# Quarter ten-squares.

Ten-Squares and quarter ten-squares

A tautonym was originally the same word repeated for genus and species, though in Word Ways it is used of a single word consisting of two identical halves, such as Wallawalla, a North American Indian people (OED). I take it that it is not necessary for the two halves to have the same meaning, ie for the semantic split to occur also in the middle. Suppose we start a 10-letter word square with a tautonym ABCDEABCDE. The second row must begin with B, say BFGHI (we will just use the first half for brevity), the third with CG, eg CGJKL, and so on:
```A B C D E
B F G H I
C G J K L
D H K M N
E I L N O
```

I define a quarter ten-square as one in which this pattern is replicated precisely to the fight (because the five words are tautonyms), and the definition of a word square necessarily ensures the remaining two quadrants are the same. Given an adequate supply of tautonyms, such squares are very quick to find, as they are essentially five-squares. There are, after all, only 15 letters that can be chosen independently, whereas, in a ten-square, there are 55. In computational terms, finding the ten-squares from 10-letter tautonyms within a word list can be 50 million times faster than looking for ten-squares in the complete 10-letter word list. Quick it may be, but first you must catch your tautonyms. I found almost 500 quarter squares, and these account for an estimated 29% of all ten-squares, despite tautonyms being a mere 0.2% of my 10-letter wordlist. A further 18% of ten-squares contain nine tautonyms. Almost exactly 20% of all my quarter-squares consist solely of placenames. In all, I found 123 distinct top row words, though none starting with E, F, Q, or Z.

The best-known quarter square is probably that in Borgmann's Language on Vacation. Arthur Holt was reputed to have a list of hundreds of 10-letter examples. Such a list would certainly have presented by far and away the easiest way to make a ten-square (although there is the issue of repeated words). I needed to find the words in order to ascerrtain

whether they were solid hyphenated, or two-word phrases, in order to decide how much merit the square had. Unfortunately, my own resources, significant in some of the subject areas, delivered none of the five (and Borgmann' s references on pages 199 and 212 are not easy to check). However, a search of the Internet gave some meanings different from his for some of them, but two still eluded me. Any help would be welcome. Here is his square:

ORANG Borgmlmn: orang-orang Javanese name for the plant Pouzolzia glomerata in an Index by Watson, London 1868. Poulzolzia and glomerata are genus/species names, but I could not find them together. However, orangorang in Indonesian means `all sorts of men' (http://www.linguistics.ucla.edu/people/gunlogson/ling20_class02.pdf).

RANGA Borgmann: parsley fern, Christian: The Caroline Islands, London, 1899. I cannot find that, but it is a word in Maori: rangaranga, n.(under Ranga (i)) a short quick stroke in paddling, as opposed to kuumea). (www.arts.auckland.ac.nz/maori/bbiggs/whfeb00.htm), and Te Rangaranga was a place of battle on 21st June 1864 (http://www.digitalus.co.nz/mokomokai/hgrobley.html)

ANDOL Borgmann: chinese fly in Foster: An Illus Ency Med Dict, NY 1888-94. I cannot find this independently.

NGOTA Borgmann: town Lake Nyasa, now Kota Kota. I could not find either, but ngotangota is to be found in Isaiah 41.15 of the Maori bible (www.christianisrael.com/maori/B23C041.htm)

GALAN Borgmann: mountain in Philippines, from A Pronouncing Gaz. and Geogr. Dict. of the Philippine Islands, War Dept, Washington, 1902. I cannot find this independently.

The validity and forms of ANDOL and GALAN are important, because without them, I found it impossible to make any ten-squares at all from the quarter of a million words that Chris Long's formula predicts should be sufficient, except for the following two, which are heavily tautonymic:

MOCCO moccomocco, OED moco-moco OOOOO O-O-O-O-O-O-O-O-O-O, Palindromicon zebra cry CORRO corrocorro, OED corocoro 1798q CORRO OOOOO

and the square consisting of the ten identical words OOOOOOOOOO (a quarter square!). This last is a truly wonderful square, and unique, as all diagonals are also words: it's just a shame that the words are all the same, and that there are 90 hyphens in it!

Given just GALAN, one can make one more square:

RENGARENGA Rengarenga Point, New Zealand, -38[degrees] 09', 174[degrees] 75', www.linz.govt.nz/databases

EQUALAQUAL equal-aqual Web2

NULLANULLA nulla-nulla, OED

GALANGALAN qv

ALANGALANG alang-alang Web2

This has the five words repeated (not all tautonymic, so not a quarter square)
```Even given both ANDOL and GALAN, there are just six squares, including
one quarter-square:

ORANGOTANG
RANGARANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
ORANGOTANG *
TANGATANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
all-tautonymic
--

ORANGUTANG
RANGARANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
URANGUTANG
TANGATANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
--
--

RENGARENGA
EQUALAQUAL
NULLANULLA
GALANGALAN
ALANGALANG
RANGARANGA
EQUALAQUAL
NULLANULLA
GALANGALAN
ALANGALANG
--
--

URANGUTANG
RANGARANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
URANGUTANG
TANGATANGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
all-tautonymic
--

WHANGWHANG
HUNGAHUNGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
WHANGWHANG
HUNGAHUNGA
ANDOLANDOL
NGOTANGOTA
GALANGALAN
all-tautonymic
quarter-square

* or ORANGUTANG, which means the square is not tautonymic
```

