κ Differential Geometry

ບົດຮຽນ

Calculus on curved things. Curvature measures how a surface bends, geodesics are its straight lines, and manifolds let the same ideas run in any dimension. Einstein's equations are a statement in this language.

ບົດຮຽນ​ເພີ່ມເຕີມ

ບົດຮຽນບາງບົດນີ້ ແມ່ນໄດ້ນຳເອົາຈາກບົດຂຽນເປີດ: Wikipedia. ທຸກໆ​ໜ້າ​ບົດຮຽນ​ມີ​ຊື່​ແຫຼ່ງ​ຂອງ​ມັນ ແລະ ໃບອະນຸຍາດ​ຂອງ​ມັນ.

ຕົວ​ສະ​ແດງ​ທີ່​ໃຊ້​ຢູ່​ທີ່​ນີ້

ກົດ​ຕົວ​ອັກສອນ​ໃດ​ໜຶ່ງ​ເພື່ອ​ເບິ່ງ​ຄວາມ​ໝາຍ​ເຕັມ, ຮູບ ແລະ ຕົວອັກສອນ​ແຕ່ລະ​ຕົວ​ໃນ​ມັນ​ໝາຍ​ຄວາມ​ວ່າ​ແນວໃດ.

f'(x)derivative
Instantaneous rate of change; slope of the graph.\frac{\partial f}{\partial x}partial derivative
Derivative with respect to x, holding the other variables fixed.\nabla fgradient (nabla, del)
Vector of partial derivatives; points uphill.\kappacurvature, Gaussian curvature
How fast a curve turns; the product of a surface's principal curvatures.

ຄໍາຖາມທີ່ຄົນຖາມ

What is curvature?

For a curve, how fast its direction turns per unit length; for a surface, Gauss's combination of the two principal bendings, and Gauss's theorem says it can be measured from inside the surface without leaving it.

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