{"id":2222,"date":"2024-03-08T08:00:39","date_gmt":"2024-03-08T13:00:39","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=2222"},"modified":"2024-03-07T15:47:36","modified_gmt":"2024-03-07T20:47:36","slug":"math-digests-february-2024","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2024\/","title":{"rendered":"Math Digests February 2024"},"content":{"rendered":"<ul>\n<li><a href=\"#1\">Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game<\/a><\/li>\n<li><a href=\"#2\">Mathematicians have finally proved that Bach was a great composer<\/a><\/li>\n<li><a href=\"#3\">Oakland Filmmaker\u2019s Documentary Details Achievements Of Black Mathematicians<\/a><\/li>\n<li><a href=\"#4\">The Strangely Serious Implications of Math&#8217;s &#8216;Ham Sandwich Theorem&#8217;<\/a><\/li>\n<li><a href=\"#5\">Geometry can shape our world in unexpected but useful ways<\/a><\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/theconversation.com\/anyone-can-play-tetris-but-architects-engineers-and-animators-alike-use-the-math-concepts-underlying-the-game-220915\">Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game<\/a><\/h3>\n<p><em>The Conversation<\/em>, February 28, 2024.<\/p>\n<p>In this article, education professor Leah McCoy argues that the game of Tetris is intrinsically linked to an area of mathematics known as <em>transformational geometry<\/em>. Introduced in middle school, transformational geometry involves linking two distinct mathematical objects through transformations like translation or reflection. What\u2019s more, transformational geometry is used by a wide variety of professions, including animation and architecture. \u201cThere\u2019s far more to Tetris than the elusive promise of winning,\u201d McCoy writes.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>geometry, optimization<\/em><\/p>\n<ul>\n<li>(All levels) Have each student play five minutes of Tetris on their own. Then, teach the definitions of the four basic geometric transformations: Translation, reflection, rotation and dilation. Ask each student to answer the following questions:\n<ul>\n<li>Which transformations show up in Tetris?<\/li>\n<li>How and when do they show up as you play? Be specific. For example, in what direction, by how much, and in what context are the objects transformed?<\/li>\n<li>Which types of transformations do not show up in Tetris?<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Have students come up with their own variation on Tetris by changing at least one of the types of transformations used in the game. (Students cannot just add a new transformation to the game\u2014they must \u201cdelete\u201d at least one existing one. Other features of the game, such as the way new shapes appear, or the shapes that are included, can be changed.) Students will create prototypes of their game using posterboard and construction paper shapes, and present to the class.<\/li>\n<li>(All levels) Play a game of \u201cTetris musical chairs.\u201d Have students play Tetris in class. At random time intervals, alert them that it\u2019s time to pause the game. Based on their paused screen, students will write down the transformations needed to get their piece where they want it to go.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><em>\u00a0<\/em><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.newscientist.com\/article\/2415469-mathematicians-have-finally-proved-that-bach-was-a-great-composer\/\">Mathematicians have finally proved that Bach was a great composer<\/a><\/h3>\n<p><em>New Scientist<\/em>, February 2, 2024.<\/p>\n<p>To physicist Suman Kulkarni, music is more than just sound, rhythm, and notes. She sees the greatest works of Western classical music as complex networks of information. Kulkarni recently analyzed the works of revered composer Johann Sebastian Bach with tools from the field of information theory, which describes data based on its individual parts and the connections between them. It applies to cryptology just as well as it applies to linguistics. Kulkarni wanted to identify <em>why<\/em> Bach\u2019s music is so revered. Bach \u201cproduced an enormous number of pieces with many different structures, including religious hymns called chorales and fast-paced, virtuosic toccatas,\u201d writes Karmela Padavic-Callaghan for <em>New Scientist<\/em>. In this article, Padavic-Callaghan describes Kulkarni\u2019s experiment and analysis.