The sources (not already given) for the six squares above are:

TANGATANGA Tangatanga, Bolivia, -19[degrees] 39', -68[degrees] 35', NIMA

ORANGUTANG orangutang, OED orang-outang

URANGUTANG urang-utang, OED

WHANGWHANG whang-whang, OED whang 1889q

HUNGAHUNGA Hungahunga, New Zealand, -37[degrees] 68', 175[degrees] 73', source as for Rengarenga above

Best Quarter Ten-Squares

Because of the paucity of quarter-squares with a mere 250,000 10-letter words, I expanded the vocabulary for the remainder of this article, principally with place names, to get the following results. In the following, qv for a source means that the source has already been given, including in the material above. Place names are from the NIMA database unless otherwise indicated. ITIS is a database of the USDA. In the many cases where a word has multiple meanings (or locations), I have selected one. For the source of New Zealand place names, please see Rengarenga above. I cannot find the exact forms of two words, so I simply attribute them to Borgmann (see above). I found 103 quarter squares consisting solely of place names--about 20% of all quarter squares.

Squares consisting solely of place names are marked with an asterisk. I evaluated the squares, scoring less for proper nouns, phrases, and so on. The best of the 500 in my view follow, only the first (actually a pair) being given in full. In the second example, note that all five vowels are possible in the second position of LANGA.

ANTINANTIN antin-antin, OED, anting-anting 1900q

NDALANDALA Ndalandala, Fiji, -16[degrees] 53', 177[degrees] 26', or NTALA Ntalantala, SouthAffica, -28[degrees] 53', 30[degrees] 04'

TAUANTAUAN Tauantauan Creek, Philippines, 8[degrees] 02', 124[degrees] 57'

ILANGILANG ilang-ilang Web2

NANGANANGA Nangananga, Madagascar, -22[degrees] 21', 47[degrees] 21'

ANTINANTIN

NDALANDALA

TAUANTAUAN

ILANGILANG

NANGANANGA

CLANG clang-clang, OED clang

LANGA Mount Langalanga, Papua New Guinea, -5[degrees] 06', 150[degrees] 06', or LENGA Lengalenga, Tanzania, -10[degrees] 42', 34[degrees] 42', or LINGA Lingalinga, Dem Rep Congo, -1[degrees] 23', 19[degrees] 15', or LONGA Longalonga, Dem Rep Congo, -2[degrees] 14', 26[degrees] 17', or LUNGA Lungalunga, Papua New Guinea, -4[degrees] 13', 151[degrees] 59'. Note all five vowels are possible.

ANDOL Borgmann

NGOTA qv

GALAN Borgmann

HANGI Hangihangi, New Zealand, -35[degrees] 80, 173[degrees] 78'

ALGAL algal-algal, Web2

NGILA qv

GALAN Borgmann

ILANG qv

ILANG qv

MANGI Naivi Mangimangi, Fiji -19[degrees] 02', 178[degrees] 25'

LANGA qv, five possibilities

ALGAL qv

ANDOL Borgmann

NGILA qv

NGOTA qv

GALAN Borgmann

GALAN Borgmann

ILANG qv

SANGA sanga-sanga Web2, or Sangasanga Island, Fiji, -18[degrees] 08', 178[degrees] 35'

ALGAL qv

NGILA qv

GALAN Borgmann

ALANG qv

SANGI Batu Sangisangi, Indonesia, -4[degrees] 10', 123[degrees] 12' or TANGI Tangitangi Creek, Fiji, -17[degrees] 26', 177[degrees] 48'

ALGAL qv

NGILA qv

GALAN Borgmann

ILANG qv

WALLA walla-walla, OED

ANDOL Borgmann

LDING Ldinglding, Cameroon, 10[degrees] 55', 13[degrees] 45'

LONGA qv

ALGAL qv

WANGI Pulau Wangiwangi, Indonesia -5[degrees] 20', 123[degrees] 35'

ALGAL qv

NGILA Ngilangila Island, Fiji -19[degrees] 07', -178[degrees] 33'

GALAN Borgmann

ILANG qv

YLANG ylangylang, OED

LANGA qv see above for AEIOU

ANDOL Borgmann

NGOTA qv

GALAN Borgmann

Top Row Words with most Quarter Ten-Squares

Here are 27 squares beginning with INGITINGIT:

INGIT Ingit Ingit, Indonesia, 0[degrees] 41', 103[degrees] 32'

NDALA qv

GALAN Borgmann

ILANG qv

TANGA qv, or TANGE Tangetange, Solomon Islands, -8[degrees] 04', 156[degrees] 52', or TANGI qv

