Editing Octagon (section)

===Diagonality===
The regular octagon, in terms of the side length ''a'', has three different types of [[diagonal]]s:

*Short diagonal;
*Medium diagonal (also called span or height), which is twice the length of the inradius;
*Long diagonal, which is twice the length of the circumradius.

The formula for each of them follows from the basic principles of geometry. Here are the formulas for their length:<ref>{{citation|title=A Panoply of Polygons|volume=58|series=Dolciani Mathematical Expositions|first1=Claudi|last1=Alsina|first2=Roger B.|last2=Nelsen|publisher=American Mathematical Society|year=2023|isbn=9781470471842|page=124|url=https://books.google.com/books?id=LqatEAAAQBAJ&pg=PA124}}</ref>

*Short diagonal: <math>a\sqrt{2+\sqrt2}</math> ;
*Medium diagonal: <math>(1+\sqrt2)a</math> ; (''[[silver ratio]]'' times a) 
*Long diagonal: <math>a\sqrt{4 + 2\sqrt2}</math> .