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>information theory, graph theory<\/em><\/p>\n<ul>\n<li>(Mid level) The article describes Kulkarni parsing Bach\u2019s compositions into a graph of \u201cnodes\u201d connected by \u201cedges.\u201d Watch this short TED-Ed video about the origins of <a href=\"https:\/\/www.youtube.com\/watch?v=nZwSo4vfw6c\">graph theory<\/a> for more context and to answer the following questions.\n<ul>\n<li>Based on the article and video, describe what the \u201cnodes\u201d and \u201cedges\u201d are in the Bach graphs. What would it mean when two nodes are connected by an edge?<\/li>\n<li>Can one node be directly connected to more than two other nodes? If so, what would this mean in the Bach piece?<\/li>\n<li>How would you expect the graphs of a Bach Toccata to differ from a Bach chorale, based on the information in the article?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Learn more about graph theory methods, such as depth-first search (DFS), with <a href=\"https:\/\/www.teachengineering.org\/lessons\/view\/uno_connection_lesson01\">this free TeachEngineering lesson<\/a>. Complete the Making the Connection lesson <a href=\"https:\/\/www.teachengineering.org\/content\/uno_\/lessons\/uno_connection\/uno_connection_lesson01_assessment_v2_tedl_dwc.pdf\">worksheet<\/a>, which asks you to define terms and analyze a graph. (An alternative to the \u201cfriends in class\u201d criteria could be \u201cstudents with more than one class together\u201d or \u201cstudents who share an extracurricular activity.\u201d)<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/www.sfgate.com\/news\/bayarea\/article\/oakland-filmmaker-s-documentary-details-18648706.php\">Oakland Filmmaker\u2019s Documentary Details Achievements Of Black Mathematicians<\/a><\/h3>\n<p><em>SFGate<\/em>, February 5, 2024.<\/p>\n<p>In 1876, physicist Edward Bouchet became the first African American to earn a doctoral degree at a university in the United States. That long-awaited feat was delayed not by a lack of willing students, but by policies barring those students from equal rights. A new documentary titled \u201cJourneys of Black Mathematicians: Forging Resilience\u201d tells the story of similar hurdles in even more recent memory. \u201cAfrican Americans are not only underrepresented in the field, their achievements have been overlooked because the public perceives the road to excellence for African Americans is limited to sports and the arts,\u201d writes Francine Brevetti for <em>SFGate<\/em>. In this article, Brevetti speaks about the stories he uncovered by speaking with Black mathematicians.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>equity, math history<\/em><\/p>\n<ul>\n<li>(All levels) Watch the trailer (<a href=\"https:\/\/vimeo.com\/ondemand\/jbm1ind\">or rent the full film<\/a> on Vimeo) and note the names of interviewees in the documentary.\n<ul>\n<li>Research at least two of these mathematicians, and list five facts about their work or life stories.<\/li>\n<li>Describe the research or recent work of at least one of these mathematicians, in your words.<\/li>\n<li>Choose one mathematician and present what you\u2019ve learned about them in class.<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Read this profile of Christine Darden from <em>Quanta Magazine<\/em>: <a href=\"https:\/\/www.quantamagazine.org\/the-nasa-engineer-whos-a-mathematician-at-heart-20210119\/\">The NASA Engineer Who\u2019s a Mathematician at Heart<\/a>. Discuss what barriers Darden mentions existing in her career. How have things changed or not changed since Darden worked at NASA?<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.scientificamerican.com\/article\/the-strangely-serious-implications-of-maths-ham-sandwich-theorem\/\">The Strangely Serious Implications of Math&#8217;s &#8216;Ham Sandwich Theorem&#8217;<\/a><\/h3>\n<p><em>Scientific American<\/em>, February 17, 2024.