Crossword-Solution: HYPERBOLOID
Dictionary
| Word | Word Type | Definition |
|---|---|---|
| Hyperboloid | n. | A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface. |
| Hyperboloid | a. | Having some property that belongs to an hyperboloid or hyperbola. |
We have 5 clues for the answer “HYPERBOLOID”
| Clue | Answers |
|---|---|
| SOLID of the second degree (geom.) | 1 answer |
| SURFACE of the second degree (geom.) | 1 answer |
| a solid figure in which some of the plane sections are hyperbolas | 1 answer |
| solid of the second degree | 1 answer |
| surface of the second degree | 1 answer |
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Form of quartz with coloured bands
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Hint 1 meaning
A semipellucid, uncrystallized variety of quartz, presenting
various tints in the same specimen. Its colors are delicately arranged
in stripes or bands, or blended in clouds.
Hint 2 anagram
TAGEA
Hint 3 another clue
CERTAIN BRAIN SIZE
9 +1
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Sentences with HYPERBOLOID (5)
Even the hyperboloid of two sheets, obtained by revolving the hyperbola about its major axis, was known to them, but probably not the hyperboloid of one sheet, which results from revolving a hyperbola about the other axis.
The second is the _obtuse-angled conoid_, which is a hyperboloid of revolution described by the revolution of a hyperbola (a "section of an obtuse-angled cone") about its transverse axis.
Suppose, for instance, that the equations of a line (depending on the variable parameter [theta]) are x/a + y/c = [theta] (1 + y/b), x/a - z/c = 1/[theta] (1 - y/b); then, eliminating [theta] we have x²/a² - z²/c² = 1 - y²/b², or say, x²/a² + z²/b² - z²/c² = 1, the equation of a quadric surface, afterwards called the hyperboloid of one sheet; this surface is consequently a scroll.
Consequently a quadric surface is covered by two sets of straight lines, a pair through every point on it; these are imaginary for the ellipsoid, hyperboloid of two sheets, and elliptic paraboloid.
Writing the equation of the focal ellipse of the Darboux hyperboloid through H, enlarged to double scale so that O is the centre, (30) x²/[alpha]² + y²/ß² + z²/O = 1, with [alpha]² + [lambda], ß² + [lambda], [lambda] denoting the squares of the semiaxes of a confocal ellipsoid, and [lambda] changed into µ and [nu] for a confocal hyperboloid of one sheet and of two sheets.