'+pages+''); $('.stream > div:odd').addClass('bgr_color'); updateHeight('#history'); }); window.activateTabArea = ensure(function(tab, areas){ var parsed = false; var parts = (areas || '').split('/'); window.fsonload = $.inArray('fs', parts) >= 0; if(fsonload){ parts.splice(parts.indexOf('fs'), 1); } var replayMode = false; if($.inArray('replay', parts)>=0){ replayMode = 'replay'; } var noSoundMode = false; if($.inArray('nosound', parts)>=0){ noSoundMode = 'nosound'; } if($.inArray('ns', parts)>=0){ noSoundMode = 'ns'; } var previewMode = null; if($.inArray('p', parts)>=0){ previewMode = 'p'; } if($.inArray('preview', parts)>=0){ previewMode = 'preview'; } if($.inArray('repeat', parts)>=0){ replayMode = 'repeat'; } if($.inArray('r', parts)>=0 || $.inArray('ro', parts)>=0){ replayMode = 'r'; } if(replayMode){ parts.splice(parts.indexOf(replayMode), 1); } if(noSoundMode){ parts.splice(parts.indexOf(noSoundMode), 1); } if(previewMode){ parts.splice(parts.indexOf(previewMode), 1); } if(previewMode){ if(!parts.length){ parts = ['1-14', '999:59']; } } var area = parts[0]; if(tab == 'history' && false){ var page = parseInt(area || '1') || 1; $.ajax({ url: 'https://login.wn.com/recent/json/?pp='+history_pp+'&skip='+history_pp*(page-1), dataType: 'jsonp', success: function(response){ $ensure(function(){ renderHistory(response, page); }); } }); return true; } if(tab == 'global_history' && false){ var page = parseInt(area || '1') || 1; globalHistory.fetchStream(page, '', function(){ updateHeight('#global_history'); }); return true; } if(tab == 'my_playlists' && false){ var page = parseInt(area || '1') || 1; myPlaylists.fetchStream(page, '', function(){ updateHeight('#my_playlists'); }); return true; } if(tab == 'my_videos' && false){ var page = parseInt(area || '1') || 1; myVideos.fetchStream(page, '', function(){ updateHeight('#my_videos'); }); return true; } if(tab == 'related_sites' && areas && matchPosition(areas)){ var seconds = parsePosition(areas); scrollRelated(seconds); return false; } if(matchPosition(area) || matchAction(area)){ parts.unshift('1'); area = parts[0]; } if(tab == 'expand' && area && area.match(/\d+/)) { var num = parseInt(area); if(num < 100){ //FIX ME. Load news page with ajax here } else if(num > 1900){ //FIX ME. Load timeline page with ajax here } } else if(tab.match(/^playlist\d+$/)){ var playerId = parseInt(tab.substring(8)); var vp = videoplayers[playerId]; window.descriptionsholder = $('.descriptionsplace'); if(!vp) return; // why? no player? if(replayMode){ $('.replaycurrent'+playerId).attr('checked', true); vp.setReplayCurrent(true); } var playQueue = []; window.playQueue = playQueue; var playQueuePosition = 0; var playShouldStart = null; var playShouldStop = null; var parseList = function(x){ var items = x.split(/;|,/g); var results = []; for (i in items){ try{ var action = parseAction(vp, items[i]); if(!action.video){ if(window.console && console.log) console.log("Warning: No video for queued entry: " + items[i]); }else{ results.push(action); } }catch(e){ if(window.console && console.log) console.log("Warning: Can''t parse queue entry: " + items[i]); } } return results; }; var scrollToPlaylistPosition = function(vp){ var ppos = vp.getPlaylistPosition(); var el = vp.playlistContainer.find('>li').eq(ppos); var par = el.closest('.playlist_scrollarea'); par.scrollTop(el.offset().top-par.height()/2); } var updateVolumeState = function(){ if(noSoundMode){ if(noSoundMode == 'turn-on'){ clog("Sound is on, vsid="+vp.vsid); vp.setVolumeUnMute(); noSoundMode = false; }else{ clog("Sound is off, vsid="+vp.vsid); vp.setVolumeMute(); noSoundMode = 'turn-on'; } } } var playQueueUpdate = function(){ var playPosition = playQueue[playQueuePosition]; vp.playFromPlaylist(playPosition.video); scrollToPlaylistPosition(vp); playShouldStart = playPosition.start; playShouldStop = playPosition.stop; }; var playQueueAdvancePosition = function(){ clog("Advancing play position..."); playQueuePosition ++; while(playQueuePosition < playQueue.length && !playQueue[playQueuePosition].video){ playQueuePosition ++; } if(playQueuePosition < playQueue.length){ playQueueUpdate(); }else if(vp.getReplayCurrent()){ playQueuePosition = 0; playQueueUpdate(); vp.seekTo(playShouldStart); vp.playVideo(); }else{ vp.pauseVideo(); playShouldStop = null; playShouldStart = null; } }; function loadMoreVideos(playerId, vp, start, finish, callback){ var playlistInfo = playlists[playerId-1]; if(playlistInfo.loading >= finish) return; playlistInfo.loading = finish; $.ajax({ url: '/api/upge/cheetah-photo-search/query_videos2', dataType: 'json', data: { query: playlistInfo.query, orderby: playlistInfo.orderby, start: start, count: finish-start }, success: function(response){ var pl = vp.getPlaylist().slice(0); pl.push.apply(pl, response); vp.setPlaylist(pl); callback(); } }); } if(parts.length == 1 && matchDash(parts[0])){ var pl = vp.getActualPlaylist(); var vids = parseDash(parts[0]); parts = []; for(var i = 0; i < vids.length; i++){ playQueue.push({ 'video': pl[vids[i]-1], 'start': 0, 'stop': null }) } if(vids.length){ if(vids[vids.length-1]-1>=pl.length){ loadMoreVideos(playerId, vp, pl.length, vids[vids.length-1], function(){ if(fsonload){ activateTabArea(tab, parts[0]+'/fs'); }else{ activateTabArea(tab, parts[0]); } var pls = vp.getPlaylist(); vp.playFromPlaylist(pls[pls.length-1]); vp.playVideo(); scrollToPlaylistPosition(vp); }); return true; } } if(playQueue){ playQueueUpdate(); vp.playVideo(); parsed = true; playShouldStart = 0; } } if(previewMode){ var vids = []; var dur = 0; var pl = vp.getActualPlaylist(); area = parts[0]; if(parts.length == 1 && matchPosition(parts[0])){ vids = parseDash('1-'+pl.length); dur = parsePosition(parts[0]); parts = []; }else if(parts.length == 1 && matchDash(parts[0])){ vids = parseDash(parts[0]); dur = parsePosition("999:59"); parts = []; } if(parts.length == 2 && matchDash(parts[0]) && matchPosition(parts[1])){ vids = parseDash(parts[0]); dur = parsePosition(parts[1]); parts = []; } for(var i = 0; i < vids.length; i++){ playQueue.push({ 'video': pl[vids[i]-1], 'start': 0, 'stop': dur }) } if(playQueue){ playQueueUpdate(); vp.playVideo(); parsed = true; } } if(parts.length>1){ for(var i = 0; i < parts.length; i++){ var sel = findMatchingVideo(vp, parts[i]); if(sel){ playQueue.push({ 'video': sel, 'start': 0, 'stop': null }) } } if(playQueue){ playQueueUpdate(); vp.playVideo(); parsed = true; } }else if(area){ var sel = findMatchingVideo(vp, area); if(sel){ vp.playFromPlaylist(sel); playShouldStart = 0; parsed = true; } } if(fsonload || replayMode){ playShouldStart = 0; } if(document.location.search.match('at=|queue=')){ var opts = document.location.search.replace(/^\?