New Views over Megalithia

[Mick Harper]

Well, I a not a Civil Engineer. Neither am I an Architect. But I'm pretty damn sure that none of 'em would design and build any aesthetically pleasing building without a very thorough knowledge of geometry. And an understanding of all the classic forms of architecture (Doric etc) depends on understanding the differences in their geometric rules.

Alas, all the finest buildings of antiquity were done without a knowledge of geometry. Euclid lived much later, if at all. If you would care to name an English builder/architect/civil engineer of the eighteenth and nineteenth centuries who had studied geometry, I'd be obliged. After that it is impossible to say because geometry was compulsorily taught to everyone so it is impossible to say whether they used geometry or not. (They didn't.)

Even with t'interweb technology, geometry has a crucial role to play. Minimum radius of optical-fibre plumbing is a geometric issue. So is the layout of integrated circuits and microprocessors.

Sorry, old chum, it isn't. A minimum radius is not a geometric question but, again, one of trial and error measurement. I played the triangle in my infant school band but that didn't mean I knew how many degrees the angles added up to. It's 360 for those still at infants school.

[TisILeclerc]

I thought geometry was measurement?

Put three squares next to each other. Then another three on top. And three more on top of them and you can calculate the area by counting the squares.

From that you can create cubes, triangles and even work out radii and circumferences.

Something essential for a plumber who has to bend a pipe to a particular angle. He must know the thickness of the pipe walls as well as the diameter of the pipe. Get it wrong and you'll need a longer piece of pipe to play with.

And some of these people get to build aeroplanes. Still, it's not that difficult really. A couple of weeks on a YTS scheme and anyone can do it.

[Mick Harper]

I've got the plumbers in right now -- an unfortunate accident with the toilet -- and they confess they can't remember any geometry they learned at school.

[Boreades]

Sorry, old chum, it isn't. A minimum radius is not a geometric question but, again, one of trial and error measurement. I played the triangle in my infant school band but I didn't know how many degrees the angles added up to. It's 360 for those still at infants school.

Sorry old chum, you've missed the boat. Go back and start again. A good place to start would be Interference Cross Sections. If you don't understand the problem, you have no chance of understanding the subject.

Then (if you can understand the mathematics) you can go onto differential geometry, topology, fractal geometry, and cellular automata.

Fractal geometry is an especially-pleasing niche area, all the better to understand the special geometry of many living organisms. In which the Harmony Of The Spheres is taken from the macro level to the micro level.

[Mick Harper]

Oh, so many living organisms have a knowledge of geometry, do they, Borry? You are confusing the fact that the universe is indeed made up of shapes that are geometric with the study of geometry.

[Boreades]

Alas, all the finest buildings of antiquity were done without a knowledge of geometry.

Blimey, were you there? As one of the original bodging builders? Otherwise, citation required.

If you would care to name an English builder/architect/civil engineer of the eighteenth and nineteenth centuries who had studied geometry, I'd be obliged.

I'm happy to oblige.

Example #1 is John Wood, the Elder. He studied the Seven Liberal Arts in some depth. Which (as I'm sure you already know) includes Geometry.

Wood created one of the greatest attractions in the world, recognised by UNESCO for embodying a number of outstanding universal values — including the deliberate creation of a beautiful and unified city.

Based on geometric forms.

[Mick Harper]

Blimey, were you there? As one of the original bodging builders? Otherwise, citation required.

So you feel I have to provide a citation for something that didn't happen (or so I claim) whereas you and Tissie don't have to provdie a citation for something that did happen (or so you claim)? Tricky.

I'm happy to oblige.

I do not doubt for one moment that many of the grander architects followed their Vitruvian style books. Not that for one moment I accept Vitruvius as being of the Augustan Age. Seventeenth century if I'm any judge.

Example #1 is John Wood, the Elder. He studied the Seven Liberal Arts in some depth. Which (as I'm sure you already know) includes Geometry.

Let us hope not your only example since you have seized on the one genuinely eccentric genius who was obsessed with geometry. And mocked for his enthusiasms.

[Boreades]

Let us hope not your only example since you have seized on the one genuinely eccentric genius who was obsessed with geometry. And mocked for his enthusiasms.

Actually, I don't need to provide any more examples, as your implied premise has already been falsified.

<< If you would care to name an English builder/architect/civil engineer of the eighteenth and nineteenth centuries who had studied geometry, I'd be obliged. >>

There's a name (of the genre and era you stipulate) who has studied geometry.

[Mick Harper]

You won! You won!

[TisILeclerc]

I don't know what all the fuss is about.

Either geometry is an esoteric subject of no earthly use or it is something that can be used and so is put to good use in a variety of ways.

The Ordnance survey would have got nowhere without triangles and the knowledge of how to use them not only in triangulation which basically studies the horizontal or in 'levelling' in which heights are calculated about sea level using millions of tiny triangles as the surveyor and his assistants move up or down the landscape.

The Romans did that sort of thing as well.

But wiki takes it a lot further back

The earliest recorded beginnings of geometry can be traced to early peoples, who discovered obtuse triangles in the ancient Indus Valley (see Harappan Mathematics), and ancient Babylonia (see Babylonian mathematics) from around 3000 BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. Among these were some surprisingly sophisticated principles, and a modern mathematician might be hard put to derive some of them without the use of calculus. For example, both the Egyptians and the Babylonians were aware of versions of the Pythagorean theorem about 1500 years before Pythagoras and the Indian Sulba Sutras around 800 B.C. contained the first statements of the theorem; the Egyptians had a correct formula for the volume of a frustum of a square pyramid;

https://en.wikipedia.org/wiki/History_of_geometry

Geometry is a practical discipline invented for practical purposes as its name suggests, for measuring the earth