THE PAPERS
> The castrum or filleted rectangle is geometrically
analysed in terms of a "calipered" diagonal parallel to opposite corner quadrant
bisectors. This leads to a trigonometric equation that permits determination of
Corner Radius from knowledge of the absolute Castrum Width, Aspect Ratio and
"Calipered" Diagonal only.
Actual calculation of this radius necessitates,
however, an application of a suitable iterative numerical differentiation.
The only appropriate resource found was The Ridders Method that soon
converges to an "exact" expression for the radius.
This pseudoanalytic
formula is dauntingly complicated and expensive-looking invoking inter alia
eight square roots ( some redundant ) and eight trigonometric
functions.
The implication of transcendental functions does of course render
the formula not truly exact and essentially incomplete.
Read this Paper
Two simple substitutions of well-known algebraic
equivalents for their relative nested trigonometric forms facilitates a
simplification of the very complicated equation for Castrum Corner Radius that
was derived in CASTRUM.
A series of derivations reduces that equation to a
very simple and economical seven-term algebraic expression.
Incompleteness persists in the form of the indeterminate root of two.
Read this Paper
Using surveyors' plans, many based upon aerial
photographs, the Corner Radii and Aspect Ratios of more than one hundred
castrum-like British Roman encampments are tabulated.
Several derived
statistics are educed and attempts made to relate these to putative methods of
perimeter layout.
The encampments are placed within the context of Ancient
Roman strategic doctrine.
Read this Paper
| NAME OF PAPER: | Pseudoanalytic Mensuration of the Castrum |
| by Means of The Ridders Method | |
| DATE OF WRITING: | 3 November 2012 |
| LENGTH: | 29 A4 Pages at Times New Roman 12 |
| ILLUSTRATIONS: | 5 |
| EQUATIONS: | 63 |
| TABLES: | 7 |
| REFERENCES: | 1 |
| APPENDICES: | All Appendices included in the Internet Version |
| FILENAME: | castrum-compressed.pdf |
| ABSTRACT: |
analysed in terms of a "calipered" diagonal parallel to opposite corner quadrant
bisectors. This leads to a trigonometric equation that permits determination of
Corner Radius from knowledge of the absolute Castrum Width, Aspect Ratio and
"Calipered" Diagonal only.
Actual calculation of this radius necessitates,
however, an application of a suitable iterative numerical differentiation.
The only appropriate resource found was The Ridders Method that soon
converges to an "exact" expression for the radius.
This pseudoanalytic
formula is dauntingly complicated and expensive-looking invoking inter alia
eight square roots ( some redundant ) and eight trigonometric
functions.
The implication of transcendental functions does of course render
the formula not truly exact and essentially incomplete.
Read this Paper
| NAME OF PAPER: | A Simple and Non-Trigonometric |
| Development of Castrum Mensuration | |
| DATE OF WRITING: | 20 November 2012 |
| LENGTH: | 27 A4 Pages at Times New Roman 12 |
| ILLUSTRATIONS: | 7 |
| EQUATIONS: | 45 |
| TABLES: | 7 |
| REFERENCES: | 63 |
| APPENDICES: | All Appendices included in the Internet Version |
| FILENAME: | castsimp-compressed.pdf |
| ABSTRACT: |
Two simple substitutions of well-known algebraic
equivalents for their relative nested trigonometric forms facilitates a
simplification of the very complicated equation for Castrum Corner Radius that
was derived in CASTRUM.
A series of derivations reduces that equation to a
very simple and economical seven-term algebraic expression.
Incompleteness persists in the form of the indeterminate root of two.
Read this Paper
| NAME OF PAPER: | Some Design Aspects of |
| Roman Encampments in Britain: | |
| An Extended Study | |
| DATE OF WRITING: | 18 February 2013 |
| LENGTH: | 88 A4 Pages at Times New Roman 12 |
| ILLUSTRATIONS: | 27 |
| EQUATIONS: | 45 |
| TABLES: | 20 |
| REFERENCES: | 14 |
| APPENDICES: | All Appendices included in the Internet Versions |
| FILENAME: | fortgeom3-compressed.pdf |
| ABSTRACT: |
Using surveyors' plans, many based upon aerial
photographs, the Corner Radii and Aspect Ratios of more than one hundred
castrum-like British Roman encampments are tabulated.
Several derived
statistics are educed and attempts made to relate these to putative methods of
perimeter layout.
The encampments are placed within the context of Ancient
Roman strategic doctrine.
Read this Paper
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"Castra and their British Traces"
"Castra and their British Traces"