{"id":143,"date":"2020-12-03T10:33:08","date_gmt":"2020-12-03T02:33:08","guid":{"rendered":"https:\/\/www.fibonance.com\/?p=143"},"modified":"2020-12-03T10:51:41","modified_gmt":"2020-12-03T02:51:41","slug":"ouzhouzhongshijidejisuanfangfa","status":"publish","type":"post","link":"https:\/\/www.fibonance.com\/index.php\/2020\/12\/03\/ouzhouzhongshijidejisuanfangfa\/","title":{"rendered":"\u6b27\u6d32\u4e2d\u4e16\u7eaa\u7684\u8ba1\u7b97\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u672c\u8282\u9009\u81ea\u300a<a href=\"https:\/\/www.amazon.com\/gp\/product\/1532393490\/ref=as_li_tl?ie=UTF8&amp;camp=1789&amp;creative=9325&amp;creativeASIN=1532393490&amp;linkCode=as2&amp;tag=fibonacci0a6-20&amp;linkId=55924148550d18b8e6d6b0a1b4f4ea39\">\u6590\u6ce2\u90a3\u5951\u5927\u5e08\uff1a\u6539\u53d8\u6570\u5b66\u7684\u4eba<\/a>\u300b\u3002\u6240\u6709\u7684\u5f15\u6587\u90fd\u5728\u5f15\u6587\u9875\u4e0a\u7f16\u76ee\u3002<\/p>\n\n\n\n<h2>FIBONACCI\u5e8f\u5217\u7684\u8d77\u6e90<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"690\" height=\"1024\" src=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Master-Fibonacci-Jacket-690x1024.png\" alt=\"\" class=\"wp-image-148\" srcset=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Master-Fibonacci-Jacket-690x1024.png 690w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Master-Fibonacci-Jacket-202x300.png 202w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Master-Fibonacci-Jacket-768x1140.png 768w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Master-Fibonacci-Jacket.png 770w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><figcaption><a href=\"https:\/\/amzn.to\/2SDmJC0\">\u8d2d\u4e70\u94fe\u63a5<\/a><\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<p>\u5341\u4e09\u4e16\u7eaa\u521d\uff0c\u4e2d\u4e16\u7eaa\u7684\u610f\u5927\u5229\u6b63\u5904\u4e8e\u5267\u70c8\u53d8\u9769\u7684\u65f6\u671f\uff0c\u5546\u4e1a\u663e\u8457\u589e\u957f\uff0c\u7ecf\u6d4e\u7a33\u5b9a\u3002\u8be5\u56fd\u8d44\u672c\u5145\u88d5\uff0c\u7528\u4e8e\u8d44\u52a9\u5efa\u9020\u4ee4\u4eba\u60ca\u53f9\u7684\u54e5\u7279\u5f0f\u5927\u6559\u5802\u548c\u4f17\u591a\u5927\u5b66\u3002\u8fd9\u4e9b\u94b1\u5927\u90e8\u5206\u6765\u81ea\u4e8e\u5bf9\u65e0\u6570\u5546\u4eba\u5f81\u6536\u7684\u7a0e\u6b3e\uff0c\u8fd9\u4e9b\u5546\u4eba\u7ecf\u5e38\u5f80\u8fd4\u4e8e\u897f\u8fb9\u7684\u5730\u4e2d\u6d77\u57ce\u5e02\u548c\u6e2f\u53e3\uff0c\u4ee5\u53ca\u4e1c\u