{"id":2411,"date":"2024-06-21T08:00:13","date_gmt":"2024-06-21T12:00:13","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=2411"},"modified":"2024-06-20T15:44:05","modified_gmt":"2024-06-20T19:44:05","slug":"math-digests-may-2024","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-may-2024\/","title":{"rendered":"Math Digests May 2024"},"content":{"rendered":"<ul>\n<li><a href=\"#1\">Mathematics for social justice in <em>Nature News<\/em><\/a><\/li>\n<li><a href=\"#2\">New trigonometric proofs of the Pythagorean theorem on <em>60 Minutes<\/em><\/a><\/li>\n<li><a href=\"#3\">The Monty Hall problem on Radio New Zealand<\/a><\/li>\n<li><a href=\"#4\">Applying number theory to 276 leads to a mysterious integer sequence in Numberphile<\/a><\/li>\n<li><a href=\"#5\">Connecting number theory to geometry in <em>Quanta<\/em><\/a><\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/www.nature.com\/articles\/d41586-024-01494-7\">Can mathematicians help to solve social-justice problems?<\/a><\/h3>\n<p><em>Nature News<\/em>, May 22, 2024.<\/p>\n<p>In this article for <em>Nature<\/em>, Rachel Crowell discusses the work of several mathematicians who have brought their quantitative skills to bear on social justice issues \u2014 from developing a tool that helps residents of Rhode Island\u2019s Woonasquatucket River Watershed find healthcare resources to exploring the dependencies among Sustainable Development Goals set by the United Nations. \u201cMathematicians can experience first-hand the messiness and complexity \u2014 and satisfaction \u2014 of applying maths to problems that affect people and their communities,\u201d writes Crowell.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>statistics, data science<\/em><\/p>\n<ul>\n<li>(All levels) Read the article. Choose one of the featured projects and describe how mathematics helps the relevant social justice cause.\n<ul>\n<li>(Mid level) Identify a social justice cause you care about. How might mathematics be helpful in studying it?<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Navigate to the CDC\u2019s interactive <a href=\"https:\/\/www.cdc.gov\/vaccines\/imz-managers\/coverage\/covidvaxview\/interactive\/adult-coverage-vaccination.html\">CovidVaxView<\/a> page for adults. View Figure 3A. This figure shows the percent of a population over time that has received the latest Covid-19 booster. Under \u201cJurisdiction,\u201d select \u201cNational.\u201d For each of the following \u201cDemographics\u201d selections, plot the 95% confidence intervals of the most recent figures. Then, interpret the results. Which of the demographic differences are statistically significant?\n<ul>\n<li>\u201cDisability Status\u201d<\/li>\n<li>\u201cGender Identity\u201d<\/li>\n<li>\u201cHealth Insurance\u201d<\/li>\n<li>\u201cPoverty Status\u201d<\/li>\n<li>\u201cRace\/Ethnicity\u201d<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Try these statistics activities on the relationship between earnings, education, and gender from the US Census Bureau\u2019s Statistics in Schools program: <a href=\"https:\/\/www.census.gov\/programs-surveys\/sis\/activities\/math\/line-to-data.html\">One on plotting and analyzing scatterplots<\/a> for 8<sup>th<\/sup> graders, and <a href=\"https:\/\/www.census.gov\/programs-surveys\/sis\/activities\/math\/earnings.html\">one interpreting box plots<\/a> for 9<sup>th<\/sup> graders.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.cbsnews.com\/news\/teens-come-up-with-trigonometry-proof-for-pythagorean-theorem-60-minutes-transcript\/\">Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries<\/a><\/h3>\n<p><em>60 Minutes<\/em>, May 5, 2024.<\/p>\n<p>Last year, two teenagers from New Orleans announced a rare trigonometric proof of the Pythagorean theorem, which states that a right triangle\u2019s hypotenuse squared equals the sum of its shorter sides squared ($a^2 + b^2 = c^2$). Many trigonometric principles depend on the Pythagorean theorem, so some mathematicians once thought using these principles was self-referential. In this <em>60 Minutes<\/em> segment, the two students describe their work and achievement in discovering up to five new proofs.