Eksempler på brug af Curvature integral på Engelsk og deres oversættelser til Dansk
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Thus the contribution of the ridge lines to the curvature integral is zero.
Dermed bidrager den ridge linjer til krumningen integreret er nul.So again the contribution to the curvature integral of a vertex is equal to its angular deficit.
Så igen bidraget til krumningen integreret en vertex er lig med sin kantede underskud.The contribution of each of the eight vertices of a cube to the curvature integral is 4π/8=π/2.
Bidraget fra hver af de otte knudepunkter for en kube til krumningen integral er 4π/ 8 =π/2.It would be nice to have this contribution to the curvature integral expressed as a function of the angular deficit of the vertex; i.e.
Det ville være rart at have bidraget til den krumning integreret udtrykt som funktion af The number of vertices of a dodecahedron is 20 so the contribution of each to the curvature integral is 4π/20=π/5.
Antallet af knudepunkter i et dodecahedron er 20 så bidraget til hver af krumningen integral er 4π/ 20 =π/5.If the crease has a straight edge it contribution to the curvature integral of a surface is zero, as is the case of a ridge with a straight edge.
Hvis de folder har en lige kant det bidrag til krumningen integralet af en overflade er nul, som det er tilfældet med en rand med en lige kant.Thus the angular deficit at each vertex is(2π-5π/3)=π/3. Each vertex contributes 4π/12=π/3 to the curvature integral.
De kantede underskud på hvert toppunkt er (2π-5π/3)=π/3.__> Each vertex contributes 4π/12=π/3 til krumningen integreret.For a regular polyhedron having V vertices the curvature integral of each vertex is then 4π/V.
For en almindelig polyhedron under V knækpunkter krumningen integreret i hvert toppunkt er 4π/V.Thus the angular deficit for a vertex of a cube is( 2π-3π/2)=π/2The contribution of each of the eight vertices of a cube to the curvature integral is 4π/8=π/2.
De kantede underskud til et toppunkt for en kube er(2π 3π/ 2)=π/2. Bidraget fra hver af de otte knudepunkter for en kube til krumningen integral er 4π/ 8 =π/2.The effect of such indented points on the curvature integral of a surface is thus already included within the previous analysis for points.
Virkningen af en sådan indrykkede punkter på jordens krumning integralet af en overflade er således allerede indgår i den foregående analyse for point.If a polyhedron is scaled up the lengths of the ridge lines are also scaled up but the curvature integral remains constant at 4π.
Hvis en polyhedron skaleres op til længder i ridge er også skaleres op men krumningen integreret konstant 4π.It would be nice to have this contribution to the curvature integral expressed as a function of the angular deficit of the vertex; i.e., the difference between 2π and the sum of the angles at the vertex. For example, the angles at the corner of a cube are three angles of π/2 radians each.
Det ville være rart at have bidraget til den krumning integreret udtrykt som funktion af Since the faces of the polyhedra are flat andhave zero Gaussian curvature the entire curvature integral is due to the contribution of the vertices.
Da ansigter polyhedra er flad oghar nul Gauss-krumning hele krumning integreret skyldes bidrag knækpunkter.The above equation which make the contribution of the ridge line to the curvature integral inversely proportional to the radius of curvature of the ridge line suggests that a straight ridge line, one for which the radius of curvature is infinite, would make no contribution to the curvature integral.
Ovenstående ligning, som gør bidrag i ridge linje til krumningen integreret omvendt proportional med krumningsradius i ridge linje antyder, at en lige ridge linje, som krumningsradius er uendelig, vil ikke yde noget bidrag til krumningen integreret.The area of a ribbon of width rdφ at latitude φ is(2πrcos(φ))rdφ so the value of the curvature integral over the area between latitude φ0 and the pole at π/2 is.
Arealet af et bånd af bredde rdφ på latitude φ er 2 πrcos(φ)rdφ så værdien af krumningen integral over området mellem bredde- φ0 og sydpolen på π/2.For a regular polyhedron having V vertices the curvature integral of each vertex is then 4π/V. It would be nice to have this contribution to the curvature integral expressed as a function of the angular deficit of the vertex; i.e., the difference between 2π and the sum of the angles at the vertex.
For en almindelig polyhedron under V knækpunkter krumningen integreret i hvert toppunkt er 4π/V. Det ville være rart at have bidraget til den An additional argument for the contribution of straight ridge lines to the curvature integral of a surface being zero comes from a consideration of polyhedra.
Et yderligere argument for bidrag af lige ridge linjer til den krumning integreret i en overflade er nul kommer fra en betragtning af polyhedra.The Gaussian curvature of a sphere of radius r is 1/r2. The area of a ribbon of width rdφ at latitude φ is(2πrcos(φ))rdφ so the value of the curvature integral over the area between latitude φ0 and the pole at π/2 is.
Gauss-krumning af en kugle med radius r er 1/r2. Arealet af et bånd af bredde rdφ på latitude φ er 2 πrcos(φ)rdφ så værdien af krumningen integral over området mellem bredde- φ0 og sydpolen på π/2.Then the integral of curvature over the surface of revolution is equal to.
Then the integral of curvature over the surface of revolution is equal to 2πsin(φ(a))-sinφb.
Da integralet af krumning over overfladen af revolution er lig med 2πsin(φ(a))-sinφb.He studied homotopy classes andvector fields producing a formula about the integral curvature.
Han studerede Homotopiteori klasser ogvektor felter producerer en formel, om den integrerende krumning.