*INGIT qv

*NDARA Ndarandara Creek, Fiji, -16[degrees] 35', 179[degrees] 49'

*GABON Mount Gabongabon, Philippines, 8[degrees] 39', 125[degrees] 47'

*IRONG Irongirong Point, Philippines, 11[degrees] 51', 124[degrees] 49'

*TANGA qv, or TANGE qv, or TANGI qv

*INGIT qv

*NDARI Ndarindari, Fiji,--16[degrees] 39', 179[degrees] 18'

*GABON qv

*IRONG qv

*TINGA Tinga-Tinga, Mozambique, -23[degrees] 42', 35[degrees] 21', or TINGI Tingitingi, Dem Rep Congo, -3[degrees] 42', 26[degrees] 56'

*INGIT qv

*NDOBA Ndoban-doba River, Swaziland, -26[degrees] 51', 31[degrees] 55'

*GOBOL Gobolgobol, Somalia, 9[degrees] 36', 46[degrees] 42'

*IBONG Ibongibong Point, Philippines, 14[degrees] 27', 120[degrees] 25'

*TALGA Talga Talga Mining Centre, Australia, -21[degrees] 01', 119[degrees] 49'

INGIT qv

NGALI Ngalingali, Fiji, -18[degrees] 56', -178[degrees] 56'

GALAN Borgmann

ILANG qv

TINGA qv, or TINGI qv

INGIT qv

NGALO Ngalongalo River, Fiji, -16[degrees] 47', 179[degrees] 31'

GALAN Borgmann

ILANG qv

TONGA Tongatonga Creek, Fiji, -18[degrees] 03', 177[degrees] 38', or TONGI Tongitongi, Fiji, -17[degrees] 57', 177[degrees] 31', or TONGO tongotongo, ITIS plant

*INGIT qv

*NGARE Ngarengare Island, Solomon Islands, -8[degrees] 38', 158[degrees] 07'

*GABON qv

*I RONG qv

*TENGA Tengatenga, Niger, 18[degrees] 34', 13[degrees] 07, or TENGE Tengetenge, Dem Rep Congo, -4[degrees] 23', 27[degrees] 26'

*INGIT qv

*INGIT qv

*NGARI Ngaringari Island, Solomon Islands, -8[degrees] 28', 157[degrees] 54'

*NGORA Ngorangora Point, Solomon Islands, -9[degrees] 42', 161[degrees] 59'

*GABON qv

*GOBOL qv

*IRONG qv

*IRONG qv

*TINGA qv, or TINGI qv

*TALGA qv

*INGIT qv

INGIT qv

*NIARA Niara Niara, Mali, 15[degrees] 11', -10[degrees] 49'

NTALA qv

*GABON qv

GALAN Borgmann

*IRONG qv

ILANG qv

*TANGA qv, or TANGE qv, or TANGI qv

TANGA qv, or TANGE qv, or TANGI qv

*INGIT qv

*NTARE Ntarentare, Tanzania, -2[degrees] 32', 30[degrees] 29'

*GABON qv

*IRONG qv

*TENGA qv, or TENGE qv

Here are 21 squares beginning with UNGAS:

UNGAS Ungas Ungas, Philippines, 4[degrees] 40', 119[degrees] 28'

UNGAS qv

NDALA qv

NDARA qv

GALAN Borgmann

GALAN Borgmann

ALANG qv

ARANG Arangarang, Indonesia, -1[degrees] 36', 103[degrees] 48'

SANGA qv, or SANGI qv, or SANGO Sangosango Creek, Fiji, -16[degrees] 42', 179[degrees] 26'

SANGA qv, or SANGI qv, or SANGO qv

UNGAS qv

UNGAS qv

NDARI qv

NGALI qv

GALAN Borgmann

GALAN Borgmann

ARANG qv

ALANG qv

SINGA Singasingau Creek, Fiji, -16[degrees] 54', 178[degrees] 44'

SINGA qv

UNGAS qv

NGARE qv

GALAN Borgmann

ARANG qv

SENGA Monte Senga-Senga, Mozambique, -17[degrees] 32', 33[degrees] 07', or SENGI Sengisengi, Sierra Leone, 8[degrees] 55', -10[degrees] 37, or SENGO Sengo Sengo, Mozambique, -18[degrees] 49', 34[degrees] 01'

UNGAS qv

UNGAS qv

NGARI qv

NIARA qv

GALAN Borgmann

GALAN Borgmann

ARANG qv

ARANG qv

SINGA qv

SANGA qv, or SANGI qv, or SANGO qv

UNGAS qv UNGAS qv

NTALA qv

NTARE qv

GALAN Borgmann

GALAN Borgmann

ALANG qv

ARANG qv

SANGA qv, or SANGI qv, or SANGO qv

SENGA qv, or SENGI qv, or SENGO qv

The next most common top row words are ANTINANTIN (18 quarter squares), ALANGALANG (12), and ABANGABANG (10).
```REX GOOCH
Letchworth, Herts, England
rexgooch@ntlworld.com
```