The Keys of Atlantis

A Study of Ancient Unified Numerical and Metrological Systems

by Peter Wakefield Sault

Copyright © Peter Wakefield Sault 1973-2005
All rights reserved worldwide

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The Keys of Atlantis

Appendix F.

The Parthenon Trapeza

Figure F-1. The Trapeza within The Composite Tetrahedron

Volume of The Trapeza

The trapeza can be decomposed into nine separate modules, comprising four types identified as V₁ through V₄ in Figure F-2 below.

Figure F-2. Plan View of The Trapeza

The heights, h (normal to the view in Figure F-2), of the modules are all equal. The lengths of the edges are:

Where, by definition:

The volumes of the module types are:

from which it can be seen that V₂ = V₃.

Therefore the total volume of the trapeza:

Volume of The Rectangle-Based Axehead

The rectangle-based axehead can be decomposed into three separate modules, comprising two types identified as V₅ and V₆ in Figure F-3 below.

Figure F-3. Plan View of The Rectangle-Based Axehead

The heights, 2h (normal to the view shown in Figure F-3), of the modules are all equal, where h is the height of the trapeza. The lengths of the edges are:

Where d = b + c

The volumes of the module types are:

Therefore the total volume of the axehead:

Volume of The Square-Based Axehead

The square-based axehead can be decomposed into three separate modules, comprising two types identified as V₇ and V₈ in Figure F-4 below.

Figure F-4. Plan View of The Square-Based Axehead

The heights, 2h (normal to the view shown in Figure F-4), of the modules are all equal, where h is the height of the trapeza. The lengths of the edges are:

Where e = a + c

The volumes of the module types are:

Therefore the total volume of the axehead:

from which it becomes clear that the volumes of the two axeheads are equal.

Volume of The Composite Tetrahedron

Figure F-5. Plan View of The Composite Tetrahedron