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Modified Plant Design

Castel del Monte

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Page 107

        Enlarged Octagon Center

A promising enlargement for the tower has been recognized in the area that starts at tower corner A and ends at the footing corner EE, folio 107:01.

The goal then is to fit an enlarged tower octagon in this space, between tower corner A and footing corner EE.

This means that the diagonal of the enlarged tower octagon t' is the diagonal of the older tower octagon increased by the footing corner measure k, folio 107:02:

t’ = t + k

There are various ways to construct an octagon from the minor diagonal t'. The geometric approach followed here is to identify first the circle circumscribing the octagon, and then mark the new tower octagon corners on the circle. Two of the new tower corners are already defined, these are corners A and EE that define the end points of the new diagonal t'.

The center of the circumscribing circle lays midway along the new diagonal t'. A geometric means to locate this center point is the bisecting technique.

The plant minor diagonals anchored at the plant octagon footing corners are needed to assist in the definition of the new tower octagon side and are defined first, folio 107:03.

New diagonal t' bisectioning:

  1. A circle is drawn centered on corner A with an arbitrary radius but close to the the measure t', folio 107:04.

  2. A similar circle is drawn of the same radius but centered on corner EE, folio 107:05.

  3. The two circles form intersection points X, Folio 107:06.

  4. A bisecting line is drawn trough the intersection points X, folio 107:07.

  5. The bisecting line intersects the new tower diagonal t' at its midpoint, folio 107:08.

This intersection point O' between the bisecting line and the new minor diagonal is the center the new tower circumscribing circle, folio 107:09.


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