Most-perfect magic square

template:4x4 type square — special:Prefixindex/template:4x4 type square

Please see en:user talk:לערי ריינהארט#Text reading and translation request First responce. Thanks a lot Mahitgar! · ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 15:17, 9 August 2015 (UTC)
Thanks w:en:user:Cmglee · user:Cmglee! · 11 August 2015 (UTC)
see #Guru: chiffres Gurmukhi plus proches de l'original + translittération + numération indienne Thanks fr:user:Anne Bauval · user:Anne Bauval! · ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 14:47, 12 August 2015 (UTC)

theory and applications

rakonto 11 in Esperanto	rakonto 12 in Esperanto	rakonto 13 in Esperanto
rakonto ydd in Esperanto	rakonto 01.png\|binary square	rakonto ydd in Yiddish
c:project:Story (game) - multilingual interdisciplinary collaborative work · #Media (examples)

→ c:project:rakonto
→ w:en:…sandbox (text)
→ w:en:…sandbox (table)
$2^{n}\cdot ({\frac {n}{2}}!)^{2}\cdot \beth (e_{1},...,e_{M})\,$ different squares

tesseract (8-cell)	24-cell
SVG: file:Hypercubecentral.svg SVG: file:Hypercube.svg SVG: file:Hypercube cubes.svg SVG: file:4dcube.svg	SVG: file:24 Cell Polytope.svg SVG: file:24 Cell Polytopeb.svg SVG: file:24-cell duals.svg SVG: file:Versor action on Hurwitz quaternions.svg
tesseract	24-cell


Clarke's third law: Any sufficiently advanced technology is indistinguishable from magic.

→ 24
→ 384
$384=2^{7}\cdot 3\,$
As a result one can interpret the noncommutative group of the 384 mutually indistinguishable most-perfect magic square of order 4 as construct which is homomorphic with a cross product of a tesseract with a 24-cell in the 8 dimensional space.

restored from meta: (work prior to 2007)

different representations of the reference square revID: - ^diff · PAGEID: 82332 ^{links here · #focus · W3C CSS Validator} ⧼code-rev-purge-link⧽ ↺

transition T001

00	01	02	03
10	11	12	13
20	21	22	23
30	31	32	33

→ * * * * * * * * * * * (*)

:|00|01|02|03|10|11|12|13|20|21|22|23|30|31|32|33|:

values 1 to 16

09	16	05	04
07	02	11	14
12	13	08	01
06	03	10	15

→ * * * * * * * * * * * (*)

:|09|16|05|04|07|02|11|14|12|13|08|01|06|03|10|15|:

values 0 to 15

08	15	04	03
06	01	10	13
11	12	07	00
05	02	09	14

→ * * * * * * * * * * * (*)

:|08|15|04|03|06|01|10|13|11|12|07|00|05|02|09|14|:

values -15 to 15

1	15	-7	-9
-3	-13	5	11
7	9	-1	-15
-5	-11	3	13

→ * * * * * * * * * * * (*)

:|1|15|-7|-9|-3|-13|5|11|7|9|-1|-15|-5|-11|3|13|:

complement of last

-1	-15	7	9
3	13	-5	-11
-7	-9	1	15
5	11	-3	-13

→ * * * * * * * * * * * (*)

:|-1|-15|7|9|3|13|-5|-11|-7|-9|1|15|5|11|-3|-13|:

links
↑ about
→ reference ^WLH, 384, …
→ patterns
→ examples …
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WMF resources

Euler diagram of requirements of some types of 4×4 magic squares. Cells of the same colour sum to the magic constant.
* In 4×4 most-perfect magic squares, any 2 cells that are 2 cells diagonally apart (including wraparound) sum to half the magic constant, hence any 2 such pairs also sum to the magic constant.

15	10	3	6
4	5	16	9
14	11	2	7
1	8	13	12

15	10	6	3
4	5	9	16
1	8	12	13
14	11	7	2

generic abstract pattern

1. SVG file

file:PanmagicSquare-Order4.png

reversible variant

3	10	15	6
13	8	1	12
2	11	14	7
16	5	4	9

3	10	6	15
13	8	12	1
16	5	9	4
2	11	7	14

PNG file

2. SVG file
(draft)

reversible variant

0	14	9	7
11	5	2	12
6	8	15	1
13	3	4	10

0	14	7	9
11	5	12	2
13	3	10	4
6	8	1	15

3. SVG file

reversible variant

SVG file source code 01

→→ #collapsed SVG file source code 01

modified SVG code

→→ #collapsed modified SVG code

first step

→→ #collapsed first step

participants

^#top → /invited

לערי ריינהארט lɛʁi ʁɑjnhɑʁt (Leri Reinhart) ^{You may reach me via the freenode channel kavehoyz where my username are gangleri|back, gangleri|away or similar gangleri|foobar or at Skype where my username is irelgnag}
user:Alkanot4ran freenode: fluktusduktus@irc.freenode.net
(your signature)

stepwise improvements

→→ #collapsed stepwise improvements

SVG interactive animation

→ m:template talk:Translatable template#BiDi issues

→→ #collapsed SVG interactive animatio

BiDi issues

**meta:BiDi workgroup**
phabricator?**BiDi**

list of RTL and / or BiDi WMF subdomains:

