This ultimately produces all of the cosines for the 17 17 -gon, again understood as particular line segments. Original answer (11 August 2016): Given a unit of length and segments of various lengths, one can, using compass and straightedge, construct sums, differences, products, quotients, and square roots of lengths.

Jan 1, 2014 · Given convex 17-gon. What is the maximal count of triangles we can divide it if we draw all it's diagonals? (for 4-gon,answer is 4, for 5-gon answer is 11)

Nov 8, 2019 · I am currently very interested in the derivation of the constructability of the 17-gon by Carl Friedrich Gauß. Has someone got an easy explanation for the solution of

Apr 2, 2019 · Interesting trivia: Of all the mathematical achievements of the mighty Gauss, he personally considered his 1796 proof of the construction of a regular 17-gon as his most beautiful theorem. Gauss found an unexpected link between contructible polygons and prime numbers.

Oct 3, 2024 · (Note: All images except the $13$-gon are from Antonia Buitrago's 2007 article "Polygons, Diagonals, and the Bronze Mean".) I. The golden ratio We are familiar with how $\\phi$ appears in ...

Jun 3, 2019 · A 17 be a regular 17-gon as in the following figure: Question: How can one prove that the Simson line of A9 A 9 with respect to the triangle A1A8A14 A 1 A 8 A 14 is perpendicular to the side A15A16 A 15 A 16?

Dec 23, 2018 · whose roots are ϵk = e(k 17) =cos kα +i sin kα ϵ k = e (k 17) = c o s k α + i s i n k α, with α = 2π 17 α = 2 π 17, and the notation e(τ) =def e2π i τ e (τ) = d e f e 2 π i τ, and with k = 1, …, 16 k = 1, …, 16 here. Below on the same page, variables x1 x 1 and x2 x 2 are each defined as sums of the ϵ ϵ 's, in such a way that it is immediately obvious that their sum is ...

It's not clear what you mean by "polygons in a 17-gon." If you mean polygons whose vertices are vertices of a 17-gon, then it would be 17 choose 3 plus (not times) 17 choose 4 plus 17 choose 5, etc.

$\begingroup$In Introduction To Geometry by Coxeter , there are surprisingly simple constructions shown for a side of the regular 17-gon and 257-gon inscribed in a given circle.

How many quadrilaterals are there whose vertices are the vertices of the 17-gon and have 2 sides that are diagonals?