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.

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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

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"