/,'').split(/&/g); for(var o in opts){ if(opts[o].match(/^at=(\d+:)?(\d+:)?\d+$/)){ playShouldStart = parsePosition(opts[o].substr(3)) } if(opts[o].match(/^queue=/)){ playQueue = parseList(opts[o].substr(6)); if(playQueue){ playQueuePosition = 0; playQueueUpdate(); } } } } if(matchPosition(parts[1])){ playShouldStart = parsePosition(parts[1]); parsed = true; } if(matchAction(parts[1])){ var action = parseAction(vp, area+'/'+parts[1]); playShouldStart = action.start; playShouldStop = action.stop; parsed = true; } if(playShouldStart !== null && !playQueue.length){ playQueue.push({ video: vp.getCurrentVideo(), start: playShouldStart, stop: playShouldStop }); } if(playShouldStart != null){ setInterval(function(){ if(playShouldStop && vp.currentPlayer && vp.currentPlayer.getCurrentTime() > playShouldStop){ playShouldStop = null; if(vp.getCurrentVideo() == playQueue[playQueuePosition].video){ playQueueAdvancePosition(); }else{ playShouldStart = null; } } }, 500); vp.playerContainer.bind('videoplayer.player.statechange', function(e, state){ if(state == 'ended'){ // advance to the next video playQueueAdvancePosition(); } }); vp.playerContainer.bind('videoplayer.player.readychange', function(e, state){ if(state){ updateVolumeState(); if(playShouldStart !== null){ vp.seekTo(playShouldStart); playShouldStart = null; }else{ playShouldStop = null; // someone started other video, stop playing from playQueue } } if(fsonload) { triggerFullscreen(playerId); fsonload = false; } }); } } else if(tab.match(/^wiki\d+$/)){ if(firstTimeActivate){ load_wiki($('#'+tab), function(){ if(area){ var areaNode = $('#'+area); if(areaNode.length>0){ $('html, body').scrollTop(areaNode.offset().top + 10); return true; } } }); } } return parsed; }) window.activateTab = ensure(function(tab, area){ window.activeArea = null; if(tab == 'import_videos'){ if(area){ import_videos(area); }else{ start_import(); } return true; } if(tab == 'chat'){ update_chat_position($('.chat').eq(0)); window.activeArea = 'chat'; jQuery('.tabtrigger').offscreentabs('activateTab', 'chat'); return true; } if(tab in rev_names){ tab = rev_names[tab]; } if(tab.match(':')){ return false; } var sup = $('ul li a[id=#'+tab+']'); if(sup && sup.length>0){ window.activeArea = area; sup.first().click(); if(!window.activateTabArea(tab, area)){ window.activeArea = null; } window.activeArea = null; return true; }else{ var have_tabs = $('#playlist_menu li').length; if(tab.match(/^playlists?\d+$/)){ var to_add = +tab.substring(8).replace(/^s/,'')-have_tabs; if(to_add>0 && have_tabs){ add_more_videos(to_add); return true; } } } return false; }); window.currentPath = ensure(function(){ return window.lastHistory.replace(basepath, '').split('?')[0]; }); window.main_tab = window.main_tab || 'videos'; window.addHistory = ensure(function(path){ if(window.console && console.log) console.log("Adding to history: "+path); if(window.history && history.replaceState && document.location.hostname.match(/^(youtube\.)?(\w{2,3}\.)?wn\.com$/)){ if(path == main_tab || path == main_tab+'/' || path == '' || path == '/') { path = basepath; } else if( path.match('^'+main_tab+'/') ){ path = basepath + '/' + path.replace(main_tab+'/', '').replace('--','/'); } else { path = basepath + '/' + path.replace('--','/'); } if(document.location.search){ path += document.location.search; } if(window.lastHistory) { history.pushState(null, null, path); } else if(window.lastHistory != path){ history.replaceState(null, null, path); window.lastHistory = path; } } else{ path = path.replace('--','/'); if(path == main_tab || path == main_tab+'/' || path == '' || path == '/') { path = ''; } if(window.lastHistory != '/'+path){ window.location.hash = path? '/'+path : ''; window.lastHistory = '/'+path; } } }); $('.tabtrigger li a').live('click', ensure(function() { var tab = $(this).attr('id'); if(tab.substring(0,1) == '#'){ var name = tab.substring(1); if(name in menu_names){ name = menu_names[name][0]; } realTab = rev_names[name]; $('#'+realTab).show(); if(window.console && console.log) console.log("Triggering tab: "+name+(window.activeArea?" activeArea="+window.activeArea:'')); var path = name; if(window.activeArea){ path = path + '/' + window.activeArea; } if(tab.match(/#playlist\d+/) || tab.match(/#details\d+/)){ $('.multiple-playlists').show(); $('.related_playlist').show(); $('.longest_videos_playlist').show(); }else { $('.multiple-playlists').hide(); $('.related_playlist').hide(); $('.longest_videos_playlist').hide(); } // start the related script only when the tab is on screen showing if (tab.match(/related_sites/)) { if (mc) { mc.startCredits(); } } window.activeTab = realTab; addHistory(path); setTimeout(ensure(function(){ if(tab.match(/language--/)){ $('.tabtrigger').offscreentabs('activateTab', 'language'); } if(tab.match(/weather/)) { $('.tabtrigger').offscreentabs('activateTab', 'weather'); loadContinent(); } updateMenus(tab); updateHeight(); }), 10); } return false; })); }); -->

