Some Elementary Aspects of 4-Dimensional Geometry
نویسندگان
چکیده
We indicate that Heron’s formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in four-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms and other elementary four-dimensional solids.
منابع مشابه
SOME POINTS ON CASIMIR FORCES
Casimir forces of massive ferrnionic Dirac fields are calculated for parallel plates geometry in spatial space with dimension d and imposing bag model boundary conditions. It is shown that in the range of ma>>l where m is mass of fields quanta and a is the separation distance of the plates, it is equal to massive bosonic fields Casimir force for each degree of freedom. We argue this equalit...
متن کاملPreservice Primary School Teachers’ Elementary Geometry Knowledge
Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good base in elementary Geometry. The aim of this paper...
متن کامل/ 02 01 12 4 v 1 1 6 Ja n 20 02 NIKHEF 01 - 018 Aspects of BRST Quantization †
BRST-methods provide elegant and powerful tools for the construction and analysis of constrained systems, including models of particles, strings and fields. These lectures provide an elementary introduction to the ideas, illustrated with some important physical applications. † Lectures given at the Summerschool on Geometry and Topology in Physics (Rot a/d/ Rot, Germany) sept 2001 ∗ E-mail: v.ho...
متن کاملLectures on Four -
I give an elementary introduction to the theory of four-manifold invariants and its relation with topological eld theory. I review the recent developments in the theory of Donaldson and Seiberg-Witten invariants. Why another set of lectures on four-manifolds and topological eld theory? Apart from the contractual obligations imposed upon the lecturer there might be some justiication in the follo...
متن کاملBruns And
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Symmetry
دوره 7 شماره
صفحات -
تاریخ انتشار 2015