→ m:BiDi workgroup · m:interwiki map · m:special:SiteMatrix

Arab: ar:, arz:, azb:, ckb:, dv:, fa:, glk:, ha: ^BiDi, ks:, ku: ^BiDi, lrc:, mzn:, pnb:, ps:, sd: ^BiDi, tk: ^BiDi ?, ug:, ur:, etc.

Aram: arc:

Hebr: he:, lad: ^BiDi, yi:, etc.

added: 18:44, 15 August 2015 (UTC)

Latn

^{#top template talk:4x4 type square#Latn}

search Unicode beside ASVII; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

The bottom row shows the numeral glyphs as they appear in type in German incunabula (Nicolaus Kesler, Basle, 1486)

Magic square#Europe · Magic Square of Jupiter

This page from Athanasius Kircher's *Oedipus Aegyptiacus* (1653) belongs to a treatise on magic squares and shows the *Sigillum Iovis* associated with Jupiter

In 1300, building on the work of the Arab Al-Buni, Greek Byzantine scholar Manuel Moschopoulos wrote a mathematical treatise on the subject of magic squares, leaving out the mysticism of his predecessors.^[6] ...

numerals in daily life

add collection of "Banknotes of foobar" images

c:License plates

re: numerals 0..9 and their (Unicode) encoding
"Arabic numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9."
There should be a note about these glyphs. While Latn.a is a homoglyph of Cyrl.а the digits are coded the same way in Latn, Cyrl, Grec, secular Hebr and other ISO 15924 scripts. ar.Wikipedia is using Western Arabic numerals in years, paragraph counting, etc. while the number plates in some Arabic countries are using the digits from the Arab Unicode block.
A note about numeral encoding is missing in most articles about such scripts.

Roman numerals

^{#top template talk:4x4 type square#Latn/Roman}
use UTF-8 and fonts; search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

VII	XII	I	XIV
II	XIII	VIII	XI
XVI	III	X	V
IX	VI	XV	IV

^{#top template talk:4x4 type square#Latn/binary}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

binary

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

0111	1100	001	1110
0010	1101	1000	1011
10000	0011	1010	0101
1001	0110	1111	0100

binary transcription of
the indian numerals

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

quaternions

from w:en:Frénicle standard form:

Generalising the concept of essentially different squares

For each group of magic squares one might identify the corresponding group of automorphisms, the group of transformations preserving the special properties of this group of magic squares. This way one can identify the number of different magic square classes.

From the perspective of Galois theory the most-perfect magic squares are not distinguishable. This means that the number of elements in the associated Galois group is 1. Please compare {{OEIS2C|A051235}} Number of essentially different most-perfect pandiagonal magic squares of order 4n. with {{OEIS2C|A000012}} The simplest sequence of positive numbers: the all 1's sequence.

reversible variants

to do:
- Done Jupiter versus Saturn
- Done Lo Shu versus Yang-Hui
- Done the original of w:en:File:Magic square 4x4 Shams Al-maarif3 (Arabic magics).jpg contains an error`: the value 4 is shown twice

Melancholie I

16	3	2	13
5	10	11	8
9	6	7	12
4	15	14	1

16	3	13	2
5	10	8	11
4	15	1	14
9	6	12	7

detail

reversible variant

Melancholie I
by Albrecht Dürer, 1514

Yang-Hui square also referred to as the Magic Square of Jupiter

一六	五	九	四
二	一一	七	一四
三	十	六	一五
一三	八	一二	一

16	5	9	4
2	11	7	14
3	10	6	15
13	8	12	1

16	5	4	9
2	11	14	7
13	8	1	12
3	10	15	6

Yang-Hui square

transcription
reversible variant

w:en:File:Magic square 4x4 Shams Al-maarif3 (Arabic magics).jpg

Yang-Hui square also referred to as the Magic Square of Jupiter

arabic version of the Magic Square of Jupiter

٤	١٤	١٥	١
٩	٧	٦	١٢
٥	١١	١٠	٨
١٦	٢	٣	١٣

4	14	15	1
9	7	6	12
5	11	10	8
16	2	3	13

4	14	1	15
9	7	12	6
16	2	13	3
5	11	8	10

detail

digital square

transcription
reversible variant

^{#top template talk:4x4 type square#Deva}

arabic version of the Magic Square of Jupiter

comparision of some Magic Square of Jupiter versions

16	5	9	4
2	11	7	14
3	10	6	15
13	8	12	1

4	14	15	1
9	7	6	12
5	11	10	8
16	2	3	13

16	3	2	13
5	10	11	8
9	6	7	12
4	15	14	1

Yang-Hui square

arabic version
Shams Al-maarif3
(Arabic magics)

