---
OA_place: publisher
OA_type: hybrid
_id: '18157'
abstract:
- lang: eng
text: "Interest in sliding block puzzles dates back to the 15-puzzle, seemingly
invented by Noyes Chapman in 1874 (see [23] for an account of the fascinating
history of the puzzle). The game consists of fifteen movable square blocks numbered
\r\n and arranged within a \r\n square box, leaving one empty space (see Figure
1). The task at hand is to start from a given configuration of the numbered blocks
and reach the desired target configuration, where the only allowed move is to
slide a numbered block into an adjacent empty space. This task seemed to be unpredictably
either very easy to accomplish, or completely impossible, and the puzzle turned
into a worldwide sensation in the spring of 1880. A particularly challenging instance,
known as the 13-15-14 puzzle, consisted of initial and target configurations that
differed by a single swap (historically this swap involved the blocks labeled
14 and 15). The craze of this puzzle was such that it consistently made newspaper
headlines in 1880, with an article in the New York Times lamenting that it was
“threatening our free institutions” [23, p. 9]. Various prizes were offered for
anyone who could solve this challenge, beginning with a $25 set of teeth and culminating
with Sam Loyd’s famous $1,000 cash prize."
acknowledgement: Open access funding provided by Copenhagen University.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Florestan R
full_name: Brunck, Florestan R
id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d
last_name: Brunck
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
citation:
ama: 'Brunck FR, Kwan MA. Books, Hallways, and social butterflies: A note on sliding
block puzzles. Mathematical Intelligencer. 2025;47:52-65. doi:10.1007/s00283-024-10358-x'
apa: 'Brunck, F. R., & Kwan, M. A. (2025). Books, Hallways, and social butterflies:
A note on sliding block puzzles. Mathematical Intelligencer. Springer Nature.
https://doi.org/10.1007/s00283-024-10358-x'
chicago: 'Brunck, Florestan R, and Matthew Alan Kwan. “Books, Hallways, and Social
Butterflies: A Note on Sliding Block Puzzles.” Mathematical Intelligencer.
Springer Nature, 2025. https://doi.org/10.1007/s00283-024-10358-x.'
ieee: 'F. R. Brunck and M. A. Kwan, “Books, Hallways, and social butterflies: A
note on sliding block puzzles,” Mathematical Intelligencer, vol. 47. Springer
Nature, pp. 52–65, 2025.'
ista: 'Brunck FR, Kwan MA. 2025. Books, Hallways, and social butterflies: A note
on sliding block puzzles. Mathematical Intelligencer. 47, 52–65.'
mla: 'Brunck, Florestan R., and Matthew Alan Kwan. “Books, Hallways, and Social
Butterflies: A Note on Sliding Block Puzzles.” Mathematical Intelligencer,
vol. 47, Springer Nature, 2025, pp. 52–65, doi:10.1007/s00283-024-10358-x.'
short: F.R. Brunck, M.A. Kwan, Mathematical Intelligencer 47 (2025) 52–65.
date_created: 2024-09-29T22:01:38Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2025-05-19T14:00:09Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: MaKw
doi: 10.1007/s00283-024-10358-x
external_id:
arxiv:
- '2303.09459'
isi:
- '001318056000001'
file:
- access_level: open_access
checksum: c932ebe45c460d4a73f5b2dcca643db1
content_type: application/pdf
creator: dernst
date_created: 2025-04-08T11:17:45Z
date_updated: 2025-04-08T11:17:45Z
file_id: '19530'
file_name: 2025_MathIntelligencer_Brunck.pdf
file_size: 1760643
relation: main_file
success: 1
file_date_updated: 2025-04-08T11:17:45Z
has_accepted_license: '1'
intvolume: ' 47'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 52-65
publication: Mathematical Intelligencer
publication_identifier:
issn:
- 0343-6993
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Books, Hallways, and social butterflies: A note on sliding block puzzles'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2025'
...
---
_id: '13270'
abstract:
- lang: eng
text: "Consider a geodesic triangle on a surface of constant curvature and subdivide
it recursively into four triangles by joining the midpoints of its edges. We show
the existence of a uniform δ>0\r\n such that, at any step of the subdivision,
all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit
stabilising behaviours for both angles and lengths as this subdivision progresses."
acknowledgement: Open access funding provided by the Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Florestan R
full_name: Brunck, Florestan R
id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d
last_name: Brunck
citation:
ama: Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature.
Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5
apa: Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant
curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5
chicago: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces
of Constant Curvature.” Discrete and Computational Geometry. Springer Nature,
2023. https://doi.org/10.1007/s00454-023-00500-5.
ieee: F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant
curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer
Nature, pp. 1059–1089, 2023.
ista: Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant
curvature. Discrete and Computational Geometry. 70(3), 1059–1089.
mla: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant
Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer
Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5.
short: F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.
corr_author: '1'
date_created: 2023-07-23T22:01:14Z
date_published: 2023-07-05T00:00:00Z
date_updated: 2024-10-09T21:06:01Z
day: '05'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s00454-023-00500-5
external_id:
arxiv:
- '2107.04112'
isi:
- '001023742800003'
file:
- access_level: open_access
checksum: 865e68daafdd4edcfc280172ec50f5ea
content_type: application/pdf
creator: dernst
date_created: 2024-01-29T11:15:22Z
date_updated: 2024-01-29T11:15:22Z
file_id: '14897'
file_name: 2023_DiscreteComputGeometry_Brunck.pdf
file_size: 1466020
relation: main_file
success: 1
file_date_updated: 2024-01-29T11:15:22Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
issue: '3'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 1059-1089
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Iterated medial triangle subdivision in surfaces of constant curvature
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2023'
...