Sunday, May 10, 2026
Entities:
A Schoolgirl Problem for Zorro Ranch
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A Schoolgirl Problem for Zorro Ranch
A Schoolgirl Problem for Zorro Ranch
Friday, November 17, 2023
Schoolgirl Problem: Not Queen of the Desert
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Friday, April 16, 2021
Schoolgirl Problem (Kirkman’s, not Epstein’s)
As for Epstein’s problem . . .
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Thursday, November 19, 2020
Set Design and the Schoolgirl Problem
Underlying Structure of the Design —
Schoolgirl Problem —
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Sunday, July 7, 2019
Schoolgirl Problem
Anonymous remarks on the schoolgirl problem at Wikipedia —
"This solution has a geometric interpretation in connection with
Galois geometry and PG(3,2). Take a tetrahedron and label its
vertices as 0001, 0010, 0100 and 1000. Label its six edge centers
as the XOR of the vertices of that edge. Label the four face centers
as the XOR of the three vertices of that face, and the body center
gets the label 1111. Then the 35 triads of the XOR solution correspond
exactly to the 35 lines of PG(3,2). Each day corresponds to a spread
and each week to a packing."
See also Polster + Tetrahedron in this journal.
There is a different "geometric interpretation in connection with
Galois geometry and PG(3,2)" that uses a square model rather
than a tetrahedral model. The square model of PG(3,2) last
appeared in the schoolgirl-problem article on Feb. 11, 2017, just
before a revision that removed it.
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Saturday, August 25, 2018
Schoolgirl Problem
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Sunday, July 15, 2018
Schoolgirl Problems
A Warren, Pennsylvania, newspaper article from May 12, 2018,
“A terrorist among them,” quotes Ann Creal of Warren on
schooldays of the late 1950’s and on a German exchange student,
Gudrun Ensslin, who later became famous for her violent political
activities:
“She said Ensslin dated while here (the man
she identified as Ensslin’s date told the Times Observer
he had no recollection of her).”
I am the man that was identified as Ensslin’s date, and I still
have no recollection of her.
Ann Creal is the former Ann Fuellhart, who was a college freshman
in the fall of 1959, when I was a high school senior —
Ann Creal apparently confused me with Scott Mohr, who
graduated from Warren High School in 1958. See the Log24
posts Crux and Doppelgänger.
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Tuesday, November 29, 2016
Thursday, August 4, 2016
Schoolgirl Problems
Compare and contrast the recent films
"The Diary of a Teenage Girl" and "Strangerland."
(This post was suggested by yesterday's
"How Deep the Rabbit Hole Goes.")
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Monday, February 22, 2016
Schoolgirl Problems…
and versions of "Both Sides Now"
See a New York Times version of "Both Sides Now."
I prefer a version by Umberto Eco.
Related material for storytellers and the Church of Synchronology —
This journal on the date of the above shooting script, 03/19/15.
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Tuesday, September 15, 2015
Schoolgirl Problem
Or: Ten Years and a Day
In memory of film director Robert Wise,
who died ten years ago yesterday.
A search in this journal for "Schoolgirl" ends with a post
from Sept. 10, 2002, The Sound of Hanging Rock.
See as well a Log24 search for "Strangerland"
(a 2015 film about a search for a schoolgirl) and
a Log24 search for "Weaving."
Related mathematics: Symplectic.
Some related images (click to enlarge) —
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Friday, August 14, 2015
Schoolgirl Problem
But first, a word from our sponsa* …
Sir Laurence Olivier in "Term of Trial" (1962),
a film starring Sarah Miles as a schoolgirl —
* Bride in Latin. See also "bride's chair,"
a phrase from mathematical pedagogy.
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Friday, June 19, 2015
Schoolgirl Problem
The star of the new film "Chappie" is on tour.
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Friday, September 27, 2019
Algebra for Schoolgirls
The 15 points of the finite projective 3-space PG(3,2)
arranged in tetrahedral form:
The letter labels, but not the tetrahedral form,
are from The Axioms of Projective Geometry , by
Alfred North Whitehead (Cambridge U. Press, 1906).
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
Screen Rant on July 31, 2019:
A Google Search sidebar this morning:
Apocalypse Soon! —
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Thursday, August 15, 2019
Schoolgirl Space — Tetrahedron or Square?
The exercise in the previous post was suggested by a passage
purporting to "use standard block design theory" that was written
by some anonymous author at Wikipedia on March 1, 2019:
Here "rm OR" apparently means "remove original research."
Before the March 1 revision . . .
The "original research" objected to and removed was the paragraph
beginning "To explain this further." That paragraph was put into the
article earlier on Feb. 28 by yet another anonymous author (not by me).
An account of my own (1976 and later) original research on this subject
is pictured below, in a note from Feb. 20, 1986 —
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Saturday, August 10, 2019
Schoolgirl Space* Revisited:
The Square "Inscape" Model of
the Generalized Quadrangle W(2)
Click image to enlarge.
