{"id":1559,"date":"2019-01-16T21:31:42","date_gmt":"2019-01-16T21:31:42","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1559"},"modified":"2019-01-16T22:32:01","modified_gmt":"2019-01-16T22:32:01","slug":"circles-and-polygons","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2019\/01\/16\/circles-and-polygons\/","title":{"rendered":"Circles and Polygons"},"content":{"rendered":"

[latexpage]<\/span><\/p>\n

Fun Math for Girls
\n<\/span>By Kelly Tan<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

What kind of pie do you like to eat? Apple, pumpkin, blueberry, key lime? Do you like baking pie too?<\/span><\/p>\n

Imagine if you baked a pie, and you want to cut even slices for you and your family to eat. Let\u2019s say that you have 5 people in your family: your mother, father, brother, and sister. Do you know how to divide a circle into 5 even pieces?<\/span><\/p>\n

We know that a circle is $360^o$<\/span>. So, to divide it into 5 pieces, we would do: $\\frac{360}{5} = 72^o$<\/span>. This means that every $72^o$<\/span> you would make a cut in the pie.<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

Maybe your pie was too small, and everyone wanted more. So you bake a large pie next week. How would you cut it into even pieces? You do so in exactly the same way you cut the smaller pie (every $72^o$<\/span>).<\/span><\/span><\/p>\n

This shows an important property of circles. The sum of the angles in any circle, no matter how big or small, will be the same ($360^o$<\/span>).<\/span><\/span><\/p>\n

In fact, the sum of interior angles of any 2 shapes that have the same number of sides will be the same. Angles of any quadrilaterals (squares, rectangles, trapezoid, etc) will always add up to $360^o$<\/span>. Angles of any hexagons will always add up to $720^o$<\/span>. Even angles of any tetracontagon (40 sides) will always add up to $6840^o$<\/span>! Some shapes and the sum of their interior angles are shown below:<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

You may be wondering how you get the different angle values. There is a very simple equation for this: $(n-2)\u00d7 180^o$<\/span>, where <\/span>n<\/span><\/i> is the number of sides of the polygon.<\/span><\/span><\/p>\n

You can test this out by drawing any polygon on a piece of paper, and using a protractor to measure the angles and adding them up. Using the equation above, you can check to see whether you get the same number.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

[latexpage] Fun Math for Girls By Kelly Tan What kind of pie do you like to eat? Apple, pumpkin, blueberry, key lime? Do you like baking pie too? Imagine if you baked a pie, and you want to cut even slices for you and your family to eat. Let\u2019s say that you have 5 people […]<\/p>\n","protected":false},"author":1,"featured_media":1560,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1559","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/kellyfish.me\/wp-content\/uploads\/2019\/01\/6076181270_90d8fc4fff_b.jpg?fit=1024%2C768&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/comments?post=1559"}],"version-history":[{"count":5,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1559\/revisions"}],"predecessor-version":[{"id":1569,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1559\/revisions\/1569"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media\/1560"}],"wp:attachment":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media?parent=1559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/categories?post=1559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/tags?post=1559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}