Melancholie I
by Albrecht Dürer, 1514

comparision of some Magic Square of Jupiter versions

Deva

w:hi:आदर्श जादुई वर्ग ^g

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

७	१२	१	१४
२	१३	८	११
१६	३	१०	५
९	६	१५	४

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

भारतीय अंकों

का ट्रांस्क्रिप्शन

आदर्श जादुई वर्ग

Guru

^{#top template talk:4x4 type square#Guru} search Unicode; add relevant data / links / images; add improved wikitable code

chiffres Gurmukhi plus proches de l'original + translittération + numération indienne Thanks fr:user:Anne Bauval · user:Anne Bauval!

https://pa.wikipedia.org/?curid=602#multiscript_collaboration

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

भारतीय अंकों

का ट्रांस्क्रिप्शन

आदर्श जादुई वर्ग

Sriramachakra

९	१६	५	४
७	२	११	१४
१२	१३	८	१
६	३	१०	१५

9	16	5	4
7	2	11	14
12	13	8	1
6	3	10	15

see Sriramachakra
transcription of
the indian numerals

While the values 7, 2, 11 and 14 belong to a (broken) 2x2 subsquare of the Khajuraho square they form the second line of the Sriramachakra most magic square. It is evident that such a transformation is not a transformation specified in the definition of the Frénicle standard form: neither neighbour relations nor orthogonal relations are preserved. The transformation illustrates the necessity of a generalised concept of essentially different squares. ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 08:46, 9 August 2015 (UTC)

Arab

^{#top template talk:4x4 type square#Arab}
add all relevant Unicode blocks for Arab, list of WMF subdomains using Arab, Farsi more ? #Aran ^{Arabic (Nastaliq variant)} #Xpeo ^{Old Persian cuneiform}
search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

ISO 15924: Guru

global setting test

٧	١٢	١	١٤
٢	١٣	٨	١١
١٦	٣	١٠	٥
٩	٦	١٥	٤

ISO 15924: Arab

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

ISO 15924: Latn
transcription of
the Indian numerals

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho, Rajasthan

Persia

Not done investigate
w:en: https:special:Prefixindex/file:Magic_square_4x4_Shams_Al-maarif

w:en:file:Magic square 4x4 Shams Al-maarif (Arabic magics).jpg not used
w:en:file:Magic square 4x4 Shams Al-maarif2 (Arabic magics).jpg|thumb|widthpx|Original script from the w:en:Shams al-Ma'arif.
w:en:file:Magic square 4x4 Shams Al-maarif3 (Arabic magics).jpg|thumb|widthpx|Printed version of the previous manuscript Eastern Arabic numerals were used.

Arabia

Not done investigate

Aran

^{#top template talk:4x4 type square#Aran}
add all relevant Unicode blocks for Aran, list of WMF subdomains using Aran, Farsi more ?
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→ Arabic (Nastaliq variant)

Xpeo

^{#top template talk:4x4 type square#Xpeo}
add all relevant Unicode blocks for Xpeo, list of WMF subdomains using Xpeo, Farsi more ?
search Unicode; add relevant data / links / images; add improved wikitable code

→ Old Persian cuneiform

Armi

^{#top template talk:4x4 type square#Armi}
→ Aramaic alphabet (d:26978) · Unicode range: U+ U+10840–U+1085F · Unicode numerals: N/A · Unicode alias: Imperial Aramaic

The Ancient Aramaic alphabet is adapted from the Phoenician alphabet ^#Phnx and became distinctive from it by the 8th century BCE. It was used to write the Aramaic language. The letters all represent consonants, some of which are matres lectionis, which also indicate long vowels

The Aramaic alphabet is historically significant, since virtually all modern Middle Eastern writing systems can be traced back to it, as well as numerous non-Chinese writing systems of Central and East Asia. This is primarily due to the widespread usage of the Aramaic language as both a lingua franca and the official language of the Neo-Assyrian Empire, and its successor, the Achaemenid Empire. Among the scripts in modern use, the Hebrew alphabet ^#Hebr bears the closest relation to the Imperial Aramaic script of the 5th century BC, with an identical letter inventory and, for the most part, nearly identical letter shapes.

