{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T05:58:24Z","timestamp":1792735104208,"version":"4.5.0"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,10,24]],"date-time":"2008-10-24T00:00:00Z","timestamp":1224806400000},"content-version":"unspecified","delay-in-days":13691,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Proc. Camb. Phil. Soc."],"published-print":{"date-parts":[[1971,5]]},"abstract":"<jats:p>Besicovitch's construction(1) of a set of measure zerot containing an infinite straight line in every direction was subsequently adapted (2, 3, 4) to provide the following answer to Kakeya's problem (5): a unit segment can be continuously turned round, so as to return to its original position with the ends reversed, inside an arbitrarily small area. The last word on Kakeya's problem itself seems to be F. Cunningham Jr.'s remarkable result(6)\u2021 that this can be done inside a simply connected subset of arbitrarily small measure of a unit circle.<\/jats:p>","DOI":"10.1017\/s0305004100046867","type":"journal-article","created":{"date-parts":[[2008,11,7]],"date-time":"2008-11-07T15:28:31Z","timestamp":1226071711000},"page":"417-421","source":"Crossref","is-referenced-by-count":63,"title":["Some remarks on the Kakeya problem"],"prefix":"10.1017","volume":"69","author":[{"given":"Roy O.","family":"Davies","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,10,24]]},"reference":[{"key":"S0305004100046867_ref001","first-page":"105","article-title":"Sur deux questions de l'int\u00e9grabiit\u00e9 des fonctions","volume":"2","author":"Besicovitch","year":"1919","journal-title":"J. Soc. Phys. Math. (Perm)"},{"key":"S0305004100046867_ref007","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-43.1.717"},{"key":"S0305004100046867_ref010","unstructured":"(10) Ward J. A set of plane measure zero containing all finite polygonal arcs. Caned. J. Math., forthcoming."},{"key":"S0305004100046867_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-4.1.257"},{"key":"S0305004100046867_ref009","doi-asserted-by":"publisher","DOI":"10.4064\/cm-7-2-237-243"},{"key":"S0305004100046867_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01171101"},{"key":"S0305004100046867_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01181172"},{"key":"S0305004100046867_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1963.11992093"},{"key":"S0305004100046867_ref005","first-page":"71","article-title":"Some problems on maxima and minima regarding ovals","volume":"6","author":"Kakeya","year":"1917","journal-title":"T\u00f4hoku Sci. Reports"},{"key":"S0305004100046867_ref008","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1968.11971126"},{"key":"S0305004100046867_ref011","unstructured":"(11) Ward D. J. Some dimensional properties of generalised difference sets. Mathematika, forthcoming."},{"key":"S0305004100046867_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100029236"},{"key":"S0305004100046867_ref014","first-page":"441","article-title":"On fundamental geometric properties of plane line-sets","volume":"39","author":"Besicoviron","year":"1964","journal-title":"J. London Math. Soc"},{"key":"S0305004100046867_ref015","first-page":"30","article-title":"Review of (14)","author":"Croft","year":"1965","journal-title":"Math. Rev"},{"key":"S0305004100046867_ref006","unstructured":"(6) Cunningham F. Jr . The Kakeya problem for simply-connected and for star-shaped sets, to be published."}],"container-title":["Mathematical Proceedings of the Cambridge Philosophical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0305004100046867","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T20:08:26Z","timestamp":1559333306000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0305004100046867\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1971,5]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1971,5]]}},"alternative-id":["S0305004100046867"],"URL":"https:\/\/doi.org\/10.1017\/s0305004100046867","relation":{},"ISSN":["0305-0041","1469-8064"],"issn-type":[{"value":"0305-0041","type":"print"},{"value":"1469-8064","type":"electronic"}],"subject":[],"published":{"date-parts":[[1971,5]]}}}