Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motivated exposition of the proof of the Tverberg Theorem   We present a motivated exposition of the proof of the following Tverberg
Theorem: For every integers $d,r$ any $(d+1)(r-1)+1$ points in $\mathbb R^d$
can be decomposed into $r$ groups such that all the $r$ convex hulls of the
groups have a common point. The proof is by well-known reduction to the
B\'ar\'any Theorem. However, our exposition is easier to grasp because
additional constructions (of an embedding $\mathbb R^d\subset\mathbb R^{d+1}$,
of vectors $\varphi_{j,i}$ and statement of the Bara\'ny Theorem) are not
introduced in advance in a non-motivated way, but naturally appear in an
attempt to construct the required decomposition. This attempt is based on
rewriting several equalities between vectors as one equality between vectors of
higher dimension.

32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess