# Geometry in Nature: Regular pentagon [Oleander]

The pentagons are five-sided polygonal shapes. In case be regular, the length of these is the same for all of them. The pentagon has five vertices, and in the case of regular we differentiate between “convex” and starry.

A regular pentagon is one that has all sides and angles equal congruent. Each internal angle measured 108 grados oh 3π / 5 radianes. The sum of the angles anregular pentagon is 540 ° or 3π radianes. (W)

In nature we find in different expressions, one of them is in the distribution of many flower petals, as in the case of “Oleanders” whose image is for illustration we.

The oleander (Nerium oleander L.), also known as laurel flower, Rose Laurel, Baladre the Trinitarian, is the only species in the genus Nerium included in the family (Apocynaceae). Bushy plant that can form as small sized tree, lanceolate evergreen deep green and pink flowers (in the wild variety). Leaves, flowers, stems, branches and seeds are poisonous.(W)

The image can be obtained with higher resolution, wallpaper format by clicking the mouse.

A curious construction of a pentagon from a strip of paper that I have seen in gaussianos us proposed the challenge to prove if the geometry is regular.

This is a necessary and sufficient that each diagonal is parallel to one side Pentagon.

In the figure it can be shown as the paper strip is of constant width, so the diagonal AC is necessarily parallel to the side of. Analogously may be demonstrated for the other sides and diagonals. This property in the Pentagon may be related to the number of metrically Fibonacci, as he explains in a funny video Donald Duck and the golden section or golden ratio