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The Maths of Castles and Fortifications: Symmetry in attack and defence

The Maths of Castles and Fortifications: Symmetry in attack and defence. Chris Budd. Uncomfortable fact …. A major feature of most civilisations has been the need to protect itself from, or impress, other civilisations. In the UK this has led to the building of many castles and forts.

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The Maths of Castles and Fortifications: Symmetry in attack and defence

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  1. The Maths of Castles and Fortifications: Symmetry in attack and defence Chris Budd

  2. Uncomfortable fact ….. A major feature of most civilisations has been the need to protect itself from, or impress, other civilisations In the UK this has led to the building of many castles and forts Maths can help in both making castles easier to defend and also in making them look good!

  3. Hill Forts Early British Forts were built on hills Questions: What is the best shape? How do you design the entrance? Where do you put the ditches?

  4. Maiden Castle

  5. Some basic axioms: 1. Want to have as short a perimeter as possible 2. Want to enclose the largest area as possible Which shape do you think is best and why?

  6. Some other features of a good design: 1. It should be convex .. Any two defenders must be able to see each other = line of vision 2. It should be symmetric .. No weak spots

  7. The shape which encloses the largest area with the smallest perimeter is also convex and is as symmetric as possible The isoperimetric theorem

  8. How to get in to a hill fort • Getting in to a hill fort presents the opposite problem … • You want the attacking forces to encounter as many defenders as possible • You can only attack them when they are close to the fort Question: How can you pack a long wall into a small space? Fractal

  9. Bad Better walls Maiden Castle

  10. Koch Snowflake

  11. Medieval Castles Medieval castles started with a Motte and Bailey design similar to a hill fort

  12. Later castles had an outer wall (with turrets) and a keep Harlech

  13. Conigsburgh Caernarfon Raglan

  14. Keeps were very symmetric Harlech Conigsburgh Raglan Caernarfon

  15. Square keep: Easy to build Circular keep: Harder to build BUT Much easier to tunnel under a square keep

  16. Danger zone

  17. Danger zone Safe zone

  18. Undefended corner

  19. Turrets help to cover blind spots

  20. Tudor Castles: Turrets on turrets

  21. Vauban’s Forts

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