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We present a motivated exposition of the proof of the following TverbergTheorem: 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 thegroups have a common point. The proof is by well-known reduction to theB\'ar\'any Theorem. However, our exposition is easier to grasp becauseadditional 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 notintroduced in advance in a non-motivated way, but naturally appear in anattempt to construct the required decomposition. This attempt is based onrewriting several equalities between vectors as one equality between vectors ofhigher dimension.

Motivated exposition of the proof of the Tverberg Theorem