Geodesic
An elementary proof of Tverberg's theorem
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 54-61

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We give a new proof of Tverberg's familiar theorem saying that an arbitrary set of $q=(d+1)(p-1)+1$ points in $\mathbb R^d$ can be split into $p$ parts whose convex hulls have a nonempty intersection. Bibl. – 9 titles. 
@article{ZNSL_2008_353_a5,
     author = {M. Yu. Zvagel'skii},
     title = {An elementary proof of {Tverberg's} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {54--61},
     publisher = {mathdoc},
     volume = {353},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a5/}
}
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M. Yu. Zvagel'skii. An elementary proof of Tverberg's theorem. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 54-61. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a5/