{"id":2970,"date":"2024-12-13T12:30:04","date_gmt":"2024-12-13T17:30:04","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=2970"},"modified":"2024-12-13T11:32:32","modified_gmt":"2024-12-13T16:32:32","slug":"math-digests-november-2024","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-november-2024\/","title":{"rendered":"Math Digests November 2024"},"content":{"rendered":"<ul>\n<li><a href=\"#1\"><em>Science News Explores<\/em> on the math of skateboarding<\/a><\/li>\n<li><a href=\"#2\"><em>Nerd Wallet<\/em> on the most (and least) reliable airlines<\/a><\/li>\n<li><a href=\"#3\">Can 200,000 chimpanzees, working together, reproduce Shakespeare? Mathematicians say no, in <em>Smithsonian Magazine<\/em><\/a><\/li>\n<li><a href=\"#4\">Algebra in 9th-century Baghdad, in <em>The Michigan Daily<\/em> student newspaper<\/a><\/li>\n<li><a href=\"#5\">Confusing coastlines in <em>Live Science<\/em><\/a><\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/www.snexplores.org\/article\/skateboard-pumping-math-physics\">Math reveals how skateboarders can ramp up their half-pipe power<\/a><\/h3>\n<p><em>Science News Explores<\/em>, November 11, 2024.<\/p>\n<p>In certain situations, a skateboarder can increase their speed just by bending and straightening their knees. This motion is called \u201cpumping.\u201d \u201cAs skateboarders roll along a U-shaped ramp called a half-pipe, they build speed and climb higher by pumping,\u201d Kendra Redmond writes for <em>Science News Explores<\/em>. Her article covers a recent study that mathematically modeled how to maximize gains in speed with pumping.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>vectors, physics<\/em><\/p>\n<ul>\n<li>(Mid level) The article includes <a href=\"https:\/\/www.youtube.com\/watch?v=8AJKN3QTfoE&amp;t=260s&amp;ab_channel=NeverStopImproving\">an embedded video<\/a> on the physics of pumping. Watch the video.\n<ul>\n<li>The explanation relies on understanding vector-valued forces. Read <a href=\"https:\/\/www.physicsclassroom.com\/class\/newtlaws\/Lesson-2\/Drawing-Free-Body-Diagrams\">this lesson from Physics Classroom<\/a> on free body diagrams.<\/li>\n<li>Learn about <a href=\"https:\/\/softschools.com\/math\/pre_calculus\/decomposing_a_vector_into_components\/\">decomposing vectors into perpendicular components<\/a> with this lesson from <em>Soft Schools.<\/em>\u00a0Work through the examples.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Watch the video again.\n<ul>\n<li>Explain, in your own words, how pumping works.<\/li>\n<li>Suppose you are skateboarding on a flat surface, and then go down a ramp, after which the surface becomes flat again. If you want to go as fast as possible, when should you pump? Why? (Include diagrams in your explanation.)<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Suppose you are on a ramp angled 30 degrees from the ground, and you pump, applying a force of 1 Newton in a direction perpendicular to the ramp.\n<ul>\n<li>Draw a diagram showing the forces involved.<\/li>\n<li>How much of the pumping force is in the horizontal direction? How much is in the vertical direction?<\/li>\n<li>Repeat your calculations for a ramp angled 60 degrees from the ground.<\/li>\n<li>Is pumping more helpful or less helpful when the angle is greater? Explain.<\/li>\n<\/ul>\n<\/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.nerdwallet.com\/article\/travel\/most-reliable-airlines\">Which Airline Is the Most Reliable?<\/a><\/h3>\n<p><em>NerdWallet<\/em>, November 6, 2024.<\/p>\n<p>After a nightmarish flight delay, you may vow never to choose the same airline again. But what does the data say? This <em>NerdWallet <\/em>article analyzes data from major airlines about everything that goes wrong: late arrivals, cancellations, diversions, lost baggage, and denied boarding. \u201cU.S. airlines have struggled to deliver on reliability over the past few years,\u201d wrote JT Genter. Mathematical analyses like this allow us to compare performance more objectively than firsthand experiences.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>data analysis, normalization<\/em><\/p>\n<ul>\n<li>(All levels) Which airlines were the most and least reliable? Explain why using the data.<\/li>\n<li>(Mid level) Enter all the data from the article into one spreadsheet table with rows for each airline and columns for each factor.\n<ul>\n<li>List 3 examples of airlines performing well in one category and poorly in another.<\/li>\n<li>Is a higher score in each category good or bad?<\/li>\n<li>Based on the methodology described in the article, do you have enough information to recreate the \u201cReliability\u201d scores (the first table)?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Create your own reliability score.\n<ul>\n<li>First, find a function to transform the data from each category into values ranging from 0 to 1. The worst performer should get a score of 0, and the best performer a score of 1.<\/li>\n<li>Now, make this reliability score personal to you by assigning a \u201cscaling factor\u201d of 2 to the two categories that matter most to you. These categories will now count double for reliability.