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.

2014年1月1日 · 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)

2019年11月8日 · 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

2019年4月2日 · 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.

2024年10月3日 · (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 ...

2018年12月23日 · As a note, this question requires some familiarity with the classic book referenced in the title, "Introduction to the Theory of Numbers", by Hardy and Wright. I have the Sixth Edition. I'm trying to

2019年6月3日 · In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson. Let A1A2…A17 be a regular 17-gon as in the following figure: Question: How can one prove that the Simson line of A9 with respect to the …

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.

How many triangles formed by three vertices of a regular 17 17 -gon are obtuse? As an extension, how many triangles formed by three vertices of a regular n n -gon are obtuse?

2016年2月9日 · Given the regular n -gon formed by the n -th roots of unity. For some n, how do we find n−−√ using the sum/difference of line segments? n = 5: It is enough to use one line segment: If x5 = 1, then it can be the distance between the root x0 on the real line, and x2 in the second quadrant,