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Algebraic Curves and Surfaces
Two-sheet hyperboloids

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Categories

A

Algebraic Curves and Surfaces

Ia

Ib

Hyperbolic paraboloids

Ic

One-sheet hyperboloids

Id

Two-sheet hyperboloids

Double leaf hyperboloid
Double leaf hyperboloid
Plane slices of the double-leaf hyperboloid

Ie

Elliptic paraboloids

If

Cones and cylinders

Ig

Confocal systems, conics

II

Generation of conics and surfaces of second order

III

Curves of third and fourth order

IV

Surfaces of third order

V

VI

Other surfaces of fourth and higher order

VII

VIII

IX

Descriptive geometry

XX

B

Combinatorical Geometry

C

D

Kinematics and Mechanics

E

Differential Geometry

F

G

Analysis, Probability Theory

H

Theory of Functions of Complex Variables

J

Differential Equations, Wave Theory

K

Geometrical Optics

L

Instruments and Devices.

M

History of Mathematis and Astronomy

Z

Models of rubric: Two-sheet hyperboloids

Model 17 Double leaf hyperboloid
Model 26 Double leaf hyperboloid
Model 41 Plane slices of the double-leaf hyperboloid

Hyperboloids of two sheets are determined by the equation \(\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=-1\) with \(a,b,c\) positive real numbers. The sections with planes normal to the \(z\)-axis are ellipses. For \(a=b\) the surface is an surface of revolation of an hyperbola.

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