{"id":3295,"date":"2025-02-21T08:00:13","date_gmt":"2025-02-21T13:00:13","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=3295"},"modified":"2025-02-20T16:48:46","modified_gmt":"2025-02-20T21:48:46","slug":"math-digests-january-2025","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-january-2025\/","title":{"rendered":"Math Digests January 2025"},"content":{"rendered":"<h3><a href=\"https:\/\/insideclimatenews.org\/news\/17012025\/todays-climate-los-angeles-fires-insurance\/\">Peering Into a Bleak, &#8216;Uninsurable Future&#8217;<\/a><\/h3>\n<p><em>Inside Climate News<\/em>, January 17, 2025<\/p>\n<p>At the beginning of this year, a series of wildfires in Southern California caused unprecedented destruction. More than 12,000 structures burned, contributing to a projected \\$250 billion of damage. Insurance companies typically reimburse homeowners for catastrophic natural disasters. But as the frequency of disasters increases, driven by climate change, some insurers have stopped serving risky areas in Southern California. And according to reporter Kiley Price, the scale of the recent destruction may make it even harder for insurers to stay in business<em>.<\/em> This <em>Inside Climate News <\/em>article explains why the climate crisis changes the math of insurance policies. \u201cInsurance premiums are getting higher, largely because they have started to factor climate risk exposure into their pricing models,\u201d Price writes.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> insurance, probability<\/em><\/p>\n<ul>\n<li>(Mid level) Complete these <a href=\"https:\/\/gems.education.purdue.edu\/wp-content\/uploads\/2019\/01\/insurancemath.pdf\">three math worksheets<\/a> about insurance from Purdue University.\n<ul>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=s9HCZZsIASg&amp;ab_channel=AccountingUniversity\">Watch this short video<\/a> for more about the value of an asset depreciating linearly over time.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) According to the article, <strong>insured <\/strong>losses from natural disasters reached \\$140 billion in 2024. Answer the following based on what you have learned.\n<ul>\n<li>What will the 2025 insured losses total be if losses increase by 15%?<\/li>\n<li>Based on your reading, list 3 <strong>controllable <\/strong>factors that would potentially increase insured losses, and 3 factors that would potentially decrease insured losses. (Hint: We are measuring only \u201cinsured\u201d losses.)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.quantamagazine.org\/rational-or-not-this-basic-math-question-took-decades-to-answer-20250108\/\">Rational or Not? This Basic Math Question Took Decades to Answer<\/a><\/h3>\n<p><em>Quanta Magazine<\/em>, January 8, 2025<\/p>\n<p>Rational numbers are any numbers\u2014decimal, negative, or whole\u2014that equal a ratio of two integers. Three mathematicians recently discovered a way of checking whether a number is rational or not. \u201cIt might seem surprising that mathematicians are still grappling with such a basic question about numbers,\u201d Erica Klarreich writes in this <em>Quanta Magazine <\/em>article. \u201cBut even though rationality is an elementary concept, researchers have few tools for proving that a given number is irrational. And frequently, those tools fail.\u201d This article tells the surprising history of the deceptive problem and describes how mathematicians solved it.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>\u00a0irrational numbers, power series, derivatives<\/em><\/p>\n<ul>\n<li>(Mid level) Which of the following are irrational numbers?\n<ul>\n<li>22\/7<\/li>\n<li>4.5<\/li>\n<li>$\\pi$<\/li>\n<li>$e$<\/li>\n<li>$\\sqrt{2}$<\/li>\n<li>Any prime divided by any other prime<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Read the article. Klarreich writes: \u201cIf you pick a point along the number line at random, it\u2019s almost guaranteed to be irrational.\u201d Explain in your own words why that is by following these guiding questions.\n<ul>\n<li>Are all integers rational?<\/li>\n<li>1.5 is an example of a rational number between 1 and 2, because it can be expressed as 3\/2. What are two other examples between 1 and 1.5?<\/li>\n<li>Is $\\pi$\/2 rational? What about $\\pi$\/2.1 and $\\pi$\/2.0001?<\/li>\n<li>Does a number line from 0 to 100 contain more integers or non-integers?<\/li>\n<li>Does a number line from 0 to infinity contain more integers or non-integers? (<a href=\"https:\/\/www.scientificamerican.com\/article\/strange-but-true-infinity-comes-in-different-sizes\/\">Hint<\/a>)<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Watch this introductory video to <a href=\"https:\/\/www.khanacademy.org\/math\/old-integral-calculus\/power-series-ic\/power-series-intro-ic\/v\/power-series-radius-interval-convergence\">power series<\/a> by Khan Academy.\n<ul>\n<li>Explain in your own words what a power series is.<\/li>\n<li>How did the mathematicians in the <em>Quanta<\/em> article use a power series to solve their problem?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.youtube.com\/watch?v=_YjNEfZ0VqU&amp;ab_channel=Mathologer\">The Helicone Numberscope: Mathematical Superpowers Hidden in a Simple Toy<\/a><\/h3>\n<p>Mathologer, January 6, 2025<\/p>\n<p>In this YouTube video, the Mathologer (Monash University mathematician Burkard Polster) explores the mathematics behind a simple-looking toy called the helicone. By simulating much larger helicones, the Mathologer can discover which integers are good approximations to irrational numbers.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>irrational numbers, approximation, recreational math<\/em><\/p>\n<ul>\n<li>(Mid level) Before watching the video, find:\n<ul>\n<li>A rational number that is less than 0.01 away from $\\pi$<\/li>\n<li>A rational number that is less than 0.005 away from $\\frac{1 + \\sqrt{5}}{2}$<\/li>\n<li>A rational number with a denominator of 8 that best approximates $\\pi$. What is the error?<\/li>\n<li>A rational number with a denominator of 50 that best approximates $\\pi$. What is the error?<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Watch <a href=\"https:\/\/www.youtube.com\/watch?v=_YjNEfZ0VqU&amp;ab_channel=Mathologer\">the intro section<\/a> of the video. If possible, give students the opportunity to play with a real helicone.\n<ul>\n<li>The video explores a helicone where every leaf is at a specified angle from the one below it: Either the golden angle (about 137.5$^{\\circ}$) or 360$^{\\circ}$ times the fractional part of $\\pi$ (about 51$^{\\circ}$). Watch the video <a href=\"https:\/\/youtu.be\/_YjNEfZ0VqU?feature=shared&amp;t=1042\">from timestamp 17:22<\/a>, until timestamp 37:24.<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Research three examples of when approximating irrational numbers might be useful. You can search online, in books, or ask people you know. Share your examples with the class and discuss your reactions.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/en.as.com\/latest_news\/mathematician-explains-the-trick-of-the-envelope-system-the-formula-for-saving-more-than-2500-a-year-n\/\">Mathematician explains the trick of the \u201cenvelope system\u201d, the formula for saving more than \\$2,500 a year<\/a><\/h3>\n<p><em>Diario AS<\/em>, January 30, 2025<\/p>\n<p>\u201cWith a pack of envelopes, a pinch of discipline and some consistency, you can save over \\$2,500 in a year,\u201d writes William Allen in this article for Spanish sports publication <em>Diario AS<\/em>. The idea comes from Santi Garc\u00eda Cremades, mathematician at Universidad Miguel Hern\u00e1ndez de Elche. The technique: Using the envelopes, randomly select an even number between 2 and 100 each week. That\u2019s the number of dollars you save that week. Over 50 weeks, you\u2019ll save \\$2 + \\$4 + \\$6 + \\$8 + \u2026 + \\$100 = \\$2,550.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>probability, series<\/em><\/p>\n<ul>\n<li>(Mid level) Read the article. Allen writes: \u201cThe mathematical key lies in the sum of these numbers. Each pair of extremes (2 and 100, 4 and 98, etc.) adds up to 102, and with 25 pairs, the total accumulated at the end of the year is exactly 2,550.\u201d Write out this calculation in your own words, showing all your work.\n<ul>\n<li>What is the sum of all numbers from 1 to 100?<\/li>\n<li>What is the sum of all multiples of 3 from 3 to 600?<\/li>\n<li>(High level) In general, if <em>N<\/em> is a natural number, what is the sum of all numbers from 1 to <em>N<\/em>?<\/li>\n<\/ul>\n<\/li>\n<li>(High level, Probability) Imagine that you follow Garc\u00eda Cremades\u2019 savings technique. Each week, after you open your randomly chosen envelope, you throw that envelope away. Once you choose a specific number, you will never choose it again. This is called <strong>sampling without replacement<\/strong>. You could also try <strong>sampling with replacement<\/strong>. In this scenario, after you select your envelope and see what\u2019s inside, you put the envelope back into the pile.\n<ul>\n<li>If you sample with replacement, what is the maximum amount you could save over the course of 50 weeks? What is the minimum amount?<\/li>\n<li>What is the expected amount you\u2019ll save?<\/li>\n<li>What is the standard deviation of how much you\u2019ll save over 50 weeks?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.artnews.com\/art-news\/news\/what-is-brutalism-brutalist-architecture-art-1234730107\/\">What Is Brutalist Architecture, and Why Is It So Controversial?<\/a><\/h3>\n<p><em>Art News<\/em>, January 14, 2025<\/p>\n<p>The new movie \u201cThe Brutalist\u201d focuses on a fictional architect famous for his use of <strong>brutalist <\/strong>designs. Brutalism is a controversial style that conjures images of giant concrete buildings with square edges and minimal decorative flare. It\u2019s both visually imposing and minimalistic\u2014\u201ctwo things that have proven divisive with critics and the public alike, who have often found this aesthetic tough to admire,\u201d writes Alex Greenberger for <em>Art News.