Octagon
- Auteur:
- Henk Hietbrink
The Cathedral of Burgos has mathematical foundations. The architects were aware of mathematics. The book "Teseros Matematicos de la Catedral de Burgos" explains the mathematics behind its architecture.
The shape of the 'Chapel of the Constable' (capilla del Condestable) is an octagon.
See Instagram for my story.
See: Wikipedia
Say we have a square with length 2 and area 4.
Four circles through the center of the square cut the vertices into pieces.
Proof that the octagon is a regular octagon with length
The area of the octagon is less than the area of the square.
Proof that the area of the octagon is .
The octagon can be split up in eight equilateral triangles.
The area of every equilateral triangle is , its base is .
Proof that the heightof the equilateral triangle is 1.
The octagon can be split up in eight kites.
The area of each kite is .
A kite has a short side and a long side.
Proof that the length of the short side is
and that the length of the long side is 1.
Each kite has a short diagonal and a long diagonal.
Proof that the length of the short diagonal is
and that the length of the long diagonal is .
If you love the algebra of squaring roots of roots and love calculating the sides of similar triangles, you may continue with these rhombuses.
