CONSTRUCTION SIDES OF A REGULAR PENTAGON WITH USINGPOLYNOMIALFACTORIZATION
DOI:
https://doi.org/10.59417/nir.2015.7.113Keywords:
regular pentagram, golden section, construction, polynomial factorizationAbstract
There is an intimate connection between the golden section and the regular 5-sided shape called a pentagon and its variation - the pentagram - that we explore first.If we look at the way a pentagram is constructed, we can see there are lots of lines divided in the golden ratio: Since the points can be joined to make a pentagon, the golden ratio appears in the pentagon also and the relationship between its sides and the diagonals (joining two non-adjacent points). Solve the problem: Given a circle, inscribe a regular pentagram.
Constructible polygon is a regular polygon that can be constructed with compass and straightedge. A regular pentagon is constructiblewith the use of polynomial factorization. In proposition IV.11, Euclid showed how to inscribe a regular pentagon in a circle. Ptolemy also gave a ruler and compass construction for the pentagon in his epoch-making work The Almagest.
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