed circle;
19. n. the inscribed and the three escribed circles;
20. n. the Feuerback or nine-point circle;
21. n. the Brocard or seven-point circle;
22. n. the Tucker or triplicate-ratio cirde;
23. n. the sine triple-angle circle (constructed as follows: on the sides of the triangle ABC take D and D' on BC, E and E' on AC, F and F' on AB such that the angle AEF =AF'E' =A, BFD =BD'F' =B, CDE =CE'D' =C; then the circle in question passes through D, D', E, E', F, F', and DD': EE': FF'=sin 3A: sin 3B: sin 3C)
24. n. the Taylor or six-point circle, which passes through the six feet of perpendiculars drawn to the sides from feet of perpendiculars on the sides from the vertices of the triangle
25. n. the Spieker circle, or circle inscribed in the triangle whose vertices are the mid-points of the sides of the primitive triangle. See circle.
26. n. the centroid, or intersection of median lines
27. n. the orthocenter, or intersection of perpendiculars from the angles upon the opposite sides
28. n. the circumcenter, or center of the circumscribed circle
29. n. the center of the Feuerbach circle;
30. n. the incenter, or center of the inscribed circle
31. n. the radical center of the escribed circles;
32. n. the symmedian, Grebe, or Lemoine point, the intersection of the three lines each bisecting a side and bisecting a perpendicular from an angle upon a side
33. n. the Spieker point, or mid-point between the circumcenter and incenter
34. n. the Brocard points, two points of the Brocard circle (which see, under circle) (through the symmedian point S of any triangle ABC lines are drawn parallel to the sides of the latter, meeting these sides in D and D' on BC, E and E' on AC, F and F' on AB, so that D, S. E' are collinear, as well as E, S, F' and F, S, D'; then the three lines through A parallel to FD, through B parallel to DE, and through C parallel to EF meet in one Brocard point P, while the lines through A parallel to D' E', through B parallel to E'F', and through C parallel to F' D' meet in the other Brocard point P')
35. n. (10) the center of the triplicate-ratio circle; besides others.

Wiktionary

1. n. geometry A polygon with three sides and three angles.
2. n. music A percussion instrument made by forming a metal rod into a triangular shape which is open at one angle. It is suspended from a string and hit with a metal bar to make a resonant sound.
3. n. cue sports A triangular shaped piece of equipment used for gathering the balls into the formation required by the game being played.
4. n. A love triangle.
5. n. systemics The structure of systems composed with three interrelated objects.

GNU Webster's 1913

1. n. (Geom.) A figure bounded by three lines, and containing three angles.
2. n. (Mus.) An instrument of percussion, usually made of a rod of steel, bent into the form of triangle, open at one angle, and sounded by being struck with a small metallic rod.
3. n. A draughtsman's square in the form of right-angled triangle.
4. n. (Mus.) A kind of frame formed of three poles stuck in the ground and united at the top, to which soldiers were bound when undergoing corporal punishment, -- now disused.
5. n. A small constellation situated between Aries and Andromeda.
6. n. A small constellation near the South Pole, containing three bright stars.

WordNet 3.0

1. n. any of various triangular drafting instruments used to draw straight lines at specified angles
2. n. a percussion instrument consisting of a metal bar bent in the shape of an open triangle
3. n. something approximating the shape of a triangle
4. n. a three-sided polygon
5. n. a small northern constellation near Perseus between Andromeda and Aries