Tuesday, September 18, 2018

Archimedes' Stomachion

A copy of The Archimedes Codex was recently loaned to me by a friend who found it interesting.
I agreed. I enjoyed the discovery, the history, the math and the science.

I especially appreciated the chapter on the Stomachion, a puzzle I had not seen before. My grandson and I had fun with all the solutions.

I already knew the square and the Lines of the Stomachion.  It is a geometric diagram used for layout and framing, part of Practical Geometry which was commonly used for construction least as far back as the 6th century BCE when it is mentioned in the Bible.

Archimedes in Syracuse, a geometer and engineer, would have known Practical Geometry as it was applied to the construction around him in the 2nd and 3rd Centuries BCE.

Here is a basic Practical Geometric  diagram, the Rule of Thirds,  drawn in 6 steps.

The points where two lines crossed were used to determine both design and structure: the size of a building and its frame, its ornamentation.

This drawing is messy... I will replace it.

I have drawn the Stomachion as a square. It could also be a rectangle or a trapezoid - but for those shapes there would be many less solutions.

In the second square I have extended the Lines in red. The dashed lines show how the small lines on the lower left corner and the middle right side were laid out.
The Stomachion uses both the division of the square into thirds and the division of the square into quarters.
The shapes are clearly based on the Rule of Thirds.

This drawing by Sebastiano Serlio, is from his book Architectura, published in France in 1537. He is discussing how to place a door in an existing facade. These Lines match the ones in the Stomachion.

Perhaps someone else has seen how the Stomachion relates to Lines, the Rule of Thirds, and Practical Geometry.  I would like to meet that person.

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The Archimedes Codex, How a Medieval Prayer Book is Revealing the True Genius of Antiquity's Greatest Scientist, Reviel Netz & William Noel, De Capo Press, Great Britian, 2007. 

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