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>trigonometry, algebra<\/em><\/p>\n<ul>\n<li>(All levels) Read more about the teens\u2019 proof presented last year in <a href=\"https:\/\/www.scientificamerican.com\/article\/2-high-school-students-prove-pythagorean-theorem-heres-what-that-means\/\">this <\/a><a href=\"https:\/\/www.scientificamerican.com\/article\/2-high-school-students-prove-pythagorean-theorem-heres-what-that-means\/\"><em>Scientific American <\/em><\/a><a href=\"https:\/\/www.scientificamerican.com\/article\/2-high-school-students-prove-pythagorean-theorem-heres-what-that-means\/\">article<\/a>. (Note: The <em>Scientific American <\/em>article was written by the editor of this column.)\n<ul>\n<li>Describe in your own words the flaw in using the equation $\\sin^2(\\theta) + \\cos^2(\\theta) = 1$ to prove the Pythagorean theorem.<\/li>\n<li>Complete the <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-march-2023\/#4\">AMS activities<\/a> based on the initial news from last year<a href=\"https:\/\/www.scientificamerican.com\/article\/2-high-school-students-prove-pythagorean-theorem-heres-what-that-means\/\">.<\/a><\/li>\n<\/ul>\n<\/li>\n<li>(High level) Follow along with the students\u2019 \u201cwaffle cone\u201d proof in the 60 Minutes video and go deeper with this <a href=\"https:\/\/www.youtube.com\/watch?v=p6j2nZKwf20\">step-by-step video from Polymathematic<\/a>.\n<ul>\n<li>Why does the proof require reflecting the initial right triangle? (Hint: Can you create the \u201cwaffle cone\u201d without doing so?)<\/li>\n<li>What is the law of sines, and how does it enable this proof?<\/li>\n<li>Explain why using \u201csimilar\u201d right triangles allows Johnson to draw a general conclusion for her proof. (Hint: think of convergent infinite series.)<\/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.rnz.co.nz\/national\/programmes\/nights\/audio\/2018939718\/call-a-mathematician-we-ve-got-a-monty-hall-problem\">Call a mathematician, we&#8217;ve got a Monty Hall problem<\/a><\/h3>\n<p><em>RNZ<\/em>, May 23, 2024.<\/p>\n<p>In the famous Monty Hall Problem, you are a contestant on a fictitious game show. In front of you are three closed doors, labeled 1, 2, and 3. One of the doors \u2014 you must guess which \u2014 conceals a valuable prize. To start, you choose a door. The game show host responds by opening one of the other two doors to reveal there is no prize behind it. You now get a chance to make your final guess: Stay with your first guess, or switch? On May 23, mathematician Chris Tuffley joined Radio New Zealand to explain what the right choice is, and why.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>probability<\/em><\/p>\n<ul>\n<li>(All levels) Before learning the solution to the Monty Hall Problem, answer the following questions individually. Then, discuss answers as a class. After a brief discussion, vote on the right answers.\n<ul>\n<li>Should you switch your choice? Why or why not?<\/li>\n<li>At the beginning of the game, what is the probability that your first choice is the right answer?<\/li>\n<li>Does this change after the host makes the reveal? Why or why not?<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Split into pairs and play 6 rounds of the Monty Hall Problem with your partner, using a quarter hidden underneath one of three plastic cups. Take turns playing the host. Jot down anything you notice while playing. (You can also use <a href=\"https:\/\/www.ms.uky.edu\/algebracubed\/lessons\/monty_hall_lesson.pdf\">this lesson plan<\/a>, in which students play the game on a simulator <a href=\"https:\/\/www.rossmanchance.com\/applets\/2021\/montyhall\/Monty.html\">such as this one<\/a> and track the results.)\n<ul>\n<li>Revisit the questions from the previous exercise and vote again if it seems like the class\u2019s perspective has changed.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Read Keith Ellis\u2019s <a href=\"https:\/\/www.montyhallproblem.com\/\">explanation of the solution<\/a>. Write out the reasoning in your own words. Read <a href=\"https:\/\/www.nytimes.com\/1991\/07\/21\/us\/behind-monty-hall-s-doors-puzzle-debate-and-answer.html\">this article<\/a> about how mathematicians and scientists reacted to this counterintuitive problem in 1990.