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(This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.) as a percentage, the formula for which is which is equivalent to the tangent of the angle of inclination times 100. In Europe and the U.S. percentage "grade" is the most commonly used figure for describing slopes.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
A plane's slope s is equal to the difference in height between its two ends, or "rise", divided by its horizontal length, or "run". [31] It can also be expressed by the angle the plane makes with the horizontal, . The inclined plane's geometry is based on a right triangle. [31]
The triangles in both spaces have properties different from the triangles in Euclidean space. For example, as mentioned above, the internal angles of a triangle in Euclidean space always add up to 180°. However, the sum of the internal angles of a hyperbolic triangle is less than 180°, and for any spherical triangle, the sum is more than 180 ...
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
Incline, inclined, inclining, or inclination may refer to: Grade (slope), the tilt, steepness, or angle from horizontal of a topographic feature (hillside, meadow, etc.) or constructed element (road, railway, field, etc.) Slope, the tilt, steepness, or angle from horizontal of a line (in mathematics and geometry) Incline may also refer to:
Here is a definition of triangle geometry from 1887: "Being given a point M in the plane of the triangle, we can always find, in an infinity of manners, a second point M' that corresponds to the first one according to an imagined geometrical law; these two points have between them geometrical relations whose simplicity depends on the more or ...
This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space.