Sunday, October 21, 2012
Representing a Number as the Sum of Three Squares using a Probabilistic Shotgun
See this post on MathOverflow - Efficient Computation of Integer Representation as Sum of Three Squares.
One example:
88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 =
3728708309692149319069486105836547569635831800611344866231809626605743446543140741338906572157111906908174220385938813888215444725007055559361034118288392106711441267490894902067351394374510189603371757744263341018713166151526298683346214125342893805012291639475722227078443761154317206380555332240855575850923487133276807555304260120129179410975007599951176226386425345496311175560711401472026399392161325224552285910886215686341134733538354919800609823980774575909850703888338271526201573341101297625937194645663741887567408937166745004054837902992947738719498311260341062479838525863315246124587329025994737831896962572251605303542008917816688105857525263899973501824564669305499^2 + 8659423954866836497222055442609569479198212006663142432779025107564215236268212089964838333998727328589210056339682895508921922562067554420365202477992005631619765951799790747911029105975651521423183103854427982379701565857188948798827049644230457335425566175730313559096014470591244755124818823620481973835142141854050641587503177488728535676941288815996010222969186688888101284376165512662389139600159011876940028243578093146223369745603888487795213374055272652379453140354950015534128847565124896267173708689765986573722289960008854542751323743735684696670546547009812267118488250157564430050257057333477696216049998331821788940995913966994169767925303505778930077956125196943941^2 + 799^2
Tuesday, October 16, 2012
A new 9-square featuring former NBA player Ron Mercer
A new 9-square featuring former NBA player Ron Mercer:
Statistically, my estimate is that I need about 76419 words in my 9-letter word list to find a single 9-square. I have 223602, so the expected number is (223602/76419)^9 = 15270 total 9-letter word squares that can be found using this word list. We'll see how close my estimate comes.
The Mathematics of Square Construction
aggressin
gerontine
grantinge
ronmercer
entercall
stirchley
sincaline
ingelends
neerlyest
Statistically, my estimate is that I need about 76419 words in my 9-letter word list to find a single 9-square. I have 223602, so the expected number is (223602/76419)^9 = 15270 total 9-letter word squares that can be found using this word list. We'll see how close my estimate comes.
The Mathematics of Square Construction
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