Writing systems that indicate consonants but do not indicate most vowels (like the Aramaic one) or indicate them with added diacritical signs, have been called abjads by Peter T. Daniels to distinguish them from later alphabets, such as Greek, that represent vowels more systematically.

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Phnx

^{#top template talk:4x4 type square#Phnx} → Phoenician ^alphabet

'

Syrc

^{#top template talk:4x4 type square#Syrc}
→ Syriac ^alphabet

'

Syre

→ Syriac (Estrangelo variant)

see: #Syrc

Syrj

→ Syriac (Western variant)

see: #Syrc

Syrn

→ Syriac (Eastern variant)

see: #Syrc

Armn

^{#top template talk:4x4 type square#Armn}

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

Է	ԺԲ	Ա	ԺԴ
Բ	ԺԳ	Ը	ԺԱ
ԺԶ	Գ	Ժ	Ե
Թ	Զ	ԺԵ	Դ

^{#top template talk:4x4 type square#Beng}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Beng

add links to Bengali and Asameese; ~~search Unicode;~~ add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

৭	১২	১	১৪
২	১৩	৮	১১
১৬	৩	১০	৫
৯	৬	১৫	৪

^{#top template talk:4x4 type square#Cyrl}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Bengali-Assamese numerals

Cyrl

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Cyrs

^{#top template talk:4x4 type square#Cyrs}

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Grek

^{#top template talk:4x4 type square#Grek}

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

Ζʹ	ΙʹΒʹ	Αʹ	ΙʹΔʹ
Βʹ	ΙʹΓʹ	Ηʹ	ΙʹΑʹ
ΙʹϚʹ	Γʹ	Ιʹ	Εʹ
Θʹ	Ϛʹ	ΙʹΕʹ	Δʹ

^{#top template talk:4x4 type square#Gujr}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Gujr

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

૭	૧૨	૧	૧૪
૨	૧૩	૮	૧૧
૧૬	૩	૧૦	૫
૯	૬	૧૫	૪

^{#top template talk:4x4 type square#Hani}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

CJK · Hani · Hans · Hant · Jpan

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CJKV ideograph 次 in traditional and simplified Chinese character|simplified Chinese, Korean, Vietnamese and Japanese.

^[7] The Unidode numerals for the ISO 15924 script codes Hani, Hans, Hant and Jpan are using the same values
0: U+3007 :〇, 1: U+4E00 :一, 2: U+4E8C :二, 3: U+4E09 :三, 4: U+56DB :四,
5: U+4E94 :五, 6: U+516D :六, 7: U+4E03 :七, 6: U+516B :八, 9: U+4E5D :九
According to the Unicode standard version 3.0, these characters are called Hangzhou style numerals ^{Suzhou numerals#Symbols}. This indicates that it is not used only by Cantonese in Hong Kong. In the Unicode standard 4.0, an erratum was added which stated:

The digits of the Suzhou numerals are designated in the CJK Symbols and Punctuation block between U+3021 and U+3029, U+3007, U+5341, U+5344, and. U+5345.

→ CJK Unified Ideographs (d:Q796156) · Unicode range: see list above · Unicode numerals: see list above · Unicode alias: Hani

The Chinese, Japanese and Korean (CJK) scripts share a common background. In the process called Han unification the common (shared) characters were identified, and named "CJK Unified Ideographs". Unicode defines a total of 80,388 CJK Unified Ideographs.^[8]

The terms ideographs or ideograms may be misleading, since the Chinese script is not strictly a picture writing system.

Historically, Vietnam used Chinese ideographs too, so sometimes the abbreviation "CJKV" ^#CJKV is used. This system was replaced by the Latin-based Vietnamese alphabet in the 1920s.

→→ Hani: ZZZZ
→→ Hans: ZZZZ
→→ Hant: ZZZZ
→→ Jpan: Japanese numerals (d:Q1337084) · Japanese writing system (d:Q190502) · Japanese language (d:Q5287) · LANG xml:lang hreflanghreflang ^g ^{HTML attribute} ja, jpn · see: CJK, Kanji

add more details

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

七	十二	一	十四
二	十三	八	十一
十六	三	十	五
九	六	十五	四

^{#top template talk:4x4 type square#Hebr}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

~~Please note that the Unicode encoding for the potential homoglyphs might differ between the Hans · Hant · Jpan etc. scripts.~~ ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 06:23, 17 August 2015 (UTC)

Hebr

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

ז׳	י״ב	א׳	י״ד
ב׳	י״ג	ח׳	י״א
ט״ז	ג׳	י׳	ה׳
ט׳	ו׳	ט״ו	ד׳

^{#top template talk:4x4 type square#Knda}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Knda

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

೭	೧೨	೧	೧೪
೨	೧೩	೮	೧೧
೧೬	೩	೧೦	೫
೯	೬	೧೫	೪

^{#top template talk:4x4 type square#Kore}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Kore

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੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

일곱	열둘	하나	열넷
둘	열셋	여덟	열하나
열여섯	셋	열	다섯
아홉	여섯	열다섯	넷

^{#top template talk:4x4 type square#Lepc}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Lepc

search Unicode; add relevant data / links / images; add improved wikitable code

→ Lepcha alphabet (d:Q1481626) · Unicode range: U+1C00–U+1C4F · Unicode numerals: U+1C40–U+1C49 · Unicode alias: Lepcha

The Lepcha script, or Róng script is an abugida used by the Lepcha people to write the Lepcha language.