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Sunday, 12 January 2025

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Measurement of a Circle

Measurement of a Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) is a treatise that consists of three propositions by Archimedes. The treatise is only a fraction of what was a longer work.

Propositions

Proposition one

Proposition one states:

Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r. This proposition is proved by the method of exhaustion.

Proposition two

Proposition two states:

This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition.

Proposition three

Proposition three states:

This approximates what we now call the mathematical constant π. He found these bounds on the value of π by inscribing and circumscribing a circle with two similar 96-sided regular polygons.

Approximation to square roots

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Measurement_of_a_Circle

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'); } } }); } } var stopAllYouTubeVideos = function() { var iframes = document.querySelectorAll('iframe'); Array.prototype.forEach.call(iframes, function(iframe) { iframe.contentWindow.postMessage(JSON.stringify({ event: 'command', func: 'pauseVideo' }), '*'); }); } jQuery(function() { jQuery(".playVideo").live("click", function() { if(!$(this).hasClass("played")){ stopAllYouTubeVideos(); var elem = $(this); setTimeout(function(){ mouseOverMe(elem); }, 1000); } }); jQuery(".description_box .expandContent").live("click", function() { elem = $(this).parent().parent().parent().find('.descContent'); if(elem.height() > 51) { elem.css('height', '44px'); $(this).html('Show More '); }else{ elem.css('height', 'auto'); $(this).html('Hide '); } }); jQuery('.interview-play-off').click(function() { $(".interview-play-off").hide(); $(".interview-play").show(); $(".videoplayer-control-pause").click(); }); jQuery(".video-desc .show_author_videos").live("click", function() { query = $(this).attr('title'); container = $(this).parent().parent().parent().find('.video-author-thumbs'); $(this).parent().parent().parent().find('.video-author-thumbs').css('height', '220px'); jQuery.ajax({ url: '/api/upge/cheetah-photo-search/videoresults', data: {'query': query}, success: function(text) { if(!text) { text = i18n("No results"); } container.html(jQuery(text)); } }); }); }); // -->

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