{"id":4197,"date":"2026-01-26T08:00:29","date_gmt":"2026-01-26T13:00:29","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=4197"},"modified":"2026-01-30T15:00:28","modified_gmt":"2026-01-30T20:00:28","slug":"math-digests-december-2025","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-december-2025\/","title":{"rendered":"Math Digests December 2025"},"content":{"rendered":"<h2 style=\"text-align: left\">December digests:<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li><a href=\"#1\">The <i>Arizona Daily Sun<\/i> on dogs&#8217; instinct for calculus<\/a><\/li>\n<li><a href=\"#2\">How fragile objects break, in <i>Live Science<\/i><\/a><\/li>\n<li><a href=\"#3\">The math of gift-wrapping, from the BBC<\/a><\/li>\n<li><a href=\"#4\">Spotify Wrapped, unwrapped, in the <i>Associated Press<\/i><\/a><\/li>\n<li><a href=\"#5\">Infinity and beyond, in <i>New Scientist<\/i><\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/azdailysun.com\/news\/local\/london-zoo-dogs-are-natural-mathematicians\/article_5f4d05f4-90c3-4a5d-808d-35a2e6db55f3.html\/?utm_medium=internal&amp;utm_source=readerShare&amp;utm_campaign=bButton\">London Zoo: Dogs are natural mathematicians<\/a><\/h3>\n<p><em>Arizona Daily Sun<\/em>, December 2, 2025.<\/p>\n<p>My father once pointed out, watching our dog race through a grassy basin, that her sidelong route was surprisingly efficient. Recently, mathematician Tim Pennings confirmed this observation during a game of fetch on Lake Michigan. After 35 trials, Pennings discovered that his dog, Elvis, pursued routes that were \u201cextremely close to the calculated optimal routes,\u201d writes Karen London in this article. This, despite Elvis having to pass through both land and water. \u201cFinding the solution to such problems requires entering the realm of calculus,\u201d London writes. Unless you\u2019re Elvis.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>calculus, geometry, optimization<\/em><\/p>\n<ul>\n<li>(Mid-level) Suppose Jane is rescuing Tarzan from quicksand. She can run 2.5 meters per second on solid ground, but she can only go 1 meter per second through quicksand.\n<ul>\n<li>Find a formula for Jane\u2019s total travel time in terms of the distance she travels on ground $d_g$ and the distance she travels through quicksand $d_q$.<\/li>\n<li>Assume Jane and Tarzan\u2019s positions are recorded in the $xy$-plane, in units of meters. Jane\u2019s starting point is $(0,0)$, Tarzan is at $(10,10)$, and the ground becomes quicksand when $x + \\frac{1}{2} y &gt; 10$. What is Jane\u2019s travel time if she (1) travels in a straight line, (2) crosses into quicksand at the point $(5,10)$, (3) crosses into quicksand at the point $(7.5,5)$?<\/li>\n<li>If Jane crosses at the point $(x,y)$, find a formula for her travel time in terms of $x$.<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Using a calculator, find Jane\u2019s fastest route.\n<ul>\n<li>Find an equation that tells you Jane\u2019s fastest route if Tarzan is at an arbitrary point within the quicksand area.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.livescience.com\/physics-mathematics\/mathematics\/law-of-maximal-randomness-explains-how-broken-objects-shatter-in-the-most-annoying-way-possible\">Law of &#8216;maximal randomness&#8217; explains how broken objects shatter in the most annoying way possible<\/a><\/h3>\n<p><em>Live Science<\/em>, December 2, 2025<\/p>\n<p>Suppose you drop your parents\u2019 favorite vase on the floor. The vase shatters into fragments, small and large. The mix of large fragments and small fragments seems random\u2014and it is. \u201cBut that randomness has to obey certain limits,\u201d writes Skyler Ware, for <em>Live Science<\/em>. Ware covers a new mathematical equation that describes how objects break, from dropped vases to exploding bubbles. Fragments tend to break in the \u201cmessiest\u201d way possible, making it harder to glue them back together before your parents get home.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> randomness, statistics<\/em><\/p>\n<ul>\n<li>(All levels) Have each student in class draw a circle, as big or small as they like.\n<ul>\n<li>Measure each diameter with a ruler and tabulate the data on a spreadsheet. (Round to one decimal place for whatever unit you choose.)<\/li>\n<li>Calculate the mean, median, mode, and range.<\/li>\n<li>Graph the data in a histogram.<\/li>\n<li>(High level) Randomly assign each student a number. Calculate the <a href=\"https:\/\/mathworld.wolfram.com\/CorrelationCoefficient.html\">correlation coefficient<\/a> for the data and infer whether the circles appear to have been drawn randomly. Explain your reasoning.