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Photographer's Note

These are famous stairs from Vatican Museums. They are one of the most photographed stairs in the world and no wonder why - Vatican Museums are visited every year by more than four million visitors and most of them are equipped with camera or at least a mobile phone with camera. Also on TE there are a lot of shots, wonderful and very successful one made by Bulent and many other not so spectacular. My friendship with Bulent began after my critique about his photo of these stairs, he sent me then his book "Math and Mona Lisa" with a dedication. So you are not surprised that it was number one of the places I had to visit (and make photos) during a visit in Rome.
If you look at the photo you can notice that the last steps are marked yellow and there are two such places. Besides, all the people are descending and two levels are empty. The reason is that there are two intertwined helical structures - one meant for people going up and one for going down. But one path is closed - you enter Vatican Museums by another stairs.
In three dimensions the structure is helical, something like a spring or a screw. When we look at the photo, flat, we see a spiral. What spiral is it? For sure, it is not Archimedean spiral, as in it the distances between turns are equal and we see them diminishing. Bulent sees here spira mirabilis - the logarithmic spiral, the most wonderful curve. It has interesting properties, one is self-similarity - we can close the picture up and down and still we see the same (in ideal mathematical case). The beautiful example of self- similarity is broccoli Romanesco - take a part of it and it looks the same as the whole, again the part of that part - still looks the same. We can see the logarithmic spirals everywhere in Nature- the approach of a hawk to its prey, the approach of an insect to a light source, the arms of spiral galaxies, the bands of tropical cyclones, many biological structures including the shells of mollusks.
But there is also another spiral - hyperbolical one. My son thinks that in fact the projection of a helix is a hyperbolical spiral. He showed me it mathematically but I am not quite convinced.
I made many shots. The stairs are wide so it is impossible to make photo of the whole stairs - maybe stitching master Didi could do it. So always there is only a part of it. My composition is very similar to that by Bulent. From all my photos this one seemed to me the best.
This spiral or that, I hope you like it.

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Additional Photos by Malgorzata Kopczynska (emka) Gold Star Critiquer/Gold Star Workshop Editor/Gold Note Writer [C: 4970 W: 81 N: 12503] (73437)
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