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 Sept. 13 is Tiger's Eye

Gemstone of the Day for Sept. 13 is Tiger’s Eye

Gemstone of the Day

Tiger’s Eye

                                                        

Hardness: 7                     Specific Gravity: 2.6                       Chemistry: SiO2 
Class: Quartz                      Crystallography: Trigonal                       Cleavage: none
Fracture: Splintery to conchoidal                       Streak: yellow – brown                         Luster:…

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Gemstone of the Day for September 12 is Emerald

Gemstone of the Day for September 12 is Emerald

Gemstone of the Day

  Emerald  
  Hardness: 7.5 – 8.0                      Specific Gravity: hexagonal; 6/m2/m2/m                      Chemistry: Be3Al2(SiO3)6                     
Class: cyclosilicates                   Crystallography: hexagonal; 6/m2/m2/m
Cleavage: poor basal cleavage is seldom visible on {0001}               Fracture: conchoidal producing smooth brilliant surfaces   

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