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Geometric Models Collection of V.N. Karazin Kharkiv National University About the Project

Tag: "#Brill"

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Pseudosphere

Pseudosphere — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Curves
    • Types of curves on surfaces
      • Asymptotic lines
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#pseudosphere#surface of revolution#constant curvature#constant Gaussian curvature#negative curvature#geodesic line#asymptotic line#tractrix#Bacharach#Brill
Space evolute of an elliptic paraboloid

Space evolute of an elliptic paraboloid  — of M. Schilling catalog

  • Surfaces
    • Quadrics (surfaces of order two)
      • Space caustics of quadrics
#principal curvature#elliptic paraboloid#center of curvature#envelope#evolute#caustic#Schleiermacher#Brill
Space evolute of a one-sheeted hyperboloid

Space evolute of a one-sheeted hyperboloid — of M. Schilling catalog

  • Surfaces
    • Quadrics (surfaces of order two)
      • Space caustics of quadrics
#principal curvature#one-sheeted hyperboloid#center of curvature#envelope#evolute#caustic#Dyck#Brill
Geodesic lines on the three-axial ellipsoid

Geodesic lines on the three-axial ellipsoid — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Quadrics (surfaces of order two)
      • Ellipsoids and spheres
#ellipsoid#three-axial#geodesic line#umbilical point#Rohn#Brill
Unduloid

Unduloid — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Сonstant mean curvature surfaces
      • Surfaces of constant non-zero mean curvature
#constant curvature#constant mean curvature#surface of revolution#geodesic line#locus#catenary#ellipse#elliptic integral#Bacharach#Brill
Nodoid

Nodoid — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Сonstant mean curvature surfaces
      • Surfaces of constant non-zero mean curvature
#constant curvature#constant mean curvature#surface of revolution#geodesic line#locus#catenary#hyperbola#elliptic integral#Bacharach#Brill
Catenoid with geodesic lines

Catenoid with geodesic lines — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Сonstant mean curvature surfaces
      • Minimal surfaces
#constant curvature#constant mean curvature#minimal surface#geodesic line#surface of revolution#catenary#Bacharach#Brill
Surface of revolution of constant negative Gaussian curvature, conic type

Surface of revolution of constant negative Gaussian curvature, conic type — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Curves
    • Types of curves on surfaces
      • Asymptotic lines
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#surface of revolution#constant curvature#constant Gaussian curvature#negative curvature#geodesic line#asymptotic line#conical singularity#Bacharach#Brill
Surface of revolution of constant negative Gaussian curvature, hyperboloid type

Surface of revolution of constant negative Gaussian curvature, hyperboloid type — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#surface of revolution#constant curvature#constant Gaussian curvature#negative curvature#hyperboloid type#geodesic line#geodesic circle#Dyck#Brill
Trajectory of a heavy point on a sphere

Trajectory of a heavy point on a sphere — of M. Schilling catalog

  • Curves
    • Curves with physical meaning
#physical model#sphere#trajectory#Schleiermacher#Brill
Three-axial ellipsoids

Three-axial ellipsoids — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
  • Surfaces
    • Quadrics (surfaces of order two)
      • Ellipsoids and spheres
#quadric#ellipsoid#three-axial#lines of curvature#umbilical point#Diesel#Brill
One-sheeted hyperboloids with asymptotic cones

One-sheeted hyperboloids with asymptotic cones — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
  • Surfaces
    • Quadrics (surfaces of order two)
      • Rulings on quadrics
#quadric#hyperboloid#one-sheeted hyperboloid#rulings#lines of curvature#asymptotic cone#Diesel#Brill
Two-sheeted hyperboloids

Two-sheeted hyperboloids — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
#quadric#hyperboloid#two-sheeted hyperboloid#lines of curvature#asymptotic cone#Diesel#Brill
Elliptic paraboloids

Elliptic paraboloids — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
#quadric#paraboloid#elliptic paraboloid#lines of curvature#cross-section#Diesel#Brill
Hyperbolic paraboloids

Hyperbolic paraboloids — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
  • Surfaces
    • Quadrics (surfaces of order two)
      • Rulings on quadrics
#quadric#paraboloid#hyperbolic paraboloid#lines of curvature#cross-section#rulings#Diesel#Brill
Elliptic cones

Elliptic cones — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Quadrics (surfaces of order two)
      • Classification of surfaces of 2nd order
#quadric#cone#lines of curvature#rulings#Diesel#Brill
Jacobi amplitude $\varphi=am(u,k)$

Jacobi amplitude $\varphi=am(u,k)$ — of M. Schilling catalog

  • Functions
    • Some special real functions
#ellipse#elliptic function#elliptic integral#special function#amplitude#Brill#Kuen#Wolff
Sphere as a rotationally symmetric surface of constant positive Gaussian curvature

Sphere as a rotationally symmetric surface of constant positive Gaussian curvature — of M. Schilling catalog

  • Surfaces
    • Quadrics (surfaces of order two)
      • Ellipsoids and spheres
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#sphere#quadric#constant curvature#constant Gaussian curvature#surface of revolution#Brill
Spindle-shaped surface of constant positive Gaussian curvature

Spindle-shaped surface of constant positive Gaussian curvature — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#constant curvature#spindle-shaped#constant Gaussian curvature#elliptic integral#geodesic line#Brill#brass
Cheese-shaped surface of constant positive Gaussian curvature

Cheese-shaped surface of constant positive Gaussian curvature — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Geodesic lines
  • Surfaces
    • Surfaces of constant Gaussian curvature
      • Surfaces of revolution of constant Gaussian curvature
#constant curvature#constant Gaussian curvature#elliptic integral#geodesic line#Brill
Helicoid

Helicoid — of M. Schilling catalog

  • Curves
    • Types of curves on surfaces
      • Asymptotic lines
  • Curves
    • Types of curves on surfaces
      • Lines of curvature
  • Surfaces
    • Сonstant mean curvature surfaces
      • Minimal surfaces
#helix#minimal surface#rulings#line of curvature#asymptotic line#Brill#Herting
Geometric Models Collection of V.N. Karazin Kharkiv National University
  • Collections and Categories
  • About the Project