8fb9\u7684\u5c0f\u4e9a\u7ec6\u4e9a\u3001\u53d9\u5229\u4e9a\u548c\u5df4\u683c\u8fbe\u4e4b\u95f4\u7684\u5e7f\u6cdb\u8d38\u6613\u3002\u4e00\u4e9b\u65e0\u754f\u7684\u5192\u9669\u5bb6\u751a\u81f3\u8fdc\u8d74\u5370\u5ea6\u548c\u4e2d\u56fd\uff0c\u5e26\u56de\u4e86\u5f02\u56fd\u7684\u7269\u8d44\u548c\u65b0\u5947\u7684\u601d\u60f3\u3001\u4fe1\u4ef0\u548c\u65b9\u6cd5\u3002\u901a\u8fc7\u8d38\u6613\u548c\u6218\u4e89\u63a5\u89e6\u5230\u4e16\u754c\u5176\u4ed6\u5730\u533a\u7684\u4eba\u548c\u6765\u81ea\u4e16\u754c\u5176\u4ed6\u5730\u533a\u7684\u4eba\u3001\u8bed\u8a00\u548c\u6587\u5316\uff0c\u9010\u6e10\u5bfc\u81f4\u4e86\u6b27\u6d32\u7684\u601d\u60f3\u53d8\u9769\u3002<\/p>\n<\/div>\n<\/div>\n\n\n\n<p>\u7f8e\u56fd\u6559\u6388R.B.\u9ea6\u514b\u83b1\u519c\u5728\u300a\u6bd4\u8428\u7684\u83b1\u6602\u7eb3\u591a\u548c\u4ed6\u7684\u81ea\u7531\u56db\u5206\u6cd5\u300b\u4e2d\u89e3\u91ca\u8bf4\uff0c\u5341\u5b57\u519b\u4e1c\u5f81 &#8220;\u628a\u6b27\u6d32\u4eba\u6c11\u4ece\u524d\u51e0\u4e2a\u4e16\u7eaa\u7684\u660f\u660f\u6b32\u7761\u4e2d\u5524\u9192&#8221;\uff0c&#8221;\u4f7f\u4ed6\u4eec\u4e0e\u4e1c\u65b9\u66f4\u5148\u8fdb\u7684\u77e5\u8bc6\u53d1\u5c55\u9762\u5bf9\u9762&#8221;\u3002\u9ea6\u514b\u83b1\u519c\u63d0\u9192\u6211\u4eec\uff0c\u9a6c\u53ef-\u6ce2\u7f57\u53ea\u662f &#8220;\u5728\u90a3\u4e9b\u6fc0\u8361\u7684\u65e5\u5b50\u91cc\u771f\u6b63\u53d1\u73b0\u65b0\u4e16\u754c\u7684\u8bb8\u591a\u4eba\u4e2d\u6700\u8457\u540d\u7684\u4e00\u4e2a&#8221;\u3002\u9664\u4e86\u4f5c\u4e3a\u5546\u54c1\u7684\u8f7d\u4f53\uff0c\u5546\u4eba\u548c\u653f\u6cbb\u4ee3\u8868\u8fd8\u6210\u4e3a &#8220;\u7f51\u7edc\u4e13\u5bb6&#8221;\uff0c\u7ec4\u6210\u4e86\u67d0\u79cd &#8220;\u6587\u5b57\u7f51\u7edc&#8221;\uff0c\u63d0\u4f9b\u4e86\u6db5\u76d6\u5546\u4e1a\u3001\u653f\u6cbb\u3001\u5b97\u6559\u548c\u6587\u5b66\u4e3b\u9898\u7684\u4e66\u9762\u6587\u672c\u7684\u6301\u7eed\u4ea4\u6d41\uff08Roselaar\uff09\u3002\u80fd\u591f\u83b7\u5f97\u72ec\u7279\u77e5\u8bc6\u8d44\u6e90\u7684\u5bab\u5ef7\u83b7\u5f97\u4e86\u7ecf\u6d4e\u4e0a\u7684\u56de\u62a5\uff1b\u56e0\u6b64\uff0c\u5bcc\u88d5\u7684\u5bab\u5ef7\u957f\u671f\u8d44\u52a9\u4e00\u4e9b\u5b66\u8005\uff0c\u8d5e\u52a9\u90a3\u4e9b\u4ece\u5bab\u5ef7\u5230\u5bab\u5ef7\u7684\u5b66\u8005\uff0c\u4fc3\u8fdb\u4e86\u65b0\u601d\u60f3\u7684\u4f20\u64ad\u3002\u77e5\u8bc6\u8fd8\u901a\u8fc7\u7ffb\u8bd1\u548c\u6284\u5199\u4e66\u7c4d\u7684\u65b9\u5f0f\u8fdb\u884c\u4f20\u64ad\uff0c\u8fd9\u4e9b\u4e66\u7c4d\u901a\u5e38