hyperboloid

American  

[hahy-pur-buh-loid] / haɪˈpɜr bəˌlɔɪd /

noun

Mathematics.

1. a quadric surface having a finite center and some of its plane sections hyperbolas. Equation: x 2 / a 2 + y 2 / b 2 − z 2 / c 2 = 1.

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hyperboloid British  

/ haɪˈpɜːbəˌlɔɪd /

noun

1. a geometric surface consisting of one sheet, or of two sheets separated by a finite distance, whose sections parallel to the three coordinate planes are hyperbolas or ellipses. Equations x ²/ a ² + y ²/ b ² – z ²/ c ² = 1 (one sheet) or x ²/ a ² – y ²/ b ² – z ²/ c ² = 1 (two sheets) where a, b, and c are constants

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hyperboloid Scientific  

/ hī-pûr′bə-loid′ /

1. Either of two surfaces generated by rotating a hyperbola about either of its main axes and having a finite center, with certain plane sections that are hyperbolas and others that are ellipses or circles.

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Other Word Forms

• hyperboloidal
  adjective

Etymology

Origin of hyperboloid

First recorded in 1720–30; hyperbol(a) + -oid

Example Sentences

See Examples For:

hyperboloid

Describe the traces of the hyperboloid of one sheet given by equation x2 + y2 − z2 = 1.

From Textbooks ● Mar. 30, 2016

E is located above the xy -plane, below z = 1, outside the one-sheeted hyperboloid x2 + y2 − z2 = 1, and inside the cylinder x2 + y2 = 2.

From Textbooks ● Mar. 30, 2016

This equation describes a hyperboloid of one sheet as shown in the following figure.

From Textbooks ● Mar. 30, 2016

Figure 4.13 A hyperboloid of one sheet with some of its level surfaces.

From Textbooks ● Mar. 30, 2016

He put on his control machine the equation of a hyperboloid of two branches, and changed the constants gradually till the two branches came close.

From Invaders from the Infinite by Campbell, John Wood