conchoidal

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.

Gemstone of the Day for April 17th is Magnetite

Gemstone of the Day for April 17th is Magnetite

Gemstone of the Day


Magnetite

Known as the “Stone of Stability”

(Color: Black)
Hardness: 5.5 – 6.5
Specific Gravity: 5.1+
Chemistry: Fe3O4, Iron Oxide
Class: Oxides and Hydroxides
Crystallography: isometric; 4/m bar 3 2/m
Cleavage: absent
Fracture: conchoidal
Streak: black
Luster: Oxides and Hydroxides

Healing: Magnetite is used to increase blood circulation. Also used as a relief for chronic…

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Gemstone of the Day for April 13th - Diamond

Gemstone of the Day for April 13th – Diamond

Gemstone of the Day

Diamond

(Color: every color of the rainbow)

Hardness: 10

Specific Gravity: 3.52

Chemistry: C

Class: Carbons

Crystallography: Isometric, usually octahedral, with many crystal faces.

Cleavage: all sides – octahedral

Fracture: Conchoidal

Streak: White

Luster: Adamantine

Birthstone for the month of April

Healing: Diamond is used to balance the metabolism. It is also used for eye…

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