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

^{#top template talk:4x4 type square#Maya}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Maya

search Unicode; add relevant data / links / images; add improved wikitable code

→ Maya script (d:Q1481626) · Unicode range: N/A · Unicode numerals: N/A · Unicode alias: N/A
→ MLaTeX (d:Q5310) · mathabx Mayan Digits page 72 table 200

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

^{#top template talk:4x4 type square#Mlym}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

: \maya{0}
: \maya{1}
: \maya{2}
: \maya{3}
: \maya{4}
: \maya{5}

\maya{0}

\maya{1}

\maya{2}

\maya{3}

\maya{4}

\maya{5}

Mlym

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

൭	൧൨	൧	൧൪
൨	൧൩	൮	൧൧
൧൬	൩	൧൦	൫
൯	൬	൧൫	൪

^{#top template talk:4x4 type square#Mymr}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Mymr

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

၇	၁၂	၁	၁၄
၂	၁၃	၈	၁၁
၁၆	၃	၁๐	၅
၉	၆	၁၅	၄

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

^{#top template talk:4x4 type square#Orya}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

w:en:Burmese numerals

Orya

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

୭	୧୨	୧	୧୪
୨	୧୩	୮	୧୧
୧୬	୩	୧୦	୫
୯	୬	୧୫	୪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

^{#top template talk:4x4 type square#Runr}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Odia language

Runr

search Unicode; add relevant data / links / images; add improved wikitable code; search fonts

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4

^{#top template talk:4x4 type square#Sinh}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Sinh

search Unicode; add relevant data / links / images; add improved wikitable code

Taml

^{#top template talk:4x4 type square#Taml}

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

௭	௧௨	௧	௧௪
௨	௧௩	௮	௧௧
௧௬	௩	௧೦	௫
௯	௬	௧௫	௪

^{#top template talk:4x4 type square#Telu}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Telu

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

౭	౧౨	౧	౧౪
౨	౧౩	౮	౧౧
౧౬	౩	౧౦	౫
౯	౬	౧౫	౪

^{#top template talk:4x4 type square#Tibt}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Tibt

search Unicode; add relevant data / links / images; add improved wikitable code

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

༧	༡༢	༡	༡༤
༢	༡༣	༨	༡༡
༡༦	༣	༡༠	༥
༩	༦	༡༥	༤

^{#top template talk:4x4 type square#Xsux}

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

Xsux

search Unicode; add relevant data / links / images; add improved wikitable code; search fonts

→ Cuneiform, Sumero-Akkadian

Babylonian numerals

੭	੧੨	੧	੧੪
੨	੧੩	੮	੧੧
੧੬	੩	੧०	੫
੯	੬	੧੫	੪

7	12	1	14
2	13	8	11
16	3	10	5
9	6	15	4
transcription of the indian numerals





Babylonian numerals

most-perfect magic square from
the Parshvanath Jain temple in Khajuraho

to do

'update', expand / new / move done
search Unicode; add relevant data / links / images; add improved wikitable code

add google link to "foobar" as:

<code>foobar</code>="foo" [[google:{{URLENCODE:foobar|PATH}}|g]]

- use google compatible link format; else add template with param
supersymmetry (in algebra and geometry)
BiDi tests
~~Runr~~ and other scripts
Nepali is using Deva
appropriate font-size as font-size:150%, fonts, font family etc.
identification and correction of potential homoglyphs using different Unicode encoding
- verify Hans · Hant · Jpan etc. scripts
add file:Khajuraho Parshvanath temple 2010.jpg, and related links (theory as text; youtube)
- add w:en:WP:GEO (d:Q10948883) ^Q10948883 to w:en:Khajuraho Group of Monuments#Chronology
add #top to first level paragraphs only
add information from w:en:Numerals in Unicode

new bugs / feature requests

→→ new bugs / feature requests at additional comments

bug: does not work in thumbs in
[[file:foo.bar|thumb|right|200px|foo
bar
foobar]]</nowiki>
bug:   is rendered inside <brnowiki>...   ...</nowiki>

feature request: edits on special:MyPage should generate notifications same as already done on special:MyTalk