\u662f\u5728\u5bfa\u9662\u91cc\u6284\u5199\u7684\uff08&#8221;\u8fc7\u6e21&#8221;\uff09\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\u4f20\u5165\u6b27\u6d32\u7684\u6700\u91cd\u8981\u7684\u601d\u60f3\u662f\u5370\u5ea6\u6559\u7684\u6570\u5b57\u7cfb\u7edf\u3002<\/p>\n\n\n\n<h2>\u5370\u5ea6\u6570\u5b57\u88ab\u5f15\u8fdb\u5230\u6b27\u6d32<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"683\" height=\"1024\" src=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Euclid-683x1024.png\" alt=\"\" class=\"wp-image-149\" srcset=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Euclid-683x1024.png 683w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Euclid-200x300.png 200w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Euclid.png 747w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><figcaption><em><strong>Antonio Cifrondi, Euclid, 17th century, oil<\/strong><\/em><\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<p>\u897f\u65b9\u6570\u5b66\u6700\u6709\u5f71\u54cd\u7684\u5b66\u8005\u4e5f\u8bb8\u662f\u5e0c\u814a\u6570\u5b66\u5bb6\u6b27\u51e0\u91cc\u5f97\uff0c\u4ed6\u751f\u6d3b\u5728\u516c\u5143\u524d325\u5e74\u5de6\u53f3\u81f3\u516c\u5143\u524d265\u5e74\u5de6\u53f3\uff0c\u4ed6\u7684\u51e0\u4f55\u5b66\u8bba\u8457\u300a\u5143\u7d20\u300b\u5206\u5341\u4e09\u5377\uff08\u7ae0\uff09\u5199\u6210\uff0c\u5305\u542b\u4e86\u5f53\u65f6\u5df2\u77e5\u7684\u4e00\u5207\u6570\u8bba\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5b83\u5305\u62ec\u4e86\u5bf9\u65e0\u7406\u6570\u7684\u539f\u59cb\u51e0\u4f55\u5b66\u5904\u7406\uff0c\u4ee5\u53ca\u7b2c\u4e00\u4e2a\u5df2\u77e5\u7684\u7ebf\u6bb5\u5927\u6bb5\u548c\u5c0f\u6bb5\u4e4b\u95f4\u7684 &#8220;\u6781\u503c\u548c\u5e73\u5747\u503c\u7684\u6bd4\u503c &#8220;\u7684\u4e66\u9762\u5b9a\u4e49\uff0c\u4e5f\u5c31\u662f\u73b0\u5728\u6240\u8c13\u7684\u9ec4\u91d1\u6bd4\uff08Fitzpatrick\uff09\u3002\u6b27\u51e0\u91cc\u5f97\u7684\u300a\u5143\u7d20\u300b\u4e00\u4e66\u7684\u610f\u4e49\uff0c\u4ece\u5f53\u65f6\u53ea\u6709\u300a\u5723\u7ecf\u300b\u88ab\u5370\u5237\u51fa\u6765\u5e76\u88ab\u7814\u7a76\u5f97\u6bd4\u8f83\u591a\uff08&#8221;\u6b27\u51e0\u91cc\u5f97&#8221;\uff09\u5c31\u53ef\u4ee5\u770b\u51fa\u3002\u53e6\u4e00\u4e2a\u91cd\u8981\u7684\u8fdb\u6b65\u8d21\u732e\u8005\u662f\u8428\u52d2\u8bfa\u533b\u751f\u541b\u58eb\u5766\u4e01\uff0c\u5728\u5341\u4e00\u4e16\u7eaa\u521d\uff0c\u4ed6\u5728\u975e\u6d32\u3001\u4e9a\u6d32\u548c\u5370\u5ea6\u