<\/p>\n<p>In 1938, mathematicians proved a principle called the Ham Sandwich theorem. The theorem states that you can always \u201ccut\u201d $n$ objects in half simultaneously under certain conditions: If those objects are $n$-dimensional, and if your cut has $n-1$ dimensions. For example, if you have 2 circles in a 2-dimensional plane, there exists a 1-dimensional line that bisects both circles simultaneously. And they don\u2019t have to be circles; they can be <em>any<\/em> shape, including discontinuous shapes like scatters of random points and blobs. \u201cContemplate the bizarre implications here,\u201d writes Jack Murtagh for <em>Scientific American<\/em>. \u201cYou can draw a line across the U.S. so that exactly half of the nation\u2019s skunks and half of its Twix bars lie above the line.\u201d Murtagh\u2019s article explains the Ham Sandwich theorem and how it complicates efforts to prevent political gerrymandering, a geographic trick often used to devalue the votes of minority groups or to favor one party.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>coordinate systems, geometry<\/em><\/p>\n<ul>\n<li>(All levels) For each example below, draw a coordinate grid spanning $x=[0,8]$ and $y=[0,10]$ using blank or graph paper. Draw the two shapes\/sets and find the line that bisects both. (All squares are upright; that is, their sides are perfectly horizontal and vertical, rather than tilted.)\n<ul>\n<li>One circle with a radius of 8 centered at (1,9); one circle of $r = 2$ centered at (4,5)<\/li>\n<li>One square with side lengths of 2 centered at (4,9); one oval with a width and height of 2 and 1, respectively, centered at (7,2)<\/li>\n<li>One set of 4 squares, each with areas of 1, centered at (2,2), (3,3), (4,1), and (6,5); one circle of $r = 2$, centered at (2,7)<\/li>\n<li>What is easiest and most challenging about these examples?<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Murtagh writes \u201cwith sufficiently many voters, any percentage edge that one party has over another (say 50.01 percent purple vs. 49.99 percent yellow) can be exploited to win every district.\u201d Demonstrate how this happens with the following exercise based on the images with purple and yellow dots in the article:\n<ul>\n<li>Describe the tally of purple and yellow votes in each district before and after the straight lines shown in the article. Which group is being advantaged and disadvantaged?<\/li>\n<li>Starting from the second image, draw four more bisecting lines to create 8 \u201cdistricts.\u201d<\/li>\n<li>Is it possible to use the \u201cHam Sandwich\u201d lines to <em>increase<\/em> the power of the minority group?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/www.snexplores.org\/article\/geometry-shape-world-useful-ways\">Geometry can shape our world in unexpected but useful ways<\/a><\/h3>\n<p><em>Science News Explores<\/em>, February 29, 2024.<\/p>\n<p>In this article, Lakshmi Chandrasekaran recounts several ways that geometry bleeds into research. One group that she covers, at George Mason University\u2019s Experimental Geometry Lab, modeled four-dimensional shapes by 3D-printed projections of the shapes. Other examples were more practical. Laura Schaposnik at the University of Illinois Chicago is studying the possible geometries of viruses, which can help researchers get ahead of as-yet-undiscovered viruses. \u201cMany people may find it hard to see the appeal or everyday uses of such math,\u201d writes Chandrasekaran. \u201cBut modern geometry is full of problems both beautiful and useful.\u201d<\/p>\n<p><strong>Classroom Activities: <\/strong><em>geometry, tiling<\/em><\/p>\n<ul>\n<li>(All levels) Read the article. In class, brainstorm other possible applications of geometry. As homework, write a paragraph about one of these possible applications. Be creative\u2014your paragraph can be hypothetical, it can incorporate research about what related geometric work has been done, or it can involve your own experiments, but it must be specific about how geometry shows up.<\/li>\n<li>(All levels) The article describes projection in terms of shadows. Try to work out what the following shadows would look like, then check your work with physical objects:\n<ul>\n<li>A sphere<\/li>\n<li>A cube oriented upright<\/li>\n<li>A cube balancing on one corner, with the opposing corner directly above it<\/li>\n<li>A rectangular prism balancing on one corner, with the opposing corner directly above it<\/li>\n<li>(High level, Linear Algebra) Now work backwards by calculating the projections explicitly. Assume light is coming from straight above your objects.