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(532) Origami of Pentagon [thought]

how to fold a pentagon s nmb.jpg
This shows how to fold a pentagon from a square paper.
origami 3.jpg
Why can this triangle change into a pentagon?
origami pentagon 1 written s.jpg 
Because the angle θ of this triangle is approximately 72 degrees. This is an important point.
tanθ=3/1
tan-1(tanθ)=tan-1(3)≒71.565[DGR]
arctan3 trimmed s.jpg

365÷5=72[DGR]
tan72≒3.0777
tan72 trimmed s.jpg
A pentagon is fold like this. This pentagon is not a perfect regular pentagon but good enough for origami.
origami 5.jpgdrawing 5.jpg
As origami⑥ and ⑦ show, unfold lower corners and fold again to make a small pocket to which the top corner of the triangle goes.

Definition of trigonometer:
  Sine, Cosine and Tangent (often shorted to sin, cos and tan) are each a ratio of sides of right angled triangle: For a given angle θ each ratio stays the same no matter how big or small the triangle is.
tanθ=a/c
tan θ with t.jpg
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