# Proof of Radon's theorem by lowering the dimension

## TL;DR

This paper presents a new proof of Radon's theorem in d-dimensional space by employing a dimension-lowering technique, offering an alternative perspective to the classical proof.

## Contribution

The paper introduces a novel proof of Radon's theorem using a dimension-lowering approach, providing insights different from traditional methods.

## Key findings

- Validates Radon's theorem through a new proof technique.
- Demonstrates the effectiveness of dimension-lowering in geometric proofs.
- Offers an alternative proof that may simplify understanding of the theorem.

## Abstract

There is the classical Radon theorem. Given integer $d \geq 1$ and $d+2$ points in d-dimensional space $R^d$. Then these points can be divided into two disjoint subsets whose convex hulls have a non-empty intersection. The original proof of this theorem is usually used. In this article, this is another proof of it, by lowering the dimension.