Question: What  a simple closed shape in Euclidean geometry, plastic bodied, and designed to damage or destroy a vehicle by blast effect?

Context articles: Foundations of geometry
Non-Euclidean geometry
Clifford parallel
Birkhoff's axioms
Euclidean space
Circle
Hilbert's axioms
Tarski's axioms
Forum Geometricorum
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Foundations of geometry is the study of geometries as axiomatic systems.
 There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries.
 These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint.
 The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view.
 The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
 As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one.
 In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
 When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry.
In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point.
 The concept was first studied by William Kingdon Clifford in elliptic space.
 Since parallel lines have the property of equidistance, the term "parallel" was appropriated from Euclidean geometry, but in fact the "lines" of elliptic geometry are curves, and they have finite length, unlike the lines of Euclidean geometry.
 The algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit.
In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms.
 These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor.
 Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry.
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
 It is named after the Ancient Greek mathematician Euclid of Alexandria.
 The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry.
 Euclidean spaces also generalize to higher dimensions.
A circle is a simple closed shape in Euclidean geometry.
 It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.
 The distance between any of the points and the centre is called the radius.
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book "Grundlagen der Geometrie" (tr.
 "The Foundations of Geometry") as the foundation for a modern treatment of Euclidean geometry.
 Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.
Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called "elementary," that is formulable in first-order logic with identity, and requiring no set theory .
 Other modern axiomizations of Euclidean geometry are those by Hilbert and George Birkhoff.
Forum Geometricorum: A Journal on Classical Euclidean Geometry (often abbreviated "Forum Geom.")
 is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.
 It was founded in 2001, is published by Florida Atlantic University, and is indexed by Mathematical Reviews.
 Its founding editor-in-chief is Paul Yiu, a professor of mathematics at Florida Atlantic.
 All papers are available online immediately upon acceptance through the journal's web site.
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