Isometry group Totally Explained

Everything about Isometry Group totally explained

In mathematics, the isometry group of a metric space is the set of all isometries from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function. An isometry group of a metric space is a subgroup of isometries; it represents in most cases a possible set of symmetries of objects/figures in the space, or functions defined on the space. See symmetry group.

Examples

Consider a triangle in the plane with unequal sides. Then, the isometry group of the set of three vertices of this triangle is the trivial group. If the triangle has two equal sides which are not equal to the third, the isometry group is the cyclic group Z/2Z. If the triangle is equilateral, its isometry group is the permutation group S₃.

The isometry group of a two-dimensional sphere is an infinite group, called the orthogonal group O(3).

The isometry group of the n-dimensional Euclidean space is the Euclidean group E(n).Further Information

Get more info on 'Isometry Group'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://isometry_group.totallyexplained.com">Isometry group Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.