Done

added class="nowrap" nowrap ^g
added "LANG" LANG="foo" ^g
added "xml:lang" xml:lang="foo" ^g
added "hreflang" hreflang="foo" ^g
added "align-right" align-right ^g

new SVG animations

about properties
about generation
about transformation

about relation to Melencolia type ^d:Q1362177(symmetrical/reversible) magical squares
- 2015.08.04: Looking at c:file:Albrecht Dürer - Melencolia I (detail).jpg and reminding the work of Amit6 at c:file:Abstrakt.svg it was possible to create file:Albrecht Dürer - Melencolia I (abstrakt detail).svg making the following changes to the 4x4 square c:file:Abstrakt.svg:

exchanged cell 3,3 with cell 4,4

exchanged cell 3,4 with cell 4,3

exchanged cell 1,3 with cell 1,4

exchanged cell 2,3 with cell 2,4

exchanged cell 3,1 with cell 4,1

exchanged cell 3,2 with cell 4,2

The modified svg files contain now the patterns of these 4x4 types squares and include comments and hints for the transformation between c:File:Abstrakt.svg (for w:en:Most-perfect magic square) and the related/corresponding generic/abstract/general pattern of File:Albrecht Dürer - Melencolia I (abstrakt detail).svg like 4x4 squares
‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 18:08, 8 August 2015 (UTC)

Can fonts be provided somehow in an SVG file? ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 21:37, 8 August 2015 (UTC)

mathematics of the most-perfect magic square

w:en:mathematics
w:en:Portal:Cryptography (Q10857776)
w:en:Wikipedia:WikiProject Mathematics

to be added soon ‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 07:24, 17 August 2015 (UTC)

notes

use references with <ref>foobar</ref>

^ T V Padmakumar (August 1997). "Strongly magic squares" (PDF). The Fibonacci Quarterly. 35 (3): 198–205. Retrieved 24 May 2013.
^ Self-taught mathematician unravels the mysteries of magic squares. Retrieved on 24 May 2013.
^ Stephan Berendonk, Providing the loneliness of the Khajuraho square, The Mathematical Gazette http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9589342
^ Inder Jeet Taneja, xxx, Equivalent Versions of "Khajuraho" and "Lo-Shu" Magic Squares and the day 1st October 2010 (01.10.2010) http://arxiv.org/pdf/1011.0451.pdf
^ T.V.Padmakumar: Arbeit über Quadrate des Typs „Sri Rama Chakra“ http://www.talent-kerala.net/previous/jul2002htm/10.htm
^ Manuel Moschopoulos – Mathematics and the Liberal Arts
^ Murray Bourne: Unicode characters for Chinese and Japanese numbers, 29 Nov 2008
^ Unicode Character Database PropList.txt

references

find more descriptive references

Kathleen Ollerenshaw, David S. Brée: Most-perfect Pandiagonal Magic Squares: Their Construction and Enumeration, Southend-on-Sea : Institute of Mathematics and its Applications, 1998, 186 pages, ISBN 0-905091-06-X
T.V.Padmakumar, Number Theory and Magic Squares, Sura books Archived 2010-02-25 at the Wayback Machine, India, 2008, 128 pages, ISBN 978-81-8449-321-4

{{MathWorld|urlname=MagicSquare|title=Magic Square}}
Nasik Square is a sort of redirect {{MathWorld|urlname=NasikSquare|title=Nasik Square}}
{{MathWorld|urlname=PanmagicSquare|title=Panmagic Square}}

Harvey Heinz: Most-perfect Magic Squares Archived 2014-11-24 at the Wayback Machine
T.V.Padmakumar: Strongly Magic Squares. (PDF; 1,9 MB)
The 4×4 Pan-Magic Squares
Michael Dörmann: A perfect magic square. (Online Generator - Magisches Quadrat 4×4 mit Javascript)

Inder Jeet Taneja: Equivalent Versions of "Khajuraho" and "Lo-Shu" Magic Squares and the day 1st October 2010 (01.10.2010)

George P. H. Styan: Some comments on old magic squares illustrated with postage stamps, October 27, 2010
Ashish Jain: Khajuraho Jain Temples Jain Square, 2011
Amir Aczel: Sex, Math, and Magic (PHOTOS)
"PuzzleSolver": [http://theosophy.net/forum/topics/3055387:Topic:127832?commentId=3055387%3AComment%3A127762 Magic Square Puzzle}

c:project:Story (game) - multilingual interdisciplinary collaborative work#Historical_issues

Not done http://users.eastlink.ca/~sharrywhite/Most-perfect.html Archived 2015-02-02 at the Wayback Machine
Not done http://www.primepuzzles.net/puzzles/puzz_671.htm
Not done http://www.nature.com/nature/journal/v395/n6699/fig_tab/395216b0_F3.html

comments

Not done

... your comments ...

