{"id":129443,"date":"2019-12-13T08:45:56","date_gmt":"2019-12-13T13:45:56","guid":{"rendered":"https:\/\/www.bates.edu\/news\/?p=129443"},"modified":"2019-12-13T13:16:27","modified_gmt":"2019-12-13T18:16:27","slug":"the-lesson-i-look-forward-to-teaching-shedding-daylight-on-trigonometry","status":"publish","type":"post","link":"https:\/\/www.bates.edu\/news\/2019\/12\/13\/the-lesson-i-look-forward-to-teaching-shedding-daylight-on-trigonometry\/","title":{"rendered":"The Lesson I Look Forward to Teaching: Shedding daylight on trigonometry"},"content":{"rendered":"\r\n

Lesson<\/strong>: Sine curves and daylight\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

Class:<\/strong> \u201cMathematics Across the Sciences\u201d\u00a0<\/p>\r\n\r\n\r\n\r\n

Professor:<\/strong> Meredith Greer, Associate Professor of Mathematics and Chair of the Program in Digital and Computational Studies\u00a0<\/p>\r\n\r\n\r\n\r\n

It\u2019s an eternal question for generations of math students: How am I going to use this in the real world?\u00a0<\/p>\r\n\r\n\r\n\r\n

At Bates, Meredith Greer answers that question with an entire course, \u201cMathematics Across the Sciences.\u201d It\u2019s designed for both students who want to major in the natural sciences and need a strong math foundation, and those who need to fill a general education requirement.\u00a0<\/p>\r\n\r\n\r\n\r\n

\r\n

The Lesson I Look Forward to Teaching<\/h4>\r\n\r\n\r\n\r\n

This is the first installment of \u201cThe Lesson I Look Forward to Teaching,\u201d an occasional series on the lessons Bates professors know, from experience, are going to capture the attention of their students.<\/p>\r\n<\/section>\r\n\r\n\r\n\r\n

Students spend the course applying mathematics principles to real-life examples: They illustrate exponential growth by studying bacteria populations, measure earthquakes with logarithms, and use straight line equations to calculate the speed of human recall.\u00a0<\/p>\r\n\r\n\r\n\r\n

\u201cIt gives them a sense of all the ways math really is used,\u201d says Greer, an associate professor of mathematics and chair of the Digital and Computational Studies program. \u201cIt\u2019s not just a separate area of study alone, but it\u2019s really relevant.\u201d\u00a0<\/p>\r\n\r\n\r\n\r\n

\"\u201cPi\r\n
Associate Professor of Mathematics Meredith Greer works with Bates students in 2018. (Phyllis Graber Jensen\/Bates College)<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n

Greer has taught \u201cMathematics Across the Sciences\u201d in both fall and winter semesters, but it\u2019s during the fall when she sees a special opportunity to make trigonometry click.\u00a0<\/p>\r\n\r\n\r\n\r\n

Toward the end of the semester, when temperatures are dropping and the sun sets depressingly close to 4 p.m., Greer explains trigonometric functions like sine and cosine.\u00a0<\/p>\r\n\r\n\r\n\r\n

Then, over the course of a class session or two, she has students collect data on the number of minutes of daylight Lewiston receives on days throughout the year. They do the same for Miami, then plot the data for both cities in an Excel chart.\u00a0<\/p>\r\n\r\n\r\n\r\n

The chart\u2019s regularly occurring peaks (the highest amount of daylight a city gets in the summer) and valleys (the lowest in the winter) constitute a classic example of a sine curve, or oscillation.\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

Two results stand out. First, Lewiston\u2019s curves from summer to winter and winter to summer are steeper than Miami\u2019s. In other words, it\u2019s true that when it gets darker in the fall, it gets darker faster.\u00a0<\/em><\/p>\r\n\r\n\r\n\r\n

\"\"\r\n
This chart shows the minutes of daylight Miami and Lewiston each receive over the course of two years. The regular curves are a classic example of oscillation, and they provide mathematical insights into the daylight differences between the two cities. (Google Sheets chart created by Meredith Greer)<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n

Now here\u2019s the cool part. We all know that Lewiston hurts for daylight in the winter. The chart bears this out, showing lower valleys at the winter solstice for Lewiston (nearly nine hours of daylight) than for Miami (10.5 hours). In mathematical terms, the sine curve representing Lewiston has a greater amplitude.<\/p>\r\n\r\n\r\n\r\n

The reverse is true in the summer: Lewiston\u2019s peaks are higher than Miami\u2019s; the northern city gets about 15.5 hours of daylight, compared to Miami\u2019s nearly 14.\u00a0<\/p>\r\n\r\n\r\n\r\n

\u201cWhat a lot of folks haven\u2019t thought through is that if you get to the summer, they peak at this much lower level, and we peak much higher,\u201d Greer says. \u201cWe have a lot more daylight in the summer.\u201d\u00a0<\/p>\r\n\r\n\r\n\r\n

Why? It has to do with the tilt of the earth\u2019s axis. The farther north or south you go, the more widely the amount of daylight varies. It\u2019s why the poles have six-month alternating periods of daylight and dark.\u00a0<\/p>\r\n\r\n\r\n\r\n

For students, Greer says, working with daylight data at the end of the semester is one of the more immediate examples of the ways math can explain the world around us.\u00a0<\/p>\r\n\r\n\r\n\r\n

\u201cA logarithmic function, a sine or cosine function, ex<\/sup>, 2x<\/sup> \u2014 they\u2019re not just developed and done in math class and nowhere else,\u201d she says. \u201cThey\u2019re intrinsically related to nature. There\u2019s a reason they were developed, and they mean something still.\u201d\u00a0<\/p>\r\n","protected":false},"excerpt":{"rendered":"

Why does Miami get more daylight in the winter than Lewiston, Maine? A classic trigonometry exercise holds the answer. <\/p>\n","protected":false},"author":1005,"featured_media":129469,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_hide_ai_chatbot":false,"_ai_chatbot_style":"","associated_faculty":[],"_Page_Specific_Css":"","_bates_restrict_mod":false,"_table_of_contents_display":false,"_table_of_contents_location":"","_table_of_contents_disableSticky":false,"_is_featured":false,"footnotes":"","_bates_seo_meta_description":"","_bates_seo_block_robots":false,"_bates_seo_sharing_image_id":0,"_bates_seo_sharing_image_twitter_id":0,"_bates_seo_share_title":"","_bates_seo_canonical_overwrite":"","_bates_seo_twitter_template":""},"categories":[4],"tags":[9828,12088],"class_list":["post-129443","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-academic-life","tag-meredith-greer","tag-the-lesson-i-look-forward-to-teaching"],"_links":{"self":[{"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/posts\/129443","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/users\/1005"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/comments?post=129443"}],"version-history":[{"count":10,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/posts\/129443\/revisions"}],"predecessor-version":[{"id":129522,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/posts\/129443\/revisions\/129522"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/media\/129469"}],"wp:attachment":[{"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/media?parent=129443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/categories?post=129443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bates.edu\/news\/wp-json\/wp\/v2\/tags?post=129443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}