Differential Geometry of Curves and Surfaces

Carmo, M. P. d. (1976). Differential Geometry of Curves and Surfaces. Prentice-Hall.

Type

Book

Intellectual base

Textbook

Year

1976

Link

https://openlibrary.org/isbn/9780132125895verified

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Parabolic line
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Ruled Surface
  • A developable ruled surface has constant tangent plane along each ruling and zero Gaussian curvature at regular points; a helicoid and one-sheet hyperboloid are ruled but not developable.
• Tangent indicatrix
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Mechanisms

• Coordinate Chart Mapping
  • You cannot lay the curved surface of the Earth onto a flat plane in one piece without stretching or cutting it — a hard fact, not a technical shortcoming, since curvature is intrinsic (Gauss's Theorema Egregium implies no flat chart can preserve all distances on a sphere).

    This sourceEstablishes curvature as intrinsic and shows that a sphere cannot be mapped isometrically to a plane, so flattening requires distortion or cutting.

Verification

Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.

Does it back the claim? Not recorded. Neither this nor any other of the 4 citations of this work carries a recorded support check.

Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://books.google.com/books?id=ggPRugEACAAJ ×1

Registry ID ref:2a6741079771 · see in the full table