{"id":1114,"date":"2025-09-01T20:13:10","date_gmt":"2025-09-01T13:13:10","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=1114"},"modified":"2025-09-09T14:48:26","modified_gmt":"2025-09-09T07:48:26","slug":"diameter-circumference-pi","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/diameter-circumference-pi\/","title":{"rendered":"Between Diameter, Circumference, and Pi"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/hubungan-diameter-keliling-lingkaran\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">How do you find the circumference of a circle from its diameter? This interactive tool lets you adjust the diameter of a circle and measure its circumference. There are two sliders: diameter slider, drag left or right to set the circle\u2019s diameter; rolling\/rotation slider, drag left or right to roll the circle.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-dark-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<div id=\"calculator\" class=\"alignwide\" style=\"width: 800px; height: 450px;\"><\/div>\n\n<script>\n  var elt = document.getElementById('calculator');\n  var calculator = Desmos.GraphingCalculator(elt, {\n    expressions: false,\n    settingsMenu: false\n  });\n\n  \/\/ Paste the state you copied here:\n  var state = {\n    \"version\": 11,\n    \"randomSeed\": \"388abc5ae475c3e0de747ab8abbe09b4\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -2.9453592814371277,\n            \"ymin\": -17.606561086046355,\n            \"xmax\": 17.054640718562876,\n            \"ymax\": 17.64398623574695\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"userLockedViewport\": true,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-2.9453592814371277\",\n            \"xmax\": \"17.054640718562876\",\n            \"ymin\": \"-17.606561086046355\",\n            \"ymax\": \"17.64398623574695\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"text\",\n                \"id\": \"55\",\n                \"text\": \"Aturlah panjang diameter (d) lingkaran pada bidang gambar!\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"75\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"57\",\n                \"text\": \"Gelindingkan lingkaran tersebut dan ukurlah kelilingnya.\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"59\",\n                \"text\": \"Lakukan kembali dua langkah sebelumnya dengan nilai d yang berbeda-beda.\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"61\",\n                \"text\": \"Catat hasilnya pada tabel di bawah ini.\"\n            },\n            {\n                \"id\": \"65\",\n                \"type\": \"table\",\n                \"columns\": [\n                    {\n                        \"values\": [\n                            \"\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"63\",\n                        \"color\": \"#6042a6\",\n                        \"latex\": \"d_{iameter}\"\n                    },\n                    {\n                        \"values\": [\n                            \"\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"64\",\n                        \"color\": \"#000000\",\n                        \"points\": false,\n                        \"latex\": \"K_{eliling}\"\n                    },\n                    {\n                        \"values\": [\n                            \"\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"66\",\n                        \"color\": \"#c74440\",\n                        \"latex\": \"\\\\frac{K_{eliling}}{d_{iameter}}\"\n                    }\n                ]\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"69\",\n                \"text\": \"Apa yang dapat kalian simpulkan?\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"72\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"76\",\n                \"text\": \"-----\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"3\",\n                \"title\": \"\u00a9 2022 Yosep Dwi Kristanto\",\n                \"collapsed\": true,\n                \"secret\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"6\",\n                \"folderId\": \"3\",\n                \"text\": \"The circle's diameter:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"1\",\n                \"folderId\": \"3\",\n                \"color\": \"#c74440\",\n                \"latex\": \"d=4\",\n                \"labelSize\": \"1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0.5\",\n                    \"step\": \"0.05\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"7\",\n                \"folderId\": \"3\",\n                \"text\": \"Pergeseran ke kanan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"a=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"\\\\pi\\\\cdot d\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"10\",\n                \"folderId\": \"3\",\n                \"text\": \"Lingkaran:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"3\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\left(x-a\\\\right)^{2}+\\\\left(y-\\\\frac{d}{2}\\\\right)^{2}\\\\le\\\\left(\\\\frac{d}{2}\\\\right)^{2}\",\n                \"fillOpacity\": \"1\",\n                \"lineOpacity\": \"0\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"13\",\n                \"folderId\": \"3\",\n                \"text\": \"Penggaris:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=\\\\left[0,-1.5\\\\right]\\\\left\\\\{0\\\\le x\\\\le30\\\\right\\\\}\",\n                \"labelSize\": \"1\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"15\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[0,30\\\\right]\\\\left\\\\{-1.5\\\\le y\\\\le0\\\\right\\\\}\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"16\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[0,0.1,...,30\\\\right]\\\\left\\\\{-0.1\\\\le y\\\\le0\\\\right\\\\}\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"0.