Euclid, the great mathematician who left us Elements and a base upon which to build modern geometry, never determined how to construct a regular seventeen-sided polygon before his death around 300 BCE. For more than 1,000 years after Euclid's death, mathematicians knew how to construct many regular n-gons, but the heptadecagon was elusive. That is, until a nineteen-year-old Gauss discovered a method to construct the polygon in 1796. He used only a straight-edge and compass, as Euclid would have done.
If you'd like to explore the numbers behind the construction, visit the explanation on this Wolfram page.
It is incredible to consider Gauss' discoveries at this young age. For example, he invented modular arithmetic only about a week after the heptadecagon construction. Gauss continued to make mathematical discoveries until his death in 1855, but he always considered the constuction of a regular heptadecagon one of his greatest.