CCXIV CCCXLIX

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x
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CCXIV CCCXLIX DLXIII
CCCXXVII CCLXIX DXCVI
214 349 563
327 269 596
CCLXXVIII CCXXIX DVII
CCCXLVII CCXIV DLXI
278 229 507
347 214 561
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Sir Winston Churchillspeaking to MPs in the
House of Lords24 October 1943

• On the night of May 10, 1941, with one of the
  last bombs of the last serious raid, our House of
  Commons was destroyed by the violence of the
  enemy, and we have now to consider whether we
  should build it up again, and how, and when.
• We shape our buildings, and afterwards our
  buildings shape us.

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• Mosque, Istanbul, Turkey

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• Buddhist Temple, Singapore

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• Synagogue, Czech Republic

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• St Pauls Cathedral, London

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Symmetry

• What symmetry does this show?
• What would you need to do to the inner dark Star
  to transform it into the outer light Star?
• How about transforming it to the outer dark Star?

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Symmetry tiling and frieze patterns
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Circles and arcs
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Circular windows

• Can you work out how to construct all these
  accurately?
• What is the angle between one lobe and the next?
• Can you draw similar windows with other numbers
  of lobes?
• How much bigger is the radius of the outer circle
  compared to the inner circle?
• What is the area of the lobes (without the inner
  circle)?
• What is the area outside the lobes and inside the
  outer circle?

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Ogee or ogive arches
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How is an ogee arch constructed?

• This is what we want to achieve how might we go
  about doing it accurately?

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Rose windows
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Designing a rose windows
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Tiling patterns

• Use the worksheet sent to you in advance.
• Get as far with the investigation as you can in
  10 minutes

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Drawing a 6-point circle

• Set your compasses to the radius
• you want AND MAKE SURE
• THE RADIUS DOESNT
• CHANGE.
• Make a mark at the top of the circle.
• Put the point of your compasses on the top mark
  and make two more marks.
• Put the point of your compasses on these marks
  and make two more marks.
• Put the point of your compasses on one of the
  last marks to make the bottom mark.

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Using the 6-point circle to construct a simple
arch
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Visits to places of worship

• I hope you will make some visits to local places
  of worship. If you can go to more than one, of
  different religions, you will be able to make
  comparisons.
• Look for symbols and see if you can see how
  mathematical properties contribute to the meaning
  of the symbols.
• Look around you with mathematical eyes find
  your own maths.