Polygons, Diagonals, and the Bronze Mean

Metallic means and Pythagorean triples

“…Example 2.3. Let F n be the n th Fibonacci number, as a result of the (10), for even n, we can represent the 2F n th metallic number in terms of golden ratio δ 1 as,…”

“…In the article [12], she studied the design aspects of the metallic means. A notion of an associated polygon with the metallic means is analyzed in [10,13]. In a recent article [14], the author relates how different taffy (a candy made by pulling sticky sugar base) pullers are related to golden and silver ratios.…”

Cyclotomic Points and Algebraic Properties of Polygon Diagonals

“…In a PBS Infinite Series broadcast, Perez-Giz raised the question of whether or not the same statement is true for φn for any n ≥ 3 [PG18]. This question was in fact answered negatively by Buitrago for the bronze ratio φ3 several years previously [Bui07]. The methods used were entirely numeric, and did not extend to n ≥ 4.…”