65c5\u884c\u4e86\u4e09\u5341\u4e5d\u5e74\uff0c\u5b66\u4e60\u4e1c\u65b9\u79d1\u5b66\uff0c\u4ed6\u7684\u624b\u7a3f\u88ab\u5f53\u4f5c\u6559\u79d1\u4e66\u4f7f\u7528\u4e86\u51e0\u4e2a\u4e16\u7eaa\uff08\u53f2\u5bc6\u65af\u548c\u5361\u5e73\u65af\u57fa\uff09\u3002<\/p>\n<\/div>\n<\/div>\n\n\n\n<p>\u5370\u5ea6\u6559\u6570\u5b57\u5f62\u5f0f\u65e9\u5728\u624b\u7a3f\u8bb0\u8f7d\u5176\u5230\u8fbe\u4e4b\u524d\u5c31\u51fa\u73b0\u5728\u57fa\u7763\u6559\u6b27\u6d32\uff0c\u56e0\u4e3a\u5546\u4eba\u3001\u65c5\u884c\u8005\u548c\u5927\u4f7f\u628a\u5b83\u4eec\u4ece\u4e1c\u65b9\u5e26\u5230\u4e86\u5404\u4e2a\u6b27\u6d32\u5e02\u573a\u3002\u5927\u591a\u6570\u5546\u4eba\u76f8\u5f53\u5584\u4e8e\u8fd0\u8f93\u548c\u5e94\u7528\u65b0\u7684\u4fe1\u606f\u548c\u5546\u4e1a\u65b9\u6cd5\uff0c\u4f46\u4e0d\u592a\u5173\u6ce8\u8bb0\u5f55\u6765\u6e90\uff0c\u6240\u4ee5\u786e\u5b9a\u5370\u5ea6\u6559\u6570\u5b57\u5f62\u5f0f\u7684\u786e\u5207\u91c7\u7528\u65e5\u671f\u4ecd\u7136\u662f\u4e00\u4e2a\u8c1c\uff08Smith\u548cKarpinski\uff09\u3002<\/p>\n\n\n\n<h2>\u8ba1\u7b97\uff1a\u624b\u6307\u5230ABACUS<\/h2>\n\n\n\n<p>\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\uff0c\u7a46\u65af\u6797\u4e16\u754c\u548c\u6b27\u6d32\u7684\u5546\u4eba\u4f7f\u7528\u624b\u6307\u7b97\u672f\u6216\u673a\u68b0\u7b97\u76d8\u8fdb\u884c\u8ba1\u7b97\u3002\u6700\u65e9\u7684\u8fd9\u4e9b\u8bbe\u5907\u662f\u7b80\u5355\u7684\u6728\u677f\uff0c\u4e0a\u9762\u6492\u6ee1\u6c99\u5b50\uff0c\u53ef\u4ee5\u5728\u4e0a\u9762\u63cf\u5199\u6570\u5b57\u3002\u5e0c\u4f2f\u6765\u8bed\u4e2d\u8868\u793a\u7070\u5c18\u7684 &#8220;\u963f\u74e6\u514b &#8220;\u53ef\u80fd\u662f &#8220;\u7b97\u76d8 &#8220;\u8fd9\u4e2a\u540d\u5b57\u7684\u6765\u6e90\u3002\u540e\u6765\u7684\u7248\u672c\u7531\u4e00\u5757\u5e73\u677f\u7ec4\u6210\uff0c\u4e0a\u9762\u753b\u6709\u6216\u523b\u6709\u89c4\u5219\u7684\u7ebf\u6761\uff1b\u5c0f\u5375\u77f3\u88ab\u653e\u7f6e\u5728\u8fd9\u4e9b\u7ebf\u6761\u4e0a\uff0c\u5e76\u5728\u8fd9\u4e9b\u7ebf\u6761\u4e0a\u79fb\u52a8\uff0c\u4ee5\u8868\u793a\u52a0\u6cd5\u6216\u51cf\u6cd5\u3002\u7531\u4e8e\u5375\u77f3\u7684\u62c9\u4e01\u8bed\u662fcalculus\uff0c\u8fd9\u79cd\u65e9\u671f\u7684\u8ba1\u7b97\u5f62\u5f0f\u5c31\u88ab\u79f0\u4e3a &#8220;\u5fae\u79ef\u5206&#8221;\uff08Devlin\uff0cFinding 