<\/li>\n<li>(Mid level) Consider a variant of the Monty Hall Problem in which the placement of the prize is not totally random. How does the optimal strategy change if everything stays the same, but at the beginning of the game:\n<ul>\n<li>There is a 50% chance the prize is behind Door 1, a 25% chance it\u2019s behind Door 2, and a 25% chance it\u2019s behind Door 3<\/li>\n<li>There is a 40% chance the prize is behind Door 1, a 30% chance it\u2019s behind Door 2, and a 30% chance it\u2019s behind Door 3<\/li>\n<li>There is a 20% chance the prize is behind Door 1, a 30% chance it\u2019s behind Door 2, and a 50% chance it\u2019s behind Door 3<\/li>\n<li>There is a 20% chance the prize is behind Door 1, a 40% chance it\u2019s behind Door 2, and a 40% chance it\u2019s behind Door 3<\/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=\"4\" href=\"https:\/\/www.youtube.com\/watch?v=OtYKDzXwDEE\">An amazing thing about 276<\/a><\/h3>\n<p><em>Numberphile<\/em>, May 1, 2024.<\/p>\n<p>Is any single number more special than the rest? It depends on what question you ask. For mathematician Ben Sparks, the number 276 stands out. It\u2019s not because 276 is an even number or a \u201ctriangular\u201d number. It\u2019s because of a special application of number theory called an aliquot sequence, in which you sum a number\u2019s divisors (excluding itself), then sum <em>that<\/em> number\u2019s divisors, and so on. Under this procedure, Spark\u2019s number packs a strange surprise. In this <em>Numberphile<\/em> video, Sparks explains the aliquot sequence process and plots the results to reveal surprising mathematical behaviors.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>aliquot sequences<\/em><\/p>\n<ul>\n<li>(All levels) Using only pen and paper, write the aliquot sequences for the following numbers: 10, 33, 15, 100.\n<ul>\n<li>Which number has the longest sequence?<\/li>\n<li>Was this surprising? Describe in your own words what factor(s) allow some numbers to have longer or shorter sequences than others.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Use this <a href=\"https:\/\/www.geogebra.org\/m\/bkpq8uqp\">GeoGebra program<\/a> to generate and plot the aliquot sequences for the numbers below.\n<ul>\n<li>79<\/li>\n<li>30<\/li>\n<li>220<\/li>\n<li>1264460<\/li>\n<li>119<\/li>\n<li>Find the definitions of <strong>perfect<\/strong>,<strong> abundant<\/strong>,<strong> amicable<\/strong>, and<strong> sociable<\/strong> numbers in <a href=\"https:\/\/math.dartmouth.edu\/~carlp\/upintconf.pdf\">this resource from Dartmouth University<\/a>, and say which word applies to each number above.<\/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.quantamagazine.org\/a-rosetta-stone-for-mathematics-20240506\/\">A Rosetta Stone for Mathematics<\/a><\/h3>\n<p><em>Quanta Magazine<\/em>, May 6, 2024.<\/p>\n<p>More than 80 years ago, French mathematician Andr\u00e9 Weil first wrote about a surprising connection between two disparate fields of mathematics: geometry and number theory. Weil\u2019s \u201cRosetta stone\u201d connected the two topics with a third, the study of finite fields: \u201cFinite fields are a place where number theory and geometry begin to blend,\u201d writes Kevin Hartnett. In this <em>Quanta Magazine <\/em>article, Hartnett tells the story of Weil\u2019s discovery and how it laid the groundwork for the Langlands program, a \u201cgrand project to unify disparate fields of mathematics.\u201d<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>number theory, geometry, finite fields<\/em><\/p>\n<ul>\n<li>(Mid level) Based on the reading and your own online searching, describe each of these areas of math in your own words, and write a simple example problem related to each.\n<ul>\n<li>Geometry<\/li>\n<li>Number theory<\/li>\n<li>Finite fields<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Write three different polynomial expressions that can be written in a finite field with the elements <strong>0<\/strong> and <strong>1<\/strong>.