caustic

(kô'stĭk)

1. Capable of burning, corroding, dissolving, or eating away by chemical action.
2. Corrosive and bitingly trenchant; cutting. See synonyms at sarcastic.
3. Causing a burning or stinging sensation, as from intense emotion: "Most of all, there is caustic shame for my own stupidity" (Scott Turow).

1. A caustic material or substance.
2. A hydroxide of a light metal.
3. The enveloping surface formed by light rays reflecting or refracting from a curved surface, especially one with spherical aberration.

[Middle English caustik, from Latin causticus, from Greek kaustikos, from kaustos, from kaiein, kau-, to burn.]

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Describing a substance that is strongly alkaline (e.g. caustic soda).

Biting, penetrating, possibly painful — that's how Richard Pryor's humor was described in an early obituary:

"Richard Pryor, the caustic yet perceptive actor-comedian who lived dangerously close to the edge both on stage and off, died Saturday. He was 65."

Link: The Boundless Gifts of Richard Pryor

Posted December 12, 2005.

See our Word Overheard blog to see interesting uses of strange words.

adjective

So sharp as to cause mental pain: acerbic, acid, acidic, acrid, astringent, biting, corrosive, cutting, mordacious, mordant, pungent, scathing, sharp, slashing, stinging, trenchant, truculent, vitriolic. See attack/defend, respect/contempt/standing.

Definition: burning, corrosive
Antonyms: calm, mild, soothing

adj

Definition: sarcastic
Antonyms: kind, nice, unsarcastic

1. burning or corrosive; destructive to tissue.
2. having a burning taste.
3. a corrosive or escharotic agent.

• c. bush — sarcostemma australe, S. viminale.
• bottle tree c. — eremophila spp.
• c. creeper — euphorbia drummondii, sarcostemma viminale.
• lunar c. — toughened silver nitrate.
• c. pencil — see silver nitrate (toughened).
• c. plant — sarcostemma australe.
• c. potash — potassium hydroxide.
• c. soda — sodium hydroxide.
• c. treated grain — grain treated with caustic to improve its digestibility; can cause abomasal ulcer and interstitial nephritis in cattle.
• c. treated roughage — roughage treated with caustic to improve its digestibility; can cause interstitial nephritis when fed to cows over long periods.
• c. vine — sarcostemma australe, S. viminale. Called also caustic bush.
• c. weed — euphorbia drummondii.

Destroying living tissue by chemical burning action.

• Tastes - caustic: (adj) sharp and acidic
• Demanding, Critical, Calculating, or Selfish

For other uses, see Caustic (disambiguation).

Reflective Caustic generated from a circle and parallel rays

In differential geometry and geometric optics, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the optical concept of caustics. The ray's source may be a point (called the radiant) or infinity, in which case a direction vector must be specified.

More generally, especially as applied to symplectic geometry and singularity theory, a caustic is the critical value set of a Lagrangian mapping (π ○ i) : L ↪ M ↠ B; where i : L ↪ M is a Lagrangian immersion of a Lagrangian submanifold L into a symplectic manifold M, and π : M ↠ B is a Lagrangian fibration of the symplectic manifold M. The caustic is a subset of the Lagrangian fibration's base space B.^[1]

Contents 1 Catacaustic 1.1 Example 2 References 3 See also 4 External links

Catacaustic

A catacaustic is the reflective case.

With a radiant, it is the evolute of the orthotomic of the radiant.

The planar, parallel-source-rays case: suppose the direction vector is (a,b) and the mirror curve is parametrised as (u(t),v(t)). The normal vector at a point is ( − v'(t),u'(t)); the reflection of the direction vector is (normal needs special normalization)

Having components of found reflected vector treat it as a tangent

(x − u)(bu'² − 2au'v' − bv'²) = (y − v)(av'² − 2bu'v' − au'²).