30\uff09\u3002\u4e2d\u4e16\u7eaa\u7684\u7b97\u76d8\u6709\u6cbf\u7740\u5bfc\u7ebf\u6ed1\u52a8\u7684\u8ba1\u6570\u5668\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u4e00\u4e2a\u7b97\u76d8\u6709\u56db\u6839\u7ebf\uff0c\u6bcf\u6839\u7ebf\u4e0a\u7684\u73e0\u5b50\u4ee3\u8868\u5355\u4f4d\u3002\u4e00\u4e2a\u7b97\u76d8\u8db3\u4ee5\u8fdb\u884c\u7b80\u5355\u7684\u7b97\u672f\u8fd0\u7b97\uff0c\u4f46\u5f53\u4f7f\u7528\u8005\u8bd5\u56fe\u5904\u7406\u66f4\u590d\u6742\u7684\u8ba1\u7b97\u65f6\uff0c\u5c31\u4f1a\u5904\u4e8e\u975e\u5e38\u4e0d\u5229\u7684\u5730\u4f4d\u3002\u7531\u4e8e\u4e2d\u4e16\u7eaa\u7684\u5546\u4eba\u5927\u90e8\u5206\u65f6\u95f4\u90fd\u662f\u7b80\u5355\u7684\u52a0\u51cf\u6cd5\uff0c\u6240\u4ee5\u4ed6\u4eec\u53ea\u9700\u7528\u624b\u6307\u8ba1\u7b97\u6216\u7f57\u9a6c\u6570\u5b57\u5c31\u80fd\u641e\u5b9a\u3002\u5f53\u7136\uff0c\u6700\u6839\u672c\u7684\u52a3\u52bf\u662f\u7f3a\u4e4f\u4e00\u4e2a\u5730\u65b9\u503c\u7cfb\u7edf\u3002Livio 93-94\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img src=\"https:\/\/fibonacci.com\/wp-content\/uploads\/2018\/12\/Rechentisch.png\" alt=\"\"\/><figcaption><strong><em>Rechentisch (Holzschnitt vermutlich aus Stra\u00dfburg) * Scan aus: Karl Menninger: &#8221;Zahlwort und Ziffer. Eine Kulturgeschichte der Zahl&#8221;, Dritte Auflage, G\u00f6ttingen 1979, S. 153<\/em><\/strong><\/figcaption><\/figure>\n\n\n\n<p>\u5728\u4eba\u7c7b\u4f7f\u7528\u4e66\u9762\u7b26\u53f7\u8fdb\u884c\u6570\u5b66\u8ba1\u7b97\u4e4b\u524d\uff0c\u4ed6\u7528\u56fe\u50cf\u6765\u8868\u793a\u6570\u5b57\u548c\u6570\u5b66\u8fd0\u7b97\u3002\u624b\u6307\u7b26\u53f7\u5728\u8ba1\u7b97\u65f6\u7279\u522b\u65b9\u4fbf\uff0c\u4e5f\u5f88\u53d7\u6b22\u8fce\uff0c\u4f46\u8981\u6210\u529f\u5730\u5229\u7528\u5b83\uff0c\u9700\u8981\u5927\u91cf\u7684\u7ec3\u4e60\u6765\u57f9\u517b\u6280\u5de7\u548c\u7075\u6d3b\u6027\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u7531\u4e8e\u5b83\u662f\u4e00\u79cd\u53ef\u9760\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u7528\u624b\u6307\u8ba1\u7b97\u7684\u6280\u80fd\u5728\u4e0d\u540c\u7684\u793e\u4f1a\u4e2d\u88ab\u4fdd\u7559\u4e0b\u6765\uff0c\u4ee3\u4ee3\u76f8\u4f20\uff08&#8221;\u8ba1\u7b97&#8221;\uff09\u3002\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\uff0c\u624b\u6307\u8ba1\u7b97\u4fc3\u8fdb\u4e86\u8de8\u8d8a\u8bed\u8a00\u969c\u788d\u7684\u4ea4\u6d41\u3002\u4e3a\u4e86\u6559\u80b2\u5927\u4f17\uff0c\u5b66\u8005\u4eec\u5c06\u624b\u6307\u8ba1\u7b97\u7684\u8868\u8ff0\u6284\u5199\u5728\u4e66\u4e2d\uff1b\u5df2\u77e5\u6700\u65e9\u7684\u6284\u5199\u662f\u7531\u82f1\u56fd\u672c\u7b03\u4f1a\u4fee\u58eb\u8d1d\u5fb7\uff08Venerable