The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{0,1\}^{m}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> <mi>m</mi> </msup> </math> </EquationSource> </InlineEquation> obtained in the series of papers (Borgs et al. in Random Struct Algorithms 27:137–184, <CitationRef CitationID="CR10">2005</CitationRef>; Borgs et al. in Ann Probab 33:1886–1944, <CitationRef CitationID="CR9">2005</CitationRef>; Borgs et al. in Combinatorica 26:395–410, <CitationRef CitationID="CR37">2006</CitationRef>; van der Hofstad and Nachmias in Hypercube percolation, Preprint <CitationRef CitationID="CR37">2012</CitationRef>). Secondly, we explain how this study can be performed without the use of the so-called “lace expansion” technique. To that aim, we provide a novel simple proof that the triangle condition holds at the critical probability. Copyright Springer-Verlag Berlin Heidelberg 2014
