{"id":628,"date":"2006-11-01T00:37:45","date_gmt":"2006-10-31T22:37:45","guid":{"rendered":"http:\/\/www.randform.org\/blog\/?p=628"},"modified":"2006-11-01T00:39:02","modified_gmt":"2006-10-31T22:39:02","slug":"ancient-mathematics","status":"publish","type":"post","link":"https:\/\/www.randform.org\/blog\/?p=628","title":{"rendered":"ancient mathematics"},"content":{"rendered":"<div align=\"center\"><img id=\"image629\" src=\"http:\/\/www.randform.org\/blog\/wp-content\/2006\/10\/stoneBalls.jpg\" alt=\"stoneBalls.jpg\" \/><\/div>\n<p>Hundreds of  approximately 3 inch stoneballs have been found in Scotland. <!--more--><\/p>\n<p>They are believed to date about 200BC and many of them (at least roughly) resemble <a href=\"http:\/\/www.math.utk.edu\/~kens\/\">circle packings of the sphere<\/a>. even more intriguig: The combinatorics of all five <a href=\"http:\/\/en.wikipedia.org\/wiki\/Platonic_solids\">platonic solids<\/a> occur &#8212; see above image (well  to be precise the two carvings in the center and right to it have the same combinatorics of their knobs but a ball having the 20 knobs for a icosahedron can be seen <a href=\"http:\/\/www.class.uidaho.edu\/ngier\/polyhedra\/goc.htm\">here<\/a>). Their use is completely unknown.<br \/>\nA big collection can be found at the <a href=\"http:\/\/www.hunterian.gla.ac.uk\/\">Hunterian<\/a> (see <a href=\"http:\/\/www.huntsearch.gla.ac.uk\/cgi-bin\/foxweb\/huntsearch\/SummaryResults.fwx?collection=all&#038;Searchterm=stone+ball\">here<\/a> and a particular nice decorated one <a href=\"http:\/\/www.arcl.ed.ac.uk\/aos1nu\/archscot1\/4_landscapes_of_conflict_and_power\/basis_of_power\/display\/display_9.htm\">here<\/a>)<br \/>\nThe balls are well documented in<br \/>\nDorothy N. Marshall, &#8220;Carved Stone Balls,&#8221; Proceedings of the Society of Antiquaries of Scotland 108, pp. 40-72, 1976\/77. The reference is online at the <a href=\"http:\/\/www.socantscot.org\/ProceedingsSAIR.html\">Scociety of Antiquaries of Scotland<\/a> pages<br \/>\n(goto <a href=\"http:\/\/ads.ahds.ac.uk\/catalogue\/library\/psas\/\">this page<\/a> and browse for the  Proceedings of the Society of Antiquaries of Scotland).<br \/>\nThe above image is from <a href=\"http:\/\/www.georgehart.com\/virtual-polyhedra\/neolithic.html\">here<\/a> and there cited as a scan from a book of Critchlow and Lawlor.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hundreds of approximately 3 inch stoneballs have been found in Scotland.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[16,4,2],"tags":[],"_links":{"self":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/628"}],"collection":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=628"}],"version-history":[{"count":0,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/628\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}