conchoidal

Don’t let obsidian steal your heart!

While this is very unlikely in today’s culture, it was almost a certainty for those individuals sacrificed by the Aztecs during religious rituals. Probably the only consolation for someone who is about to have their heart ripped out is the knowledge that the knife would be sharp. Aztec ceremonial knives were composed of flint or obsidian blades, and it is the geological properties of these rocks that would have at least made your demise swift.

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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.

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Taaffeite

  • Hexagonal crystal structure
  • 8-8.5 hardness
  • Conchoidal fracture
  • White streak
  • 3.6-3.61 specific gravity
  • Vitreous-adamantine luster

Taaffeite was first discovered when purchased by Richard Taaffe, who mistakenly believed it was spinel, until he realized his specimen had the property of double refraction, which spinel does not have. They are often mistaken for each other, due to almost identical structural properties. It’s the only mineral discovered after being faceted, and is extremely rare.So rare, in fact, that it’s only used as a gemstone. The colors range from colorless to purple to red to green, and it’s found in carbonate rocks. While it’s named after Taaffe, the official IMA approved name for it is Magnesiotaaffeite-2N’2S, and magnesium is a main component of Taaffeite. In fact, it’s the first mineral to contain both magnesium and beryllium as major components (Mg3Al8BeO16). Thanks to the anon for the request! I had no idea this rock existed!