Use ‘geodesic triangle’ in a sentence | ‘geodesic triangle’ example sentences
1- Qualitatively a surface is positively or negatively curved according to the sign of the angle excess for arbitrarily small geodesic triangles .
2- A hyperbolic triangle is a geodesic triangle for this metric: any three points in “D” are vertices of a hyperbolic triangle.
3- Gauss’ formula shows that the curvature at a point can be calculated as the limit of “angle excess” α + β + γ − Ï€ over “area” for successively smaller geodesic triangles near the point.
4- Since any closed surface can be decomposed up into geodesic triangles , the formula could also be used to compute the integral of the curvature over the whole surface.
5- His formula showed that the Gaussian curvature could be calculated near a point as the limit of area over angle excess for geodesic triangles shrinking to the point.
6- Gauss generalised these results to an arbitrary surface by showing that the integral of the Gaussian curvature over the interior of a geodesic triangle is also equal to this angle difference or excess.
7- On a sphere or a hyperboloid, the area of a geodesic triangle , i.e. a triangle all the sides of which are geodesics, is proportional to the difference of the sum of the interior angles and π. The constant of proportionality is just the Gaussian curvature, a constant for these surfaces.
8- A classical theorem of Henri Poincaré constructs Fuchsian groups as hyperbolic reflection groups generated by reflections in the edges of a geodesic triangle in the hyperbolic plane for the Poincaré metric.
9- Since every compact oriented 2-manifold “M” can be triangulated by small geodesic triangles , it follows that
10- [[File:Spherical triangle.svg|thumb|right|150px|A geodesic triangle on the sphere.
11- geodesic triangles
More Sentences:
Related Words:
triangle technique – calot triangle – triangle test – pascal’s triangle – oblique triangle – arithmetic triangle – obtuse triangle – geodesic triangle – polar triangle – scalene triangle – obtuse angled triangle – right angled triangle – circular triangle – spherical triangle – isosceles triangle –
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