\n<ul>\n<li>What if you assign numbers based on age, name, or in some other non-random way?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Evaluate the randomness of your circles with a gap analysis.\n<ul>\n<li>Sort diameters from smallest to largest.<\/li>\n<li>Calculate gaps between consecutive values. Random selection tends to produce <a href=\"https:\/\/mathworld.wolfram.com\/ExponentialDistribution.html\">exponentially distributed gaps<\/a>. Do your diameters appear to be random?<\/li>\n<\/ul>\n<\/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.bbc.com\/future\/article\/20251212-how-maths-can-help-you-wrap-your-presents-better\">How maths can help you wrap your presents better<\/a><\/h3>\n<p><em>BBC<\/em>, December 13, 2025.<\/p>\n<p>Christmas and Hanukkah are over, but Sarah Griffiths\u2019 advice on wrapping presents is useful year-round. Griffiths discusses how to minimize the wrapping paper you use for gifts of various shapes, and how to get the most persnickety of gifts\u2014like mugs and basketballs\u2014tied up as neatly as possible.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>geometry, surface area<\/em><\/p>\n<ul>\n<li>(All levels) As a class, do a Secret Santa exchange with a twist: Each giver must wrap their gift in wrapping paper, with the gift\u2019s surface area enclosed. After gifts are exchanged and unwrapped, measure how much wrapping paper was used to pack up the gift you received. Give out prizes for most creative wrapping and most economical wrapping.<\/li>\n<li>(Mid-level) Read Sarah Santos\u2019 procedure for wrapping cubes, in the section \u201cThinking outside the box.\u201d\n<ul>\n<li>Calculate the surface area of a cube with side length $\\ell$.<\/li>\n<li>Calculate the area of the wrapping paper you would use to wrap that cube.<\/li>\n<li>How much excess paper is there?<\/li>\n<li>Answer the above questions, now using the recommended method for a triangular prism or cylindrical gift (section \u201cAcute solution\u201d).<\/li>\n<li>In your own words, explain what happens if you try to wrap a cube according to Santos&#8217; method, but you don&#8217;t place your cube diagonally in the center of the paper. What changes when you rotate it to sit diagonally?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/apnews.com\/article\/spotify-wrapped-2025-release-music-tracking-8a7a7f08150eefd3a26020a4a9d046e1\">It&#8217;s time to unpack Spotify Wrapped. Here&#8217;s how the music streamer compiled your 2025 recap<\/a><\/h3>\n<p><em>Associated Press<\/em>, December 3, 2025<\/p>\n<p>Spotify\u2019s annual streaming recap is notoriously confusing. This year, people learned about their \u201cListening Age\u201d based on their musical habits and taste. \u201cSpotify is billing the 2025 edition to be its biggest yet, with a host of new features it hopes may address some disappointments,\u201d writes Wyatte Grantham-Philips for the <em>Associated Press<\/em>. The company claims that all of its metrics are based on simple rules and listening data, and this article unpacks the math behind your Wrapped.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> data analysis, unit conversion<\/em><\/p>\n<ul>\n<li>(Mid-level) Read <a href=\"https:\/\/newsroom.spotify.com\/2025-12-03\/how-your-wrapped-is-made\/\">this guide from Spotify<\/a> with more details on calculating Wrapped results.\n<ul>\n<li>If a person ranked in the top 0.5% of listeners who streamed Chappell Roan, and Chappell Roan had 40 million monthly listeners, then how many people streamed Chappell Roan songs for <em>more<\/em> minutes than that person?<\/li>\n<li>If a person listened to Lorde for 4,500 minutes this year, then how many <em>months<\/em> did they spend listening to Lorde?<\/li>\n<li>(Mid-level) Based on <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2026\/01\/December-2025-Spotify-Table.pdf\">this table<\/a> of listening data and the Spotify guide, calculate each person\u2019s \u201cListening Age.\u201d (Assume that Alex, Beatrice, Cristina, Devin, and Evan are all 18 years old, and the \u201creminiscence bump\u201d occurs when a person is 15 years old.)<\/li>\n<\/ul>\n<\/li>\n<li>\u00a0(All levels) If you use Spotify, discuss whether you were initially surprised by your Wrapped. Does the article help you better understand your results?