<\/li>\n<li>Sum the new values up for each airline. Discuss the results of your analysis.<\/li>\n<li>Is a personal reliability score objective? Why or why not?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/www.smithsonianmag.com\/smart-news\/chimpanzees-could-never-randomly-type-the-complete-works-of-shakespeare-study-finds-180985394\/\">Chimpanzees Could Never Randomly Type the Complete Works of Shakespeare, Study Finds<\/a><\/h3>\n<p><em>Smithsonian Magazine<\/em>, November 8, 2024.<\/p>\n<p>If a chimpanzee spent an infinite amount of time randomly typing, they would eventually type the works of Shakespeare in correct order, according to the \u201cinfinite monkey theorem.\u201d This is because given infinite opportunities, <em>any<\/em> strange pattern will appear at some point. But true infinity doesn\u2019t exist in practice. In this <em>Smithsonian<\/em> article, Sarah Kuta writes about a new study that determines whether the infinite monkey theorem could be realized before the end of time as we know it\u2014the so-called heat death of the universe.<\/p>\n<p>In the study, mathematicians assumed that a chimpanzee could type 1 key per second. Even with 200,000 chimpanzees working round the clock simultaneously, the probability of reproducing Shakespeare remains virtually zero. \u201cBeyond that, a single chimpanzee has just a 5 percent chance of randomly typing the word \u201cbananas\u201d within its lifetime,\u201d Kuta writes. \u201cThe odds of a chimpanzee typing a short phrase like \u2018I chimp, therefore I am\u2019 are 1 in 10 million billion billion.\u201d<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>probability, expected value<\/em><\/p>\n<ul>\n<li>(Mid level) Calculate probability of randomly typing the following words or phrases on a 30-key keyboard, starting from your first keystroke (no extraneous letters). Assume every key has equal probability of being typed at each keystroke.\n<ul>\n<li>\u201cBananas\u201d<\/li>\n<li>Your first name<\/li>\n<li>Your full name<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Assuming the \u201cheat death of the universe\u201d will occur in 10<sup>100<\/sup> years, calculate the following:\n<ul>\n<li>How many seconds until the end of the universe?<\/li>\n<li>How many keys can one chimpanzee press in one year?<\/li>\n<li>How many seconds is it expected to take for one chimpanzee to type the first letter correctly? (Hint: $\\sum_{k=1}^N k x^{k-1} = \\frac{d}{dx} \\sum_{k=0}^N x^k$. Approximate $x^{10^{100}}$ as 0 if $x$ is less than 1.)<\/li>\n<li>How many seconds is it expected to take for one chimpanzee to type the first two letters correctly?<\/li>\n<li>If there are 200,000 chimpanzees working simultaneously, how many do you expect to type the first two letters correctly in the first two seconds?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.michigandaily.com\/michigan-in-color\/introduction-to-linear-algebra\/\">Introduction to linear algebra<\/a><\/h3>\n<p><em>The Michigan Daily<\/em>, November 17, 2024.<\/p>\n<p>Algebra was introduced by Mohammed al-Khowarizmi in ninth-century Baghdad. The word \u201calgebra\u201d comes from the Arabic word \u201cal-jabr\u201d meaning restoration or completion. As the name implies, algebraic principles \u201crestore\u201d a sort of balance thrown off by unknowns. Algebra lets us solve problems in science and engineering. For instance, we can use it to determine the value of three unknown variables given three independent equations. In this article for <em>The Michigan Daily<\/em>, Madinabonu Nosirova writes about al-Khowarizmi\u2019s contributions, as well as contributions from lesser-known Muslim researchers.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>algebra, math history, systems of equations<\/em><\/p>\n<ul>\n<li>(Mid level) Solve the following algebra problems\n<ul>\n<li>4x + 6 = 28 | x = ?<\/li>\n<li>2x + 3y = 33 ; y \u2013 x = 1 | x = ?\u00a0\u00a0 y = ?<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Complete the \u201c<a href=\"https:\/\/www.khanacademy.org\/math\/algebra-basics\/alg-basics-systems-of-equations\/alg-basics-elimination-method-systems\/e\/systems_of_equations_with_elimination_0.5\">Systems of equations with elimination\u201d activity<\/a> from Khan Academy. (Hint: watch the accompanying video lesson.)\n<ul>\n<li>(All levels) Read more about a mathematician from the Muslim world with <a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Arabic_mathematics\/\">this article<\/a> from the University of St. Andrews Discuss what you\u2019ve learned about their contributions in small groups.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><em>\u00a0<\/em><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/www.livescience.com\/planet-earth\/whats-the-coastline-paradox\">What&#8217;s the &#8216;coastline paradox&#8217;?<\/a><\/h3>\n<p><em>Live Science<\/em>, November 11, 2024.<\/p>\n<p>In this article in <em>Live Science<\/em>\u2019s \u201cLife\u2019s Little Mysteries\u201d series, Alice Sun writes about the \u201ccoastline paradox.