Using the simplest envelope form

F(x,y,t) = (x − u)(bu'² − 2au'v' − bv'²) − (y − v)(av'² − 2bu'v' − au'²) = x(bu'² − 2au'v' − bv'²) − y(av'² − 2bu'v' − au'²) + b(uv'² − uu'² − 2vu'v') + a( − vu'² + vv'² + 2uu'v')

F_t(x,y,t) = 2x(bu'u'' − a(u'v'' + u''v') − bv'v'') − 2y(av'v'' − b(u''v' + u'v'') − au'u'') + b(u'v'² + 2uv'v'' − u'³ − 2uu'u'' − 2u'v'² − 2u''vv' − 2u'vv'') + a( − v'u'² − 2vu'u'' + v'³ + 2vv'v'' + 2v'u'² + 2v''uu' + 2v'uu'')

which may be unaesthetic, but F = F_t = 0 gives a linear system in (x,y) and so it is elementary to obtain a parametrisation of the catacaustic. Cramer's rule would serve.

Example

Let the direction vector be (0,1) and the mirror be (t,t²). Then

u' = 1   u'' = 0   v' = 2t   v'' = 2   a = 0   b = 1

F(x,y,t) = (x − t)(1 − 4t²) + 4t(y − t²) = x(1 − 4t²) + 4ty − t

F_t(x,y,t) = − 8tx + 4y − 1

and F = F_t = 0 has solution (0,1 / 4); i.e., light entering a parabolic mirror parallel to its axis is reflected through the focus.

References

1. ^ Arnold, V. I.; Varchenko, A. N.; Gusein-Zade, S. M. (1985). The Classification of Critical Points, Caustics and Wave Fronts: Singularities of Differentiable Maps, Vol 1. Birkhäuser. ISBN 0817631879. 

See also

• Cut locus (Riemannian manifold)

External links

• Weisstein, Eric W., "Caustic" from MathWorld.

v d e Differential transforms of plane curves Unary operations Evolute Involute Dual curve Inverse curve Parallel curve Isoptic Unary operations defined by a point Pedal & Contrapedal curves Negative pedal curve Pursuit curve Caustic Unary operations defined by two points Strophoid Binary operations defined by a point Roulette Operations on a family of curves Envelope

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Dansk (Danish)
adj. - sarkastisk, kaustisk, ætsende
n. - causticum (ætsmiddel)

idioms:

• caustic soda    kaustisk soda

Nederlands (Dutch)
brandend, bijtend

Français (French)
adj. - (Chim, fig) caustique
n. - causticité, substance caustique, hydroxyde, courbe/surface caustique

idioms:

• caustic soda    soude caustique

Deutsch (German)
adj. - ätzend, bissig
n. - Ätzmittel, (Med.) Kaustikum

idioms:

• caustic soda    Ätznatron

Ελληνική (Greek)
adj. - (χημ.) καυστικός, (μτφ.) δηκτικός, σαρκαστικός

idioms:

• caustic soda    (χημ.) καυστική σόδα

Italiano (Italian)
caustico

idioms:

• caustic soda    soda caustica

Português (Portuguese)
adj. - cáustico

idioms:

• caustic soda    soda (f) cáustica (Quím.)

Русский (Russian)
каустический, едкий

idioms:

• caustic soda    едкий натр

Español (Spanish)
adj. - cáustico
n. - cáustico

idioms:

• caustic soda    soda cáustica

Svenska (Swedish)
adj. - brännande, skarp

中文（简体）(Chinese (Simplified))
腐蚀性的, 刻薄的, 腐蚀剂

idioms:

• caustic soda    苛性钠

中文（繁體）(Chinese (Traditional))
adj. - 腐蝕性的, 刻薄的
n. - 腐蝕劑

idioms:

• caustic soda    苛性鈉

한국어 (Korean)
adj. - 부식성의, 통렬한
n. - 부식제, 빈정대는 말

日本語 (Japanese)
adj. - 痛烈な, 腐食性の, 焼灼性の, 火線の, 辛辣な, 皮肉な
n. - 火線, 腐食薬

idioms:

• caustic soda    苛性ソーダ

العربيه (Arabic)
‏(صفه) كاو, لاذع, محرق‏

עברית (Hebrew)
adj. - ‮מאכל, שורף, חריף, צורב‬
n. - ‮חומר מאכל‬

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