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If Euclid has only collected the geometry stuffs while books of the other geometer have been burnt, calling the main branch of geometry under name of him might look academically unethical for some people. Even worse, when dividing the geometry into Euclidean and Non-Euclidean.

In contrast, Non-Euclidean geometries are not usually called by the name of their discoverers. Instead, they are called Hyperbolic geometry or Elliptic geometry.

I am looking for similar name for the geometry call Euclidean. "Plane geometry" seems to be correct. However, one might confuse it with 2D geometry.

It seems searching "Euclidean geometry alternative name" brings no related result on google. It raised this question for me that does Euclidean geometry really have any conventional alternative name?

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  • $\begingroup$ vocabulary.com/dictionary/Euclidean%20geometry $\endgroup$ – Peđa Terzić Jan 9 '15 at 13:12
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    $\begingroup$ You may be confusing "parabolic geometry" with "hyperbolic geometry". Hyperbolic geometry is Lobachevsky's non-Euclidean geometry. As MathBot's page says, "parabolic geometry" has been used as an alternative name for Euclidean geometry. $\endgroup$ – Doug Chatham Jan 9 '15 at 13:17
  • $\begingroup$ @DougChatham, Thank you. I fixed the mistake in the question. $\endgroup$ – arcsin Jan 9 '15 at 13:22
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In contrast, Non-Euclidean geometries are not usually called by the name of their discoverers.

It is fairly standard to refer to hyperbolic geometry as Lobachevskian and I have also seen Bolyai's name included, too. While I didn't know this until I did a bit of web searching, elliptic geometry is sometimes called Riemannian, although one can see how the more standard application of the term could drown out the former.

Parabolic geometry, logically, refers to Euclidean geometry. So Euclidean geometry perhaps stands out here by being better well-known by its eponym (Euclid) than its descriptive name (parabolic.)

"Plane geometry" seems to be correct. However, one might confuse it with 2D geometry.

If you seek an alternative name to $3$-d geometry, this is more ordinarily called solid geometry. I also know that Klein referred to the portions of his axioms covering $2$ and $3$ dimensional geometry this way in Foundations of geometry:

"We will call them, therefore, the plane axioms of group I, in order to distinguish them from the axioms I, 3–7, which we will designate briefly as the space axioms of this group."

This makes it tempting to call $3$-d geometry "space geometry," but that has some unfortunate collision with geometry of spacetime.

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