4 ms·

The Mathematical Structure of Escher’s Print Gallery (2003) [pdf]

33 points by Schiphol 5y ago

stikit 5y ago
Original https://upload.wikimedia.org/wikipedia/en/0/02/Print_Gallery_by_M._C._Escher.jpg https://upload.wikimedia.org/wikipedia/en/0/02/Print_Gallery... Completed https://www.universiteitleiden.nl/binaries/content/gallery/ul2/main-images/science/escher-filled-in.jpg/escher-filled-in.jpg/d390xvar https://www.universiteitleiden.nl/binaries/content/gallery/u... Video https://youtube.com/watch?v=JtqmDZrpfCA&feature=share https://youtube.com/watch?v=JtqmDZrpfCA&feature=share
floydnoel 5y ago
I would’ve enjoyed a picture of the unfinished work along with the finished one. I was also left puzzled as to why the picture on the tin would be the same at exactly 7x the size, but (apparently) not at some other factor.
djmips 5y ago
Even though this is labeled 2020 this is work done in 2002 or earlier if I'm not mistaken. And I've seen many articles, videos, and interactive versions over the years. Very cool! https://web.archive.org/web/20130422193857/http://escherdroste.math.leidenuniv.nl/index.php?menu=intro https://web.archive.org/web/20130422193857/http://escherdros...
throwaway81523 5y ago
Wow neat, I hadn't seen this before. Besides watching the animations, the most interesting thing was the AMS article by Lenstra and de Smit: https://www.ams.org/notices/200304/fea-escher.pdf https://www.ams.org/notices/200304/fea-escher.pdf It explains all the math, shows Escher's work drawings, etc. Escher himself didn't seem to be completely cognizant of the math, so he worked by intuition and eyeballed things, but he came to a very close approximation of what the mathematicians worked out decades later.
- jacquesm 5y ago
  Thank you, that PDF is much better than the article. Dang, link change?
- dang 5y ago
  Ok, we've changed to that from https://www.universiteitleiden.nl/en/news/2020/04/how-mathematician-hendrik-lenstra-completed-an-unfinished-artwork-by-escher https://www.universiteitleiden.nl/en/news/2020/04/how-mathem.... Thanks!
jacquesm 5y ago
The resolution is much too low to see exactly what got added (the area that is blank in the original is quite small). Fun fact: I live within 500 meters of where Escher was born :), nice to see him pop up here on HN. Highly recommended to go see his other works if you haven't yet.
brekels 5y ago
well-explained Quora post! https://www.quora.com/What-should-be-in-the-center-of-Eschers-painting-Print-Gallery-Is-there-a-single-way-to-finish-it-Can-we-find-the-original-image-before-distortion https://www.quora.com/What-should-be-in-the-center-of-Escher...

33 points by Schiphol 5y ago

Original https://upload.wikimedia.org/wikipedia/en/0/02/Print_Gallery_by_M._C._Escher.jpg https://upload.wikimedia.org/wikipedia/en/0/02/Print_Gallery... Completed https://www.universiteitleiden.nl/binaries/content/gallery/ul2/main-images/science/escher-filled-in.jpg/escher-filled-in.jpg/d390xvar https://www.universiteitleiden.nl/binaries/content/gallery/u... Video https://youtube.com/watch?v=JtqmDZrpfCA&feature=share https://youtube.com/watch?v=JtqmDZrpfCA&feature=share

floydnoel 5y ago

I would’ve enjoyed a picture of the unfinished work along with the finished one. I was also left puzzled as to why the picture on the tin would be the same at exactly 7x the size, but (apparently) not at some other factor.

djmips 5y ago

Even though this is labeled 2020 this is work done in 2002 or earlier if I'm not mistaken. And I've seen many articles, videos, and interactive versions over the years. Very cool! https://web.archive.org/web/20130422193857/http://escherdroste.math.leidenuniv.nl/index.php?menu=intro https://web.archive.org/web/20130422193857/http://escherdros...

throwaway81523 5y ago

Wow neat, I hadn't seen this before. Besides watching the animations, the most interesting thing was the AMS article by Lenstra and de Smit: https://www.ams.org/notices/200304/fea-escher.pdf https://www.ams.org/notices/200304/fea-escher.pdf It explains all the math, shows Escher's work drawings, etc. Escher himself didn't seem to be completely cognizant of the math, so he worked by intuition and eyeballed things, but he came to a very close approximation of what the mathematicians worked out decades later.

jacquesm 5y ago
Thank you, that PDF is much better than the article. Dang, link change?
dang 5y ago
Ok, we've changed to that from https://www.universiteitleiden.nl/en/news/2020/04/how-mathematician-hendrik-lenstra-completed-an-unfinished-artwork-by-escher https://www.universiteitleiden.nl/en/news/2020/04/how-mathem.... Thanks!

jacquesm 5y ago

The resolution is much too low to see exactly what got added (the area that is blank in the original is quite small). Fun fact: I live within 500 meters of where Escher was born :), nice to see him pop up here on HN. Highly recommended to go see his other works if you haven't yet.

brekels 5y ago

well-explained Quora post! https://www.quora.com/What-should-be-in-the-center-of-Eschers-painting-Print-Gallery-Is-there-a-single-way-to-finish-it-Can-we-find-the-original-image-before-distortion https://www.quora.com/What-should-be-in-the-center-of-Escher...