Steßmann’s Surface (Wrapped Packages II)

In the paper Periodische Minimalflächen, published by the Mathematische Zeitschrift in 1934, Berthold Steßmann discusses the minimal surfaces that solve the Plateau problem for those spatial quadrilaterals for which rotations about the edges generate a discrete group. 

 

Contour

Arthur Moritz Schoenflies had classified these quadrilaterals, there are precisely six of them, up to similarity. For the three most symmetric cases, Hermann Amandus Schwarz had found the solutions to the Plateau problem in terms of elliptic integrals, and Steßmann treats the remaining cases. One of them is shown above. It is easier to describe the contour for three copies: Take a cubical box. Then the contour above consists of two (non-parallel) diagonals of top and bottom face, to vertical edges of the box, and two horizontal edges that lie diametrically across.

Piece

 

Extending the surface further produces the appealing triply periodic surface above. Below is a top view. This would make a nice design for a jungle gym. Unfortunately, this surface will not stay embedded; you see this at the corners where three pairwise orthogonal edges meet. 

 

Top

However, the conjugate surface is embedded, and concludes the story from a few weeks back. The surface introduced there is the I-WP surface of Alan Schoen, and he mentions in the appendix of his NASA report on triply periodic minimal surfaces, that the conjugate of his I-WP surface had been discussed by Steßmann. Below is a more traditional view of the I-WP surface.

I WP cube

Its name (explains Schoen), stands for Wrapped Package, because a translational fundamental piece of its skeletal graph looks like four sticks wrapped together into a package:

Wrappedpackage

 

The internet knows little about Berthold Steßmann. There is a short biographical note by the German Mathematical Society, telling that he was born on August 4, 1906 in Hüllenberg, Germany, studied in Göttingen and Frankfurt to become a high school teacher, which he completed in 1933. Then, a year later, he received his PhD about periodic minimal surfaces, with Carl Ludwig Siegel as advisor. The same year, the Mathematische Zeitschrift published a paper of Steßmann, covering the same topic. The note also mentions that Steßmann was Jewish. This leaves little hope.

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Puttabong Organic Moondrops First Flush 2017 vs 2018

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This year I had a little of last year’s first flush Organic Moondrops tea harvest from the Puttabong garden in Darjeeling left, so when the new harvest arrived I decided to compare the two.

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Both harvests show exceptional leaves (samples of 2017 above, 2018 below). Reportedly, this tea is harvested in the early morning hours when there are still dew drops on the leaves.

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The overall appearance is that the 2017 harvest is more yellow, while the 2018 more green. 

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This becomes most evident in the pictures of the steeping leaves, and is clearly an effect of the leaves maturing over time.

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In the cup, there is no visual difference. The taste, however, is miles apart. Not only is the 2018 fresher with notes of green grass, it also has the slightly liquorish aroma of an execeptional first flush Darjeeling.

I think the 2017 harvest was generally rather problematic, so that the difference in taste is less a sign of aging but rather of a difference in quality of the harvest.

 

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I was curious to learn what the effect of sweeteners on the taste would be, so I also tried both teas with a little Stevia added. While I found that this can occasionally enhance the flavor of teas (for example strong Assam teas), here it completely leveled out the differences between the two harvests. More precisely, the sweetened 2018 tasted almost exactly as the 2017 harvest. So, do not add Stevia to prime teas, you might loose the nuances.