-embedding-in-PG(3,2)-Planat-Saniga-1000w.jpg)
* The title refers to the role of PG (3,2) in Kirkman's schoolgirl problem.
For some backstory, see my post Anticommuting Dirac Matrices as Skew Lines
and, more generally, posts tagged Dirac and Geometry.
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Tuesday, July 16, 2019
Sunday, February 17, 2019
For the Schoolgirls of 1959
The dies natalis of St. Buddy Holly was Feb. 3, 1959.
This year on Feb. 3, a geometric illustration of the well-known
schoolgirl problem was added to a brand-new Wikipedia article
on the finite geometry PG(3,2).
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Thursday, February 16, 2017
Schoolgirls and Heptads
A Feb. 12 note in the "talk" section of the Wikipedia article
"Kirkman's schoolgirl problem" —
The illustration above was replaced by a new section in the article,
titled "Galois geometry."
The new section improves the article by giving it greater depth.
For related material, see Conwell Heptads in this journal
(or, more generally, Conwell) and a 1985 note citing Conwell's work.
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Wednesday, December 3, 2025
Today’s Diamond Theory Summary from NotebookLM
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Diamond Theory by NotebookLM 92 sources The sources detail the profound mathematical correspondences linking visual, combinatorial, and abstract algebraic structures, primarily focusing on the finite projective space PG(3,2) and the affine group AGL(4,2). A central component is the Cullinane diamond theorem, which uses highly symmetric 4×4 grid patterns to model the AGL(4,2) transformation group, whose large order of 322,560 governs the symmetry of the arrangements. These geometric models are tied directly to deep combinatorial structures, specifically the Miracle Octad Generator (MOG) and the sporadic simple group Mathieu group M24, offering a unified framework for understanding octads and partitions like Conwell's Heptads. Further discussion establishes how geometric entities such as spreads, packings, and the Klein correspondence provide solutions for classic problems like the "schoolgirl problem" and inform contemporary areas like error-correcting codes and the classification of group orbits. This interplay extends even to physics, connecting the geometries to quantum space-time and two-qubit observables, demonstrating how abstract finite geometry underlies sophisticated concepts across various scientific and artistic disciplines. |
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Sunday, April 13, 2025
What’s in a Name? . . . Falcone vs. Gigante
The Falcone Schoolgirl Problem . . .
|
"Searching for a definitive indication that The Penguin is charting its own course in the long history of Batman stories? Well, look no further than episode 5, when Sofia Falcone (Cristin Milioti) takes over her crime family under a new name: Sofia Gigante. Spurned by her father’s betrayal, she assumes her late mother’s name and plans to create a new legacy." |
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Wednesday, February 26, 2025
Red Dot Award
"Cristin Milioti, dressed in custom Dior, chatted with 'Extra’s'
Mona Kosar Abdi on the 2025 SAG Awards red carpet."
From this journal earlier . . .
The Falcone Schoolgirl Problem . . .
"You're very beautiful, dear, but you're no Milioti."
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Monday, November 18, 2024
Wednesday, September 18, 2019
Powers of X
Screen Rant on July 31, 2019 —
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
See as well a Log24 post from the above Screen Rant date —
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Tuesday, April 30, 2019
Heraldry for Walpurgisnacht
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Tuesday, January 2, 2018
Debs and Redhead
The above images were suggested in part by the birthdays
on Sept. 21, 2011, of Bill Murray and Stephen King.
More seriously, also in this journal on that date, from a post
titled Symmetric Generation —
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Sunday, November 12, 2017
Review
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Sunday, October 29, 2017
File System… Unlocked
|
See as well Chloë Grace Moretz portraying a schoolgirl problem.
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Thursday, November 2, 2017
History of Mathematics for All Souls’ Day
Schoolgirl Problem
"Buy this image" . . . Or not.
Related material from the date of the above photo —
For related drama, see "Child's Play" in this journal.
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Thursday, October 12, 2017
Gifted Continues
Related material — See Gifted in this journal.
See as well Tulips.
Yesterday was the International Day of the Girl Child . . .
A related archived Wikipedia article on Kirkman's schoolgirl problem :
See also the previous post— "IPFS Version"— and https://ipfs.io/.
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Wednesday, July 5, 2017
Imaginarium of a Different Kind
The title refers to that of the previous post, "The Imaginarium."
In memory of a translator who reportedly died on May 22, 2017,
a passage quoted here on that date —
Related material — A paragraph added on March 15, 2017,
to the Wikipedia article on Galois geometry —
|
George Conwell gave an early demonstration of Galois geometry in 1910 when he characterized a solution of Kirkman's schoolgirl problem as a partition of sets of skew lines in PG(3,2), the three-dimensional projective geometry over the Galois field GF(2).[3] Similar to methods of line geometry in space over a field of characteristic 0, Conwell used Plücker coordinates in PG(5,2) and identified the points representing lines in PG(3,2) as those on the Klein quadric. — User Rgdboer |
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