Bede\uff0c\u7ea6673-735\u5e74\uff09\u6240\u5199\u3002\u5728\u4ed6\u7684\u300aDe Ratione Temporum\u300b\u4e00\u4e66\u4e2d\uff0c\u4ed6\u63d0\u4f9b\u4e86 &#8220;\u5173\u4e8e\u7528\u624b\u6307\u8ba1\u7b97\u7684\u5b8c\u6574\u89e3\u91ca\u548c\u8fd9\u79cd\u8ba1\u7b97\u65b9\u6cd5\u7684\u89c4\u5219&#8221;\u3002\u4ed6\u6587\u4e2d\u7684\u56fe\u753b\u8868\u660e\uff0c\u4e00\u4e2a\u4eba\u7528\u53cc\u624b\u80fd\u591f\u8868\u793a\u4ece1\u52309999\u7684\u6240\u6709\u6570\u5b57\uff08\u300a\u8ba1\u7b97\u300b\uff09\u3002\u5373\u4f7f\u5728\u5370\u5ea6-\u963f\u62c9\u4f2f\u6570\u5b57\u95ee\u4e16\u540e\uff0c\u7528\u624b\u6307\u8ba1\u7b97\u4ecd\u7136\u5f88\u6d41\u884c\uff0c\u56e0\u4e3a\u5b83\u65e2\u80fd\u8fdb\u884c\u66f4\u9ad8\u7684\u8ba1\u7b97\uff0c\u53c8\u80fd\u8fdb\u884c\u8ba1\u6570\u3001\u52a0\u51cf\u6cd5\u3002\u5b66\u8005\u4eec\u8ba4\u4e3a\u624b\u6307\u8ba1\u7b97\u662f\u5982\u6b64\u91cd\u8981\uff0c\u4ee5\u81f3\u4e8e\u8ba1\u7b97\u624b\u518c\u5982\u679c\u4e0d\u5305\u542b\u663e\u793a\u5404\u79cd\u624b\u6307\u4f4d\u7f6e\u7684\u56fe\u753b\uff0c\u5c31\u4f1a\u88ab\u89c6\u4e3a\u4e0d\u5b8c\u6574\uff08&#8221;\u8ba1\u7b97&#8221;\uff09\u3002<\/p>\n\n\n\n<h2>\u8ba1\u7b97\u3002\u624b\u6307\u548c\u5370\u5ea6\u963f\u62c9\u4f2f\u6570\u5b57<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"717\" height=\"1024\" src=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Venerable-Bede-717x1024.png\" alt=\"\" class=\"wp-image-150\" srcset=\"https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Venerable-Bede-717x1024.png 717w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Venerable-Bede-210x300.png 210w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Venerable-Bede-768x1098.png 768w, https:\/\/www.fibonance.com\/wp-content\/uploads\/2020\/12\/Venerable-Bede.png 797w\" sizes=\"(max-width: 717px) 100vw, 717px\" \/><figcaption><em><strong>Venerable Bede, De Temporum Ratione (725), Paris BN, MS Lat. 7418, f. 3v<\/strong><\/em><\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<p>\u540e\u4e00\u4e2a\u4e8b\u5b9e\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u83b1\u6602\u7eb3\u591a-\u76ae\u8428\u8bfa\u7684\u7b2c\u4e00\u672c\u4e66\u300a\u81ea\u7531\u7684\u963f\u5df4\u5947\u300b\uff08Liber Abaci\uff09\u4e2d\u5305\u542b\u4e86\u5173\u4e8e &#8220;\u6570\u5b57\u5fc5\u987b\u5982\u4f55\u63e1\u5728\u624b\u4e2d &#8220;\u7684\u6307\u5bfc\uff08\u5fb7\u592b\u6797\uff0c\u53d1\u73b089\uff09\u3002\u5728\u7b2c\u4e00\u7ae0\u7684\u672b\u5c3e\uff0c\u4ed6\u5305\u62ec\u4e86\u4e00\u5957\u590d\u6742\u7684\u6307\u7b97\u7cfb\u7edf\uff0c\u4f5c\u4e3a &#8220;\u65b0\u7684 &#8220;\u4f4d\u503c\u7cfb\u7edf\u8ba1\u7b97\u7684\u8f85\u52a9\u5de5\u5177\u3002\u53e4\u8001\u7684\u6307\u7b97\u65b9\u6cd5\u5e76\u6ca1\u6709\u88ab\u7b97\u76d8\u6240\u5e9f\u9edc\uff0c\u4e5f\u6ca1\u6709\u771f\u6b63\u5728\u4e2d\u6b27\u88ab\u63a8\u5230\u540e\u53f0\uff0c\u76f4\u5230\u5341\u4e09\u4e16\u7eaa\u5370\u5ea6-\u963f\u62c9\u4f2f\u6570\u5b57\u4e66\u9762\u8ba1\u7b97\u7684\u80dc\u5229\uff08\u300a\u8ba1\u7b97\u300b\uff09\u3002<\/p>\n\n\n\n<p>\u7b97\u76d8\u6216\u624b\u6307\u8ba1\u7b97\u7684\u95ee\u9898\u662f\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u9700\u8981\u5927\u91cf\u7684\u7ec3\u4e60\u624d\u80fd\u8fbe\u5230\u51c6\u786e\u548c\u901f\u5ea6\u3002\u6b64\u5916\uff0c\u7531\u4e8e &#8220;\u8fd9\u4e24\u79cd\u65b9\u6cd5\u90fd\u6ca1\u6709\u7559\u4e0b\u8ba1\u7b97\u8bb0\u5f55&#8221;\uff0c\u6240\u4ee5\u6ca1\u6709\u529e\u6cd5\u7ea0\u6b63\u9519\u8bef\u6216\u68c0\u67e5\u51c6\u786e\u6027\u3002<\/p>\n<\/div>\n<\/div>\n\n\n\n<p>\u5728\u4ea4\u6613\u65f6\uff0c\u9700\u8981\u80fd\u591f\u5b9a\u671f\u68c0\u67e5\u8bb0\u5f55\u548c\u5ba1\u8ba1\u4ea4\u6613\uff0c\u8457\u6709\u300a\u5bfb\u627e\u6590\u6ce2\u90a3\u5951\uff1a\u63a2\u5bfb\u91cd\u65b0\u53d1\u73b0\u88ab\u9057\u5fd8\u7684\u6539\u53d8\u4e16\u754c\u7684\u6570\u5b66\u5929\u624d\u300b\uff0831\uff09\u7684\u6570\u5b66\u53f2\u5b66\u5bb6\u57fa\u601d-\u5fb7\u592b\u6797\u89e3\u91ca\u8bf4\u3002\u4e9f\u9700\u4e00\u79cd\u66f4\u597d\u7684\u65b9\u6cd5\u3002\u5728\u5df4\u683c\u8fbe\uff0c\u5728\u7814\u7a76\u548c\u7ffb\u8bd1\u5e0c\u814a\u548c\u5370\u5ea6\u6559\u6570\u5b66\u6587\u732e\u7684\u963f\u62c9\u4f2f\u5b66\u8005\u4e2d\uff0c\u6709\u4e00\u4f4d\u6770\u51fa\u7684\u6570\u5b66\u5bb6Abu Abdallah Muhammad ibn Musa Al-Khw\u02c6arizm\u02c6\u0131\uff08\u7ea6780\u5e74\u81f3\u7ea6850\u5e74\uff09\u3002\u5230\u4e86\u5341\u4e8c\u4e16\u7eaa\u4e2d\u53f6\uff0cAl-Khw\u02c6arizm\u02c6\u0131\u7684\u4e24\u672c\u4e66\u90fd\u88ab\u5b66\u8005\u4eec\u7ffb\u8bd1\u6210\u4e86\u62c9\u4e01\u6587\u3002\u8fd9\u4e9b\u4e66\u6210\u4e3a\u6b27\u6d32\u4eba\u5b66\u4e60\u65b0\u6570\u5b66\u7684\u91cd\u8981\u8d44\u6e90\u3002\u4f46Al-Khw\u02c6arizm\u02c6\u0131\u7684\u65b9\u6cd5\u4e0d\u5141\u8bb8\u4eba\u4eec\u7ea0\u6b63\u9519\u8bef\uff0c\u56e0\u4e3a\u5b83 &#8220;\u6d89\u53ca\u5230\u53d6\u6d88\u548c\u91cd\u5199\uff0c\u8fd9\u4f7f\u5f97\u5728\u8ba1\u7b97\u5b8c\u6210\u540e\u65e0\u6cd5\u8ddf\u8e2a\u8ba1\u7b97\u8fc7\u7a0b&#8221;\uff08Devlin\uff0cFinding 76-80\uff09\u3002\u867d\u7136Al-Khw\u02c6arizm\u02c6\u0131\u5728\u4e5d\u4e16\u7eaa\u5c31\u5199\u8fc7\u5173\u4e8e\u5370\u5ea6\u6559-\u963f\u62c9\u4f2f\u6570\u5b57\u7684\u6587\u7ae0\uff0c\u4f46\u4ed6\u7684\u4f5c\u54c1\u7684\u7ffb\u8bd1\u76f4\u5230\u5341\u4e8c\u4e16\u7eaa\u624d\u51fa\u73b0\u5728\u6b27\u6d32\u3002\u7136\u800c\uff0c\u5373\u4f7f\u5728\u90a3\u65f6\uff0c\u5370\u5ea6\u6559-\u963f\u62c9\u4f2f\u6570\u5b57\u76f4\u523015\u4e16\u7eaa\u624d\u5b8c\u5168\u53d6\u4ee3\u7f57\u9a6c\u6570\u5b57\u7684\u65e5\u5e38\u548c\u5546\u4e1a\u4f7f\u7528\u3002\u5f53\u4e00\u4e2a\u5730\u533a\u91c7\u7528\u5370\u5ea6-\u963f\u62c9\u4f2f\u6570\u5b57\u65f6\uff0c\u5f80\u5f80\u53ea\u6709\u6570\u5b66\u5bb6\u3001\u6d4b\u91cf\u5458\u548c\u79d1\u5b66\u5bb6\u4f7f\u7528\uff1b\u5373\u4f7f\u5728\u963f\u62c9\u4f2f\u571f\u5730\u4e0a\u4e5f\u662f\u5982\u6b64\uff08Devlin\uff0cMan 42\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img src=\"https:\/\/fibonacci.com\/wp-content\/uploads\/2018\/12\/Arabic_numerals-en.svg.png\" alt=\"Arabic Numerals\"\/><figcaption><em><strong>Evolution of Hindu-Arabic Numerals, Source: Wikimedia<\/strong><\/em><\/figcaption><\/figure>\n\n\n\n<p>\u7528\u5370\u5ea6\u6559-\u963f\u62c9\u4f2f\u6570\u5b57\u8ba1\u7b97\u4e0e\u7b97\u76d8\u7684\u4f7f\u7528\u5171\u5b58\uff0c\u76f4\u523013\u4e16\u7eaa\u521d\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4eba\u4eec\u4e0d\u613f\u610f\u5b8c\u5168\u629b\u5f03\u7f57\u9a6c\u6570\u5b57\u7684\u539f\u56e0\u4e4b\u4e00\uff0c\u53ef\u80fd\u5c31\u662f\u56e0\u4e3a\u5b83\u4eec 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&#8220;\u975e\u5e38\u6709\u5f71\u54cd\u529b\u7684\u5173\u4e8e\u7b97\u6cd5\u7684\u8bba\u6587&#8221;\uff0c\u8fd9\u4e9b\u8bba\u6587 &#8220;\u6bd4\u5341\u4e8c\u4e16\u7eaa\u7684\u8bd1\u672c\u66f4\u719f\u6089\u65b0\u7684\u6570\u5b57\u7cfb\u7edf&#8221;\uff08&#8221;\u8fc7\u6e21&#8221;\uff09\u3002\u7136\u800c\uff0c\u4e0d\u540c\u5730\u533a\u7684\u6570\u5b57\u5f62\u5f0f\u5dee\u5f02\u5f88\u5927\uff0c\u6b27\u6d32\u6ca1\u6709\u4e00\u4e2a\u5730\u65b9\u53ea\u4f7f\u7528\u5370\u5ea6\u6559-\u963f\u62c9\u4f2f\u6570\u5b57\u3002\u5728Al-Khw\u02c6arizm\u02c6\u0131\u4e4b\u540e\u4e0d\u4e45\uff0c\u4f1f\u5927\u7684\u57c3\u53ca\u6570\u5b66\u5bb6\u963f\u5e03-\u5361\u7c73\u5c14\uff08Abu 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