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"17\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[0.5,1,...,29.5\\\\right]\\\\left\\\\{-0.2\\\\le y\\\\le0\\\\right\\\\}\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"0.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"19\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=\\\\left[1,2,...,29\\\\right]\\\\left\\\\{-0.4\\\\le y\\\\le0\\\\right\\\\}\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"3\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"k=\\\\left[1,2,...,29\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"21\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(k,-0.7\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${k}\",\n                \"hidden\": true,\n                \"points\": false,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"79\",\n                \"folderId\": \"3\",\n                \"text\": \"Diameter:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"80\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(a+t\\\\sin\\\\left(\\\\frac{2a}{d}\\\\right),\\\\frac{d}{2}+t\\\\cos\\\\left(\\\\frac{2a}{d}\\\\right)\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"-\\\\frac{d}{2}\",\n                    \"max\": \"\\\\frac{d}{2}\"\n                },\n                \"domain\": {\n                    \"min\": \"-\\\\frac{d}{2}\",\n                    \"max\": \"\\\\frac{d}{2}\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"23\",\n                \"folderId\": \"3\",\n                \"text\": \"Lintasan:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"24\",\n                \"folderId\": \"3\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"y=0\\\\left\\\\{0\\\\le x\\\\le a\\\\right\\\\}\",\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"4\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"26\",\n                \"folderId\": \"3\",\n                \"text\": \"Titik:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"27\",\n                \"folderId\": \"3\",\n                \"color\": \"#fa7e19\",\n                \"latex\": \"\\\\left(a-\\\\frac{d}{2}\\\\cos t,\\\\frac{d}{2}+\\\\frac{d}{2}\\\\sin t\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\\\\frac{2}{d}\\\\cdot a-\\\\frac{\\\\pi}{2}\",\n                    \"max\": \"\\\\frac{3\\\\pi}{2}\"\n                },\n                \"lineOpacity\": \"1\",\n                \"lineWidth\": \"5\",\n                \"domain\": {\n                    \"min\": \"\\\\frac{2}{d}\\\\cdot a-\\\\frac{\\\\pi}{2}\",\n                    \"max\": \"\\\\frac{3\\\\pi}{2}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"51\",\n                \"folderId\": \"3\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(a-\\\\frac{d}{2}\\\\cos\\\\left(\\\\frac{2}{d}\\\\cdot a-\\\\frac{\\\\pi}{2}\\\\right),\\\\frac{d}{2}+\\\\frac{d}{2}\\\\sin\\\\left(\\\\frac{2}{d}\\\\cdot a-\\\\frac{\\\\pi}{2}\\\\right)\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"\\\\frac{3\\\\pi}{2}\"\n                },\n                \"lineOpacity\": \"1\",\n                \"pointOpacity\": \"1\",\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\",\n                \"lineWidth\": \"4\",\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"\\\\frac{3\\\\pi}{2}\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"41\",\n                \"folderId\": \"3\",\n                \"text\": \"Slider diameter:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"52\",\n                \"folderId\": \"3\",\n                \"color\": \"#388c46\",\n                \"latex\": \"s_{1}=\\\\left\\\\{a=0:0.2,0\\\\right\\\\}\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"53\",\n                \"folderId\": \"3\",\n                \"color\": \"#388c46\",\n                \"latex\": \"s_{2}=\\\\left\\\\{a=0:1,0\\\\right\\\\}\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"42\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=-3\\\\left\\\\{0\\\\le x\\\\le4\\\\right\\\\}\\\\left\\\\{a=0\\\\right\\\\}\",\n                \"lineOpacity\": \"s_{1}\",\n                \"lineWidth\": \"20\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"47\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{2d}{5},-3\\\\left\\\\{a=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"`d=${d}`\",\n                \"labelOrientation\": \"below\",\n                \"pointOpacity\": \"s_{2}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,-3\\\\left\\\\{a=\\\\pi\\\\cdot d\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"The diameter `d=${d}`\",\n                \"hidden\": true,\n                \"labelOrientation\": \"right\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"44\",\n                \"folderId\": \"3\",\n                \"text\": \"Slider putaran:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"48\",\n                \"folderId\": \"3\",\n                \"color\": \"#c74440\",\n                \"latex\": \"p=\\\\operatorname{round}\\\\left(\\\\frac{100}{\\\\pi\\\\cdot d}a,1\\\\right)\",\n                \"labelSize\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"49\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(10,-2.5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${p}%\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"45\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=-3\\\\left\\\\{8\\\\le x\\\\le12\\\\right\\\\}\",\n                \"lineOpacity\": \"0.2\",\n                \"lineWidth\": \"20\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"50\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=-3\\\\left\\\\{8\\\\le x\\\\le\\\\frac{4a}{\\\\pi\\\\cdot d}+8\\\\right\\\\}\",\n                \"lineOpacity\": \"0.4\",\n                \"lineWidth\": \"20\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"46\",\n                \"folderId\": \"3\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{4a}{\\\\pi\\\\cdot d}+8,-3\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Roll it!\",\n                \"labelOrientation\": \"below\",\n                \"pointOpacity\": \"1\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator.setState(state);\n<\/script>\n<\/div><\/div>\n\n\n\n<p>Here\u2019s how to use the tool and answer the questions:<\/p>\n\n\n\n<ul><li>Set the circle\u2019s diameter using the diameter slider. Then roll the circle until it completes 100% of a full rotation.<\/li><li>Measure the circumference by seeing how far the circle has rolled. In other words, measure the length of the orange line after the circle rolls 100%.<\/li><li>Repeat steps 1 and 2 several times, and record the diameter (<em>d<\/em>) and circumference (<em>C<\/em>) in the table below. Observe the graph of diameter vs. circumference that forms.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container\">\n<div id=\"calculator2\" class=\"alignwide\" style=\"width: 800px; height: 450px;\"><\/div>\n\n<script>\n  var elt2 = document.getElementById('calculator2');\n  var calculator2 = Desmos.GraphingCalculator(elt2, {\n    settingsMenu: false,\n    expressionsTopbar: false\n  });\n\n  \/\/ Paste the state you copied here:\n  var state2 = {\n    \"version\": 11,\n    \"randomSeed\": \"ef4d6e23bb0919598924fa6654b94b96\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -1,\n            \"ymin\": -3,\n            \"xmax\": 5.5,\n            \"ymax\": 17\n        },\n        \"xAxisArrowMode\": \"POSITIVE\",\n        \"yAxisArrowMode\": \"POSITIVE\",\n        \"xAxisLabel\": \"Diameter\",\n        \"yAxisLabel\": \"Circumference\",\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-1\",\n            \"xmax\": \"5.5\",\n            \"ymin\": \"-3\",\n            \"ymax\": \"17\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"id\": \"4\",\n                \"type\": \"table\",\n                \"columns\": [\n                    {\n                        \"values\": [\n                            \"\",\n                            \"\",\n                            \"\",\n                            \"\",\n                            \"\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"2\",\n                        \"color\": \"#2d70b3\",\n                        \"latex\": \"d\"\n                    },\n                    {\n                        \"id\": \"3\",\n                        \"color\": \"#c74440\",\n                        \"latex\": \"C\",\n                        \"pointSize\": \"10\"\n                    }\n                ]\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true\n};\n\n  calculator2.setState(state2);\n<\/script>\n<\/div><\/div>\n\n\n\n<p>Using the data you collected, answer these questions:<\/p>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>What is the circumference of a circle with a diameter of 12? In general, what is the circumference of a circle with diameter <em>d<\/em>?<\/p><\/blockquote><\/figure>\n\n\n\n<p>Have fun!<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n   <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Geometry\">Geometry<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Circle\">Circle<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Circumference\">Circumference<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>An interactive learning resource that allows manipulation of circle diameters, measurement of circumferences, and recording of data in a table to explore the relationship between diameter and circumference to discover the value of Pi.<\/p>\n","protected":false},"author":1,"featured_media":1119,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"advanced_seo_description":"","spay_email":""},"jetpack_shortlink":"https:\/\/wp.me\/P93lma-hY","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1114"}],"collection":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/comments?post=1114"}],"version-history":[{"count":7,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1114\/revisions"}],"predecessor-version":[{"id":1352,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1114\/revisions\/1352"}],"up":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media\/1119"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=1114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}