\u201d The coastline paradox observes that if you try to measure the length of a coastline, you can get two completely different numbers <a href=\"https:\/\/mathworld.wolfram.com\/CoastlineParadox.html\">depending on how long a ruler you use<\/a>. As the ruler gets smaller\u2014allowing you to capture more bends and inlets in the coastline\u2014the measurement will soar higher and higher.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>measurement, fractals<\/em><\/p>\n<ul>\n<li>(All levels) Read the article. Answer:\n<ul>\n<li>How could the Congressional Research Service and the National Oceanic and Atmospheric Administration get such different measurements for Alaska\u2019s coastline?<\/li>\n<li>How much bigger is NOAA\u2019s measurement than the Congressional Research Service\u2019s measurement?<\/li>\n<li>Which agency used a \u201csmaller ruler\u201d in their measurement?<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Students will try measuring the perimeter of the contiguous United States using different-sized rulers. Give each student a map of the US and split the class into two groups. Give each student in Group 1 a straightedge that is one inch long, and each student in Group 2 a straightedge that is two inches long. Using their straightedge and the map scale, each student will measure the length of the US perimeter.\n<ul>\n<li>Students will answer the following questions:\n<ul>\n<li>What result did you get?<\/li>\n<li>If you were in the other group, would your result have been larger? Smaller? Estimate what you think the difference might have been.<\/li>\n<li>Which parts of the map were easiest to measure? Which parts were hardest? Why?<\/li>\n<\/ul>\n<\/li>\n<li>Write on the board all the answers from Group 1, and all the answers from Group 2. As a class, discuss reactions to the results.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Calculate the mean and standard deviation for the results of Group 1, and the results of Group 2.\n<ul>\n<li>In small groups, discuss how and why the results would differ if the US was (a) a perfect square or (b) a perfect circle.<\/li>\n<\/ul>\n<\/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.scientificamerican.com\/article\/math-and-physics-cant-prove-all-truths\/\">Math and Physics Can\u2019t Prove All Truths<\/a><br \/>\n<em>Scientific American<\/em>, November 29, 2024.<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/teen-mathematicians-tie-knots-through-a-mind-blowing-fractal-20241126\/\">Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal<\/a><br \/>\n<em>Quanta Magazine<\/em>, November 26, 2024.<\/li>\n<li><a href=\"https:\/\/www.newstatesman.com\/science-tech\/2024\/11\/marcus-du-sautoy-interview-mathematician-is-storyteller\">Marcus du Sautoy: \u201cA mathematician is a storyteller\u201d<\/a><br \/>\n<em>The New Statesman<\/em>, November 13, 2024.<\/li>\n<li><a href=\"https:\/\/cosmosmagazine.com\/science\/mathematics\/subtracting-myths-out-of-maths\/\">Behind the door \u2013 subtracting the myths out of maths<\/a><br \/>\n<em>Cosmos<\/em>, November 12, 2024.<\/li>\n<li><a href=\"https:\/\/arstechnica.com\/ai\/2024\/11\/new-secret-math-benchmark-stumps-ai-models-and-phds-alike\/\">New secret math benchmark stumps AI models and PhDs alike<\/a><br \/>\n<em>Ars Technica<\/em>, November 12, 2024.<\/li>\n<li><a href=\"https:\/\/www.smartbrief.com\/original\/how-i-got-my-students-thinking-in-math\">How I got my students thinking in math<\/a><br \/>\n<em>Smart Brief<\/em>, November 6, 2024.<\/li>\n<li><a href=\"https:\/\/www.eurasiareview.com\/03112024-mathematical-model-illuminates-how-environment-impacts-life-choices-of-salmon\/\">Mathematical Model Illuminates How Environment Impacts Life Choices Of Salmon<\/a><br \/>\n<em>Eurasia Review<\/em>, November 3, 2024.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Science News Explores on the math of skateboarding Nerd Wallet on the most (and least) reliable airlines Can 200,000 chimpanzees, working together, reproduce Shakespeare? Mathematicians say no, in Smithsonian Magazine Algebra in 9th-century Baghdad, in The Michigan Daily student newspaper Confusing coastlines in Live Science Math reveals how skateboarders can<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-november-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":[6,19,168,32,267,395,393,99,73,394,135],"class_list":["entry","author-leilasloman","post-2970","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-algebra","tag-data-analysis","tag-expected-value","tag-fractals","tag-math-history","tag-measurement","tag-normalization","tag-physics","tag-probability","tag-systems-of-equations","tag-vectors"],"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\/2970","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=2970"}],"version-history":[{"count":6,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2970\/revisions"}],"predecessor-version":[{"id":2976,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2970\/revisions\/2976"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=2970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=2970"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=2970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}