\n<ul>\n<li>Write the binary form of each polynomial, as described in the article. What whole number does each binary form correspond to?<\/li>\n<li>What polynomial expression in this field would correspond to the whole number <strong>121<\/strong>?<\/li>\n<li>Are the polynomials you listed irreducible or reducible? Explain.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/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.co.uk\/teach\/microbit\/articles\/z2sgjfr\">Five times numbers helped us make sense of the world<\/a><br \/>\n<em>BBC Teach<\/em>.<\/li>\n<li><a href=\"https:\/\/www.cambridge-news.co.uk\/news\/cambridge-news\/cambridge-code-breaker-played-keira-29255556\">Cambridge code-breaker played by Keira Knightley in The Imitation Game gets blue plaque<\/a><br \/>\n<em>Cambridge News<\/em>, May 29, 2024.<\/li>\n<li><a href=\"https:\/\/www.nature.com\/articles\/d41586-024-01563-x\">How mathematician Freeman Hrabowski opened doors for Black scientists<\/a><br \/>\n<em>Nature Podcast<\/em>, May 28, 2024.<\/li>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/mg26234921-400-what-are-fractals-and-how-can-they-help-us-understand-the-world\/\">What are fractals and how can they help us understand the world?<\/a><br \/>\n<em>New Scientist<\/em>, May 21, 2024.<\/li>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/2431964-incredible-maths-proof-is-so-complex-that-almost-no-one-can-explain-it\/\">Incredible maths proof is so complex that almost no one can explain it<\/a><br \/>\n<em>New Scientist<\/em>, May 20, 2024.<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/strangely-curved-shapes-break-50-year-old-geometry-conjecture-20240514\/\">Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture<\/a><br \/>\n<em>Quanta Magazine<\/em>, May 14, 2024.<\/li>\n<li><a href=\"https:\/\/www.nature.com\/articles\/d41586-024-01413-w\">Why mathematics is set to be revolutionized by AI<\/a><br \/>\n<em>Nature<\/em>, May 14, 2024.<\/li>\n<li><a href=\"https:\/\/www.snexplores.org\/article\/scientists-say-correlation-causation-definition-pronunciation\">Scientists Say: Correlation and Causation<\/a><br \/>\n<em>Science News Explores<\/em>, May 13, 2024.<\/li>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/the-mathematical-case-for-monkeys-producing-shakespeare-eventually\/\">The Mathematical Case for Monkeys Producing Shakespeare\u2014Eventually<\/a><br \/>\n<em>Scientific American<\/em>, May 7, 2024.<\/li>\n<li><a href=\"https:\/\/theconversation.com\/why-are-algorithms-called-algorithms-a-brief-history-of-the-persian-polymath-youve-likely-never-heard-of-229286\">Why are algorithms called algorithms? A brief history of the Persian polymath you\u2019ve likely never heard of<\/a><br \/>\n<em>The Conversation<\/em>, May 7, 2024.<\/li>\n<li><a href=\"https:\/\/www.snexplores.org\/article\/math-cake-cutting-fairness-sharing\">Cake-cutting math offers lessons that go far beyond dessert plates<\/a><br \/>\n<em>Science News Explores<\/em>, May 2, 2024.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Mathematics for social justice in Nature News New trigonometric proofs of the Pythagorean theorem on 60 Minutes The Monty Hall problem on Radio New Zealand Applying number theory to 276 leads to a mysterious integer sequence in Numberphile Connecting number theory to geometry in Quanta Can mathematicians help to solve<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-may-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_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":[],"class_list":["entry","author-leilasloman","post-2411","post","type-post","status-publish","format-standard","category-uncategorized"],"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\/2411","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=2411"}],"version-history":[{"count":9,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2411\/revisions"}],"predecessor-version":[{"id":2424,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/2411\/revisions\/2424"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=2411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=2411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=2411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}