<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/www.newscientist.com\/video\/2507414-mathematicians-discover-a-strange-new-infinity\/\">Mathematicians discover a strange new infinity<\/a><\/h3>\n<p><em>New Scientist<\/em>, December 3, 2025<\/p>\n<p>Infinity is one of the strangest values in mathematics. We can use it in calculations, which suggests it\u2019s a number. But unlike other numbers, you can\u2019t say what number comes before or after infinity. Nearly 200 years ago, mathematician Georg Cantor came up with a way to organize the different versions in an \u201cinfinite ladder,\u201d says physicist Abi James in this video from <em>New Scientist.<\/em> \u201cWe may have finally reached the end of infinity.\u201d<\/p>\n<p><strong>Classroom Activities:<\/strong><em> infinity, real numbers<\/em><\/p>\n<ul>\n<li>(Mid-level) Watch the video (at least until 6:16) and answer the following\n<ul>\n<li>What is 1 + infinity?<\/li>\n<li>What is infinity + infinity?<\/li>\n<li>Which of the two is larger? Explain.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid-level) Explain the differences between the following terms: digit, number, integer, real number.<\/li>\n<li>(High level) Explain in your own words the difference between a <strong>countable infinity<\/strong> and an <strong>uncountable infinity<\/strong>. Label the following as countable infinity or uncountable infinity.\n<ul>\n<li>Every prime number<\/li>\n<li>Every odd number below 10<\/li>\n<li>Every point on the circumference of a circle<\/li>\n<li>Every integer below 10<\/li>\n<li>Every <a href=\"https:\/\/www.mathnasium.com\/math-terms\/real-number\">real number<\/a> between 1 and 3<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Watch the rest of the video and explain what the \u201cUltrafinitists\u201d believe.<\/li>\n<li>(Mid-level) For more infinity activities, refer to <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-september-2022\/\">this Math Digest from 2022<\/a>.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3>More of this month\u2019s math headlines:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/mg26835750-700-why-we-all-need-a-little-festive-pedantry-when-it-comes-to-snowflakes\/\">Why we all need a little festive pedantry when it comes to snowflakes<\/a><br \/>\n<em>New Scientist<\/em>, December 23, 2025<\/li>\n<li><a href=\"https:\/\/theconversation.com\/the-magic-of-maths-festive-puzzles-to-give-your-brain-and-imagination-a-workout-272498\">The magic of maths: festive puzzles to give your brain and imagination a workout<\/a><br \/>\n<em>The Conversation<\/em>, December 23, 2025<\/li>\n<li><a href=\"https:\/\/www.nbcbayarea.com\/video\/news\/local\/climate-in-crisis\/uc-berkeley-mathematician-tech-climate-change\/3994590\/\">UC Berkeley mathematician uses tech to combat climate change<\/a><br \/>\n<em>NBC Bay Area<\/em>, December 10, 2025<\/li>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/mathematicians-crack-a-fractal-conjecture-on-chaos\/\">Mathematicians Crack a Fractal Conjecture on Chaos<\/a><br \/>\n<em>Scientific American<\/em>, December 9, 2025<\/li>\n<li><a href=\"https:\/\/island.lk\/can-we-forecast-weather-precisely\/\">Can we forecast weather precisely?<\/a><br \/>\n<em>The Island<\/em>, December 5, 2025<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><em>\u00a0<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>December digests: The Arizona Daily Sun on dogs&#8217; instinct for calculus How fragile objects break, in Live Science The math of gift-wrapping, from the BBC Spotify Wrapped, unwrapped, in the Associated Press Infinity and beyond, in New Scientist London Zoo: Dogs are natural mathematicians Arizona Daily Sun, December 2, 2025.<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-december-2025\/\">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":[143,19,35,110,114,432,150,84,138,364],"class_list":["entry","author-leilasloman","post-4197","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-calculus","tag-data-analysis","tag-geometry","tag-infinity","tag-optimization","tag-randomness","tag-real-numbers","tag-statistics","tag-surface-area","tag-unit-conversion"],"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\/4197","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=4197"}],"version-history":[{"count":10,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/4197\/revisions"}],"predecessor-version":[{"id":4208,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/4197\/revisions\/4208"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=4197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=4197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=4197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}