Geometria Sp2

[Jamie Swearengin]

Mstarde fui desarrollando este sistema y, hoy da, me parece un tipo de geometria sencilla que bien pudo utilizarse por parte de los lauderos barrocos italianos. Con todo el respeto, por supuesto, hacia los enormes e interesantsimos trabajos y tesis al respecto.

I apologize to all of you in advance for using Cervantes' language to express myself in this forum. From now on I will do it in the English language that the Google translator seeks, so I also apologize for the expressive mistakes made by the robot.

Some of you refer me to Muratov and his art in violin design. And I refer you to Alberto Durero and his measurement instructions with a ruler and compass and his golden spiral.

The design system that I propose is simple. A template based on the golden spiral of Drer. Do you really imagine Amati or Stradivari drawing curves with the Muratov system and its clotoids?

The system that I propose to you could well be used by Italian luthiers, so that there are no construction plans for those instruments. The template allows to measure, provide the instrument and trace all the curves of the mold, as well as other important measures, such as the bridge line and the top of the ff, etc.

Think Alberto Durero had an intense relationship with Italy. He published his Underweysung der Messung in 1525, and years later many artists and craftsmen began to apply their methods and instructions ...... also the Italian luthiers.

Seems to be a mix of Muratov, Brooks&Degrotte (The violin and the golden number) and Hambidge (The elements of dynamic symmetry), with perhaps some original ideas. It would be nice to have an explanation of how it all hangs together.

In the end, it's all personal taste about what looks good and what doesn't, so I don't think explanations would help much. And getting there looks like it's all the maker's personal taste for geometry, numerology, and mathematical curlicues that end up giving what the maker thinks looks good. Having some historical cues about what the old guys did might give some extra warmfuzzies to makers who want to "do what Strad did", but there are plenty of different ways to get the same end result.

Congruentia in geometria est aequalitas formae et magnitudinis inter duas figuras vel obiecta. Duae copiae punctorum congruentes dicuntur si et solum si una in aliam verti potest per isometriam, haec est coniunctio motuum rigidorum: translationis, rotationis, ac reflexionis. Aliis verbis, utra figura moveri et reflecti potest, sed non deminui nec augi, ut cum altera exacte coincidat. Duae formae in chartae delineatae et exsecatae sunt congruentes si eas omnino componere possumus, chartas si necesse sit vertentes.

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