Segmental Pediment Math

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Segmental Pediment Math

Postby Christopher Foxe » 02 Aug 2013, 13:14

Want to draw up a template for a segmental pediment to adorn the top of a puppet booth I'm building. But I have forgotten my math :roll: .

The base is 37.5 inches and the height is 12 inches. Anyone know what the formula is?

TIA.
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Re: Segmental Pediment Math

Postby lesclarke » 02 Aug 2013, 15:25

Don't know where you are posting from Christopher, 'math' is possibly a very big clue, but over here we do have a few 'colourful' words & expressions that enrich our vocabulary, so to answer you in a particulary North British way, I would suggest that you...

'Stuff' the math, and just put a nice curve on it.

It can't really matter to the casual, or indeed the engrossed observer of a Punch & Judy show.

The simplest way to get your curve is to take a long metal ruler and bend it until you get a curve that 'looks' right, mark it off on your wood. Mark the centre line and lines at regular distances, and then check it is the same height at corresponding left and right sides of the arc, and make any adjustments.
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Re: Segmental Pediment Math

Postby Chris » 02 Aug 2013, 20:58

For the minority of Punchmen who haven't studied Greek classical architecture it might be helpful to explain that a pediment is a long low triangular top of an arch. In the segmental version the base remains flat but the two equal sides are replaced by the arc of a circle.

I would suggest the easiest way to solve this is to get a sheet of paper and a pair of compasses, and then solve it on a reduced scale. This can be done geometrically with intersecting arcs (if you remember the method?) or alternatively it should be a fairly easy trial and error excercise. Graph paper might be useful if using trial and error. All you need to find is the radius of the circle which will give you a chord of the desired length. Scale up your radius appropriately and then improvise a compass using chalk and string to draw the appropriate large curve on your plywood.

Or if you do want to do the calculation then you can find the formulae here:
http://www.dogtoby.co.uk/geometry.pdf
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Re: Segmental Pediment Math

Postby Christopher Foxe » 03 Aug 2013, 03:47

@ Les: :lol: Posting from New Zealand, actually.

@ Chris: Many thanks.

Further searching has produced the following formula:

R= (A squared + B squared)/(2A)

where R= Radius of the larger circle containing the segmented arc; A= the arc height and B= half the base length. Accordingly, the radius of the circle will be roughly 20.2 inches (or 40.4 inches diameter).

Many thanks.
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