collapsed paragraphs

'feature request:' anchor does not jump to the right paragraphs
is this reported already?

collapsed SVG file source code 01

SVG file source code 01

→ c:file:DiabolicSquare-Order4.svg created by Poccil and last modified by AnonMoos

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
   xmlns:dc="http://purl.org/dc/elements/1.1/"
   xmlns:cc="http://web.resource.org/cc/"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns="http://www.w3.org/2000/svg"
   version="1.0"
   width="488.17239"
   height="488.17239">
  <metadata
     id="metadata29">
    <rdf:RDF>
      <cc:Work rdf:about="">
        <dc:format>image/svg+xml</dc:format>
        <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
      </cc:Work>
    </rdf:RDF>
  </metadata>
  <rect style="fill:none;fill-opacity:1;stroke:black;stroke-width:7.66391373;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
     width="460" height="460"
     x="20" y="20"
     transform="matrix(1.043853,0,0,1.043853,-16.87706,-16.87706)" />
  <path style="fill:white;fill-opacity:1;stroke:black;stroke-width:4.5;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
     d="M 120,8.1723938 L 120,488.17239 M 240,8.1723938 L 240,488.17239 M 360,8.1723938 L 360,488.17239 M 0,128.17239 L 480,128.17239 M 0,248.17239 L 480,248.17239 M 0,368.17239 L 480,368.17239" />
  <text style="font-size:64px;font-style:normal;font-weight:bold;fill:black;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Arial">
    <tspan x="24.9375" y="88.1724">15</tspan>
    <tspan x="144.938" y="87.3911">10</tspan>
    <tspan x="280" y="88.1724">3</tspan>
    <tspan x="400" y="88.1724">6</tspan>
    <tspan x="40" y="438.172">1</tspan>
    <tspan x="280" y="328.172">2</tspan>
    <tspan x="40" y="208.172">4</tspan>
    <tspan x="167.156" y="207.391">5</tspan>
    <tspan x="400" y="328.172">7</tspan>
    <tspan x="160" y="438.172">8</tspan>
    <tspan x="400" y="208.172">9</tspan>
    <tspan x="150" y="328.172">11</tspan>
    <tspan x="380" y="438.172">12</tspan>
    <tspan x="264.938" y="437.391">13</tspan>
    <tspan x="24.9375" y="328.172">14</tspan>
    <tspan x="264.938" y="207.391">16</tspan></text>
</svg>

collapsed modified SVG code

modified SVG code

...
    <tspan x="24.9375" y="88.1724">15</tspan>
    <tspan x="144.938" y="87.3911">10</tspan>
    <tspan x="280" y="88.1724">3</tspan>
    <tspan x="400" y="88.1724">6</tspan>
    <tspan x="40" y="438.172">1</tspan>
    <tspan x="280" y="328.172">2</tspan>
    <tspan x="40" y="208.172">4</tspan>
    <tspan x="167.156" y="207.391">5</tspan>
    <tspan x="400" y="328.172">7</tspan>
    <tspan x="160" y="438.172">8</tspan>
    <tspan x="400" y="208.172">9</tspan>
    <tspan x="150" y="328.172">11</tspan>
    <tspan x="380" y="438.172">12</tspan>
    <tspan x="264.938" y="437.391">13</tspan>
    <tspan x="24.9375" y="328.172">14</tspan>
    <tspan x="264.938" y="207.391">16</tspan></text>
...

As a simple "hack" only the cell contents / values have been changed. The positioning is odd because the numbers are not centered. 19:29, 10 August 2015 (UTC)

collapsed first step

first step

→ text-anchor https://developer.mozilla.org/en-US/docs/Web/SVG/Attribute/text-anchor
→ url of the latest variant at commons: https://upload.wikimedia.org/wikipedia/commons/2/2f/PanmagicSquare-Order4.svg

the values are reordered according to cell values a_1,1, a_1,2, a_1,3, a_1,4 to cell values a_4,1, a_4,2, a_4,3, a_4,4

alignment is achieved via:

<text text-anchor="middle" x="foo" y="bar">foobar</text>

coordinates have been modified by guessing

...
  <text style="font-size:64px;font-style:normal;font-weight:bold;fill:black;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Arial">
    <tspan text-anchor="middle" x= "71" y= "89">3</tspan>
    <tspan text-anchor="middle" x="189" y= "89">10</tspan>
    <tspan text-anchor="middle" x="309" y= "89">15</tspan>
    <tspan text-anchor="middle" x="430" y= "89">6</tspan>
    <tspan text-anchor="middle" x= "71" y="210">13</tspan>
    <tspan text-anchor="middle" x="189" y="210">8</tspan>
    <tspan text-anchor="middle" x="309" y="210">1</tspan>
    <tspan text-anchor="middle" x="430" y="210">12</tspan>
    <tspan text-anchor="middle" x= "71" y="331">2</tspan>
    <tspan text-anchor="middle" x="189" y="331">11</tspan>
    <tspan text-anchor="middle" x="309" y="331">14</tspan>
    <tspan text-anchor="middle" x="430" y="331">7</tspan>
    <tspan text-anchor="middle" x= "71" y="451">16</tspan>
    <tspan text-anchor="middle" x="189" y="451">5</tspan>
    <tspan text-anchor="middle" x="309" y="451">4</tspan>
    <tspan text-anchor="middle" x="430" y="451">9</tspan></text>
...

‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 19:57, 12 August 2015 (UTC)

collapsed stepwise improvements

→ c:project:Help desk#today this is a draft · how to improve the SVG file

stepwise improvements

the values of the square cells should be moved to a definition part of the source code
1. the values from 0 to 16 should be defined in an arrow indexed as number[0] to number [16] or whatever indexing makes sense
2. various UTF-8 values (single characters or multiple characters used also for binary encoding samples) should be defined in a source code block one for each supported script
3. blocks for unused scripts should be commented and deactivated using <-- and -->
4. for the position where the original numbers from 1 to 16 are placed one should use matrix cells as a[1,1] to a[1..4] for the first line up to a[4,1] to a[4,4] for the forth line
5. as a future request transformations should be supported; these are codings for matrix transformations cells as:
 a[1,1] is relocated at cell a[4,2] etc. using a block of 16 lines
in the definition part it should be possible to define font families, fonts, font size and other parameter as praxis will show
multiple characters used also for binary encoding samples should support leading zeros

I suggest to use a fixed design should for LTR only. In order to avoid wrapping some sort of "nowrap" should be used.
Centering the different number strings might be different and difficult for all the mentioned scripts on this page.

background and font colors should be used as additional arrays; bold (yes|no} for each cell might be useful too
new: coordinates should be specified in pixels (not in fractional numbers used for inches)

U12038 or Babylonian001

U1230B or Babylonian010

future thoughts:

usage of symbol for scripts as Maya, Xsux (cuneiform numerals), and others; see #Xsux where PNG files are used; one can imagine both the referencing of the files as [3] or the redefinition of the corresponding symbols (named Uabcd, the hexadecimal Unicode values or Babylonian001, Babylonian010) and referencing to it (via nested transformations)
encoding via additional arrays for "number - 1", "number div 8", "(number mod 8) div 4", "(number mod 4) div 2", "number mod 2"
missing language functionality operations will be implemented via inherent encoding

testing and validation:

I am using Windows 10 And Mozilla Nightly with user agent Mozilla/5.0 (Windows NT 10.0; WOW64; rv:42.0) Gecko/20100101 Firefox/42.0. I noticed that Windows 10 supports many cuneiform characters and Tibetan script (Tibt) but my Samsung 3 does not rendewr these characters.

http://www.primepuzzles.net/puzzles/puzz_671.htm lists the square

1 8 11 14

12 13 2 7

6 3 16 9

15 10 5 4

These values can be used for another test. Another square from http://users.eastlink.ca/~sharrywhite/Most-perfect.html Archived 2015-02-02 at the Wayback Machine can be used for transformation tests

1 8 10 15

12 13 3 6

7 2 16 9

14 11 5 4

Eight values preserve their position and the remaining values will be relocated at the symmetrical position relative of the center of the square.

http://www.angelfire.com/tx4/conradchess/magic34.html lists the square

14 1 12 7

11 8 13 2

5 10 3 16

4 15 6 9

Please do not hesitate to provide feedback!

collapsed SVG interactive animation

SVG interactive animation

The chessboard animation exchanges the position of the kings and the rooks (casteling).

please click on the upload directory link of the image in order to see the animation

Valid for all most-perfect magic square (having all orders of 4n):

one can exchange two arbitrary columns having a distance of 2n
one can exchange two arbitrary rows having a distance of 2n

the two sample squares preserve the positions of the values 10, 6, 11 and 7
the values 4, 13, 16 and 1 are "mirrored" at the center of the value 11
the values 15 and 3 are changing places
the values 9 and 12 are changing places

This is an arbitrary verbose description.
Instead of the values 4, 13, 16 and 1 are "mirrored" at the center of the value 11 one could write also:

the values 4 and 13 are changing places
the values 16 and 1 are changing places

‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 19:29, 10 August 2015 (UTC)

Once knowing techniques to animate transformations one could optimize GIF files.

end of page