<\/em> This article explains the history of brutalism as an architectural trend that emphasizes utility over ornament.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>geometry, architecture<\/em><\/p>\n<ul>\n<li>(Mid level) Assume that concrete has the same volume in liquid and solid form. Answer the following questions:\n<ul>\n<li>Imagine building a cubic structure that measures 10 x 10 x 10 feet, with walls, floor and ceiling 12 inches thick. How many cubic feet of concrete would you need?<\/li>\n<li>Now imagine building a structure shaped like an equilateral triangle,\u00a0<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Triangular_prism.jpg\">as in this image<\/a>. If your triangular building has the floor area as the above rectangular room, how many cubic feet of concrete do you need?<\/li>\n<li>Repeat for a dome (flat floor and hemispherical ceiling and walls).<\/li>\n<li>Which design uses more concrete per usable area? Why?<\/li>\n<li>Suppose that you can change the wall and roof thickness of the design that requires more concrete in order to use the same amount of concrete as the more efficient design. Calculate the new wall thickness.<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Explain with math why brutalist architecture may be considered more functional than other approaches to design. Hint: think about the volume, surface area, building materials and complexity.<\/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.zmescience.com\/science\/theres-an-infinity-of-infinities-and-researchers-just-found-two-new-infinities-that-break-the-rules-of-math\/\">There\u2019s an infinity of infinities. And researchers just found two new infinities that break the rules of math<\/a><br \/>\n<em>ZME Science<\/em>, January 17, 2025<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/mathematicians-discover-new-way-for-spheres-to-kiss-20250115\/\">Mathematicians Discover New Way for Spheres to \u2018Kiss\u2019<\/a><br \/>\n<em>Quanta Magazine<\/em>, January 15, 2025<\/li>\n<li><a href=\"https:\/\/www.theroanokestar.com\/2025\/01\/11\/virginia-tech-mathematicians-target-data-center-inefficiency\/\">Virginia Tech Mathematicians Target Data Center Inefficiency<\/a><br \/>\n<em>The Roanoke Star<\/em>, January 11, 2025<\/li>\n<li><a href=\"https:\/\/www.bbc.com\/news\/articles\/c5y80n9jdj5o\">The Maths Queen with a quantum mission to mentor girls<\/a><br \/>\n<em>BBC<\/em>, January 10, 2025<\/li>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/2462654-maths-quirk-explains-why-crosswords-are-so-hard-until-they-arent\/\">Maths quirk explains why crosswords are so hard \u2013 until they aren&#8217;t<\/a><br \/>\n<em>New Scientist<\/em>, January 9, 2025<\/li>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/how-to-catch-prime-numbers\/\">How to \u2018Catch\u2019 Prime Numbers<\/a><br \/>\n<em>Scientific American<\/em>, January 6, 2025<\/li>\n<li><a href=\"https:\/\/www.popsci.com\/science\/hula-hoop-body-type\/\">Scientists identify the perfect hula hoop \u2018body type\u2019<\/a><br \/>\n<em>Popular Science<\/em>, January 2, 2025<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Peering Into a Bleak, &#8216;Uninsurable Future&#8217; Inside Climate News, January 17, 2025 At the beginning of this year, a series of wildfires in Southern California caused unprecedented destruction. More than 12,000 structures burned, contributing to a projected \\$250 billion of damage. Insurance companies typically reimburse homeowners for catastrophic natural disasters.<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-january-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_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":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[418,421,261,35,416,109,417,73,419,420],"class_list":["entry","author-leilasloman","post-3295","post","type-post","status-publish","format-standard","category-uncategorized","tag-approximation","tag-architecture","tag-derivatives","tag-geometry","tag-insurance","tag-irrational-numbers","tag-power-series","tag-probability","tag-recreational-math","tag-series"],"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\/3295","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=3295"}],"version-history":[{"count":4,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/3295\/revisions"}],"predecessor-version":[{"id":3299,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/3295\/revisions\/3299"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=3295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=3295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=3295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}