  This is a summary of mathematical tools we used in research of analyzing the
structure of proteins with amyloid form \cite{xi2024Top}. We defined several
geometry indicators on the discrete curve namely the hop distance, the discrete
curvature and the discrete torsion. Then, we used these indicators to analyze
the structure of amyloid fibrils by regarding its peptide chains as discrete
curves in $\Rds^3$. We gave examples to show that these indicators give novel
insights in the characterization analysis of the structure of amyloid fibrils,
for example the discrete torsion can detect the hydrogen bonds interactions
between layers of amyloid fibril. {Moreover,} the topological tool performs
better than the root mean square deviation (RMSD) in quantifying the difference
of the structure of amyloid fibrils, etc.
