3

A curve with polar coordinates,

(1)

studied by the Greek mathematician Nicomedes in about 200 BC, also known as the cochloid. It is the locus of points a fixed distance away from a line as measured along a line from the focus point (MacTutor Archive). Nicomedes recognized the three distinct forms seen in this family for 

, and 

. (For 

, it obviously degenerates to a circle.)

The conchoid of Nicomedes was a favorite with 17th century mathematicians and could be used to solve the problems of cube duplication,angle trisectionheptagon construction, and other Neusis constructions (Johnson 1975).

In Cartesian coordinates, the conchoid of Nicomedes may be written

(2)

or

(3)

The conchoid has 

 as an asymptote, and the area between either branch and the asymptote is infinite.

This is all according to Wolfram. See Wolfram’s website for more details.

Among the personal effects of the Doctor, Jack had once seen books, filled not with letters but with depictions of curves. These he had leafed through in times of boredom; for though he could not read, he could stare at a strange curve as well as any other man. Eliza had sat next to him and pronounced their names: the Limaçon of Pascal, the Kampyle of Eudoxus, the Conchoid of de Sluze, the Quadratrix of Hippias, the Epitrochoid, Tractrix, and the Cassinian Ovals. At the onset of the recitation Jack had wondered how geometers could be so inventive as to produce so many types and families of curves. Later he had come to perceive that of curves there was no end, and the true miracle was that poets, or writers, or whoever it was that was in charge of devising new words, could keep pace with those hectic geometers, and slap names on all the whorls and snarls in the pages of the Doctor’s geometry-books.

Now, though, he understood that geometers and word-wrights alike were nothing more than degraded and by-passed off-shoots of the South Asian weapons industry. There was not a straight blade in all of Hindoostan. Some weapons had grips at one end and were sharpened elsewhere; these might be classed as swords. Others consisted mostly of handle, with a dangerous bit at one end; these Jack conceived of as axes or spears, depending on whether they looked like they were meant to be swung, or shoved. Still others had strings, and seemed capable of projecting arrows. Jack put these down as bows. But of the sword-like ones, some were bent all the way round to form hooks; some curved first one way, then thought better of it and veered back the other; some had a different curve on either edge, so that they became broad as shovels in parts; some quivered back and forth like wriggling snakes; some forked, or spun off hooks, beaks, barbs, lobes, prongs, or even spirals. There were swords shaped like feathers, horseshoes, goat-horns, estuaries, penises, fish-hooks, eyebrows, hair-combs, Signs of the Zodiac, halfmoons, elm-leaves, dinner forks, Persian slippers, baker’s paddles, pelican’s beaks, dog’s legs, and Corinthian columns. This did not take into account the truly outlandish contraptions that seemed to have been made by piling two or more such weapons atop each other, heating, and beating. Of long-handled swinging-weapons (axes, maces, hammers, halberds, and weaponized farm-implements, viz. war-sickles, combat-flails, assault-shovels, and tactical adzes) there was a similar variety.

Most troublesome to Jack’s mind, for some reason, were the bows which instead of the good old crescent of English yew, here seemed to’ve been made from the legs of giant spiders; they were black, sinewy, glossy, spindly things that curved this way and that, and were sometimes longer on one end than the other, so that Jack could not even make out which end was up; which part was the handle; or which side was supposed to face the enemy. For each of these weapon-styles, he knew, there must be a six-thousand-year-old martial art with its own set of unfathomable rites, lingo, exercises, and secrets that could only be mastered through a lifetime of miserable study.

— 

The Confusion (Book II of the Baroque Cycle), Neal Stephenson

This is why it pays to read Stephenson’s run-on sentences. Dinner forks, estuaries, horseshoes, eyebrows, and fucking Corinthian columns.

Gemstone of the Day for Aug. 23rd - Sapphire

Gemstone of the Day for Aug. 23rd – Sapphire

Gemstone of the Day

                             Sapphire

The name Sapphire comes from the Sanskrit “sanipriya” (dear to the planet Saturn).

Hardness: 9               Specific Gravity: 3.9 – 4.1                  Chemistry: Al2O3 – Aluminum Oxide
Class: Corundum                      Crystallography: Hexagonal                       Cleavage: none
Fracture: uneven, conchoidal                  …

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My wife and I were eating French fries at 10pm on a Saturday night. It was an outside table at a little iced cream & fries shop in our neighborhood. A wee clink sound, like that of two tiny champagne glasses at a toast, got my attention. What could it be? I looked at the watch on my wrist to discover a crescent-shaped crack in its crystal. It kept advancing for about an hour after, until it finished with this elaborate conchoidal fracture, ready to lacerate any finger that nears it. I’m in the market for a new watch, is what I’m saying.

Crystal of the Day for August 20th - Garnet

Crystal of the Day for August 20th – Garnet

Crystal of the Day

Garnet

                                 
Hardness: 6.5-7.5                                                      Specific Gravity: 3.5-4.2
Chemistry: Ca3Fe2+2(SiO4)3            Class: Silicates            Crystallography: Isometric – Hexoctahedral
Cleavage: None                   Fracture: Conchoidal                         Streak: White                         Luster:…

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