<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Explore tiling with <a href=\"https:\/\/static.pbslearningmedia.org\/media\/alfresco\/u\/pr\/PBS%20Teachers\/Mathline%20Geometry%20Tiling%20the%20Plaza_c2edf56a-a55c-4b01-8644-572443d492df\/Tiling%20the%20Plaza%20LP.pdf\">this lesson plan<\/a> from PBS. For more on tiling, check out the <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-april-2023\/#2\">April digests<\/a>.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><strong>Some more of this month\u2019s math headlines<\/strong><\/h3>\n<ul>\n<li><a href=\"https:\/\/www.bbc.com\/future\/article\/20240228-leap-year-the-imperfect-solution-to-fix-the-calendar\">The mathematical muddle created by leap years<\/a><br \/>\n<em>BBC<\/em>, February 28, 2024.<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/entropy-bagels-and-other-complex-structures-emerge-from-simple-rules-20240227\/\">\u2018Entropy Bagels\u2019 and Other Complex Structures Emerge From Simple Rules<\/a><br \/>\n<em>Quanta Magazine<\/em>, February 27, 2024.<\/li>\n<li><a href=\"https:\/\/www.sciencenews.org\/article\/arithmetic-progressions-math-order-combinatorics\">How two outsiders tackled the mystery of arithmetic progressions<\/a><br \/>\n<em>Science News<\/em>, February 26, 2024.<\/li>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/2418791-mathematicians-discover-soft-cell-shapes-behind-the-natural-world\/\">Mathematicians discover &#8216;soft cell&#8217; shapes behind the natural world<\/a><br \/>\n<em>New Scientist<\/em>, February 26, 2024.<\/li>\n<li><a href=\"https:\/\/www.wired.com\/story\/solar-eclipse-2024-simulator-to-help-you-find-the-best-spot\/\">What&#8217;s the Best Place to Watch the Solar Eclipse? This Simulator Can Help You Plan<\/a><br \/>\n<em>Wired<\/em>, February 24, 2024.<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/never-repeating-tiles-can-safeguard-quantum-information-20240223\/\">Never-Repeating Tiles Can Safeguard Quantum Information<\/a><br \/>\n<em>Quanta Magazine<\/em>, February 23, 2024.<\/li>\n<li><a href=\"https:\/\/www.thisiscolossal.com\/2024\/02\/max-bruckner-polyhedra\/\">Marvel at Hundreds of Mathematician Max Br\u00fcckner\u2019s Remarkably Precise Models of Polyhedra<\/a><br \/>\n<em>Colossal<\/em>, February 22, 2024.<\/li>\n<li><a href=\"https:\/\/www.theguardian.com\/science\/2024\/feb\/18\/can-you-solve-it-the-magical-maths-that-keeps-your-data-safe\">Can you solve it? The magical maths that keeps your data safe<\/a><br \/>\n<em>The Guardian<\/em>, February 19, 2024.<\/li>\n<li><a href=\"https:\/\/www.wired.com\/story\/google-artificial-intelligence-chess\/\">Google\u2019s Chess Experiments Reveal How to Boost the Power of AI<\/a><br \/>\n<em>Wired<\/em>, February 18, 2024.<\/li>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/how-string-theory-solved-maths-monstrous-moonshine-problem\/\">How String Theory Solved Math\u2019s Monstrous Moonshine Problem<\/a><br \/>\n<em>Scientific American<\/em>, February 5, 2024.<\/li>\n<li><a href=\"https:\/\/www.theguardian.com\/science\/2024\/feb\/05\/can-you-solve-it-are-you-smarter-than-a-12-year-old\">Can you solve it? Are you smarter than a 12-year-old?<\/a><br \/>\n<em>The Guardian<\/em>, February 5, 2024.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game Mathematicians have finally proved that Bach was a great composer Oakland Filmmaker\u2019s Documentary Details Achievements Of Black Mathematicians The Strangely Serious Implications of Math&#8217;s &#8216;Ham Sandwich Theorem&#8217; Geometry can shape our world in<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2024\/\">Read More &rarr;<\/a><\/span><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[313,312,35,105,97,267,114,88],"class_list":["entry","author-leilasloman","post-2222","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-coordinate-systems","tag-equity","tag-geometry","tag-graph-theory","tag-information-theory","tag-math-history","tag-optimization","tag-tiling"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/comments?post=2222"}],"version-history":[{"count":1,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2222\/revisions"}],"predecessor-version":[{"id":2223,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2222\/revisions\/2223"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=2222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=2222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=2222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}