Definition:Conchoid of Nicomedes

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Definition

Let $\CC$ be a straight line.

Let $P$ be a fixed point not on $\CC$ but a perpendicular distance $a$ from $\CC$.


The conchoid of Nicomedes is the conchoid defined as the locus of points a constant distance $b$ from $\CC$ as measured along a straight line $\LL$ through $P$.


Conchoid-of-Nicomedes-construction.png


Examples

ConchoidOfNicomedes.png


The above diagram illustrates the conchoid of Nicomedes for $b = 1$ and various values of $a$ from $0$ to $3$.


Also known as

Some sources suggest that the conchoid of Nicomedes can also be referred to as a cochloid.

However, this usage can be confused easily with the cochleoid which some dictionaries give cochloid as an alternative for.

Others refer to it as merely a conchoid, but that term is best used to refer to the more general object of which the conchoid of Nicomedes is an example.


Also see

  • Results about the conchoid of Nicomedes can be found here.


Source of Name

This entry was named for Nicomedes.


Historical Note

Nicomedes designed the curve now known as the conchoid of Nicomedes specifically for solving the problem of Doubling the Cube.

It can also be used for Trisecting the Angle.


Linguistic Note

The word conchoid derives from the Latin concha, which means mussel.

Ultimately the word derives from the Ancient Greek κόγχη (kónkhē) plus -oid, or directly from Ancient Greek κογχοειδής (konkhoeidḗs), which refers to anything with the general shape of a mussel shell.


It is properly pronounced kon-khoid, where the kh sound is the one found in the Scots loch or German ich.

However, it is commonplace to use the pronunciation kon-koid.

Note that the pronunciations kon-tshoid and kon-shoid are technically incorrect.


Sources

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