{"id":1556,"date":"2023-03-08T11:23:09","date_gmt":"2023-03-08T16:23:09","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=1556"},"modified":"2023-03-08T11:23:09","modified_gmt":"2023-03-08T16:23:09","slug":"math-digests-february-2023","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2023\/","title":{"rendered":"Math Digests February 2023"},"content":{"rendered":"<ul>\n<li><a href=\"#1\">The Quest to Find Rectangles in a Square<\/a><\/li>\n<li><a href=\"#2\">The Math Behind the Medals: Professor Ken Ono Is Helping Virginia Revolutionize Swimming Performance<\/a><\/li>\n<li><a href=\"#3\">What&#8217;s Going On in This Graph? LeBron James Breaks NBA Scoring Record.<\/a><\/li>\n<li><a href=\"#4\">Punxsutawney Phil\u2019s Groundhog Day prediction accuracy rate calculated<\/a><\/li>\n<li><a href=\"#5\">Even the Smartest Mathematicians Can&#8217;t Solve the Collatz Conjecture<\/a><\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/www.nytimes.com\/2023\/02\/07\/science\/puzzles-rectangles-mathematics.html\"><span style=\"font-weight: 400\">The Quest to Find Rectangles in a Square<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">The New York Times<\/span><\/i><span style=\"font-weight: 400\">, February 7, 2023.<\/span><\/p>\n<p><span style=\"font-weight: 400\">In December, mathematical physicist John Carlos Baez posted <\/span><a href=\"https:\/\/mathstodon.xyz\/@johncarlosbaez\/109511663915548794\"><span style=\"font-weight: 400\">a question about rectangles<\/span><\/a><span style=\"font-weight: 400\"> on the social network Mastodon. The problem was as follows. Take a square and break it into four rectangles, where the rectangles can be of any size and orientation, but must be \u201csimilar.\u201d In other words, the rectangles should all have the same proportions, that is, the same length-to-width ratio. Baez asked: how many different solutions are there? Since the original post, mathematicians and math enthusiasts around the world have shared their progress, chipping in with a combination of <\/span><a href=\"http:\/\/ianhenderson.org\/similar-rectangles\/\"><span style=\"font-weight: 400\">computer code<\/span><\/a><span style=\"font-weight: 400\"> and <\/span><a href=\"https:\/\/mathstodon.xyz\/@Lisanne\/109636809198760215\"><span style=\"font-weight: 400\">mathematical theory<\/span><\/a><span style=\"font-weight: 400\">. The unofficial team found 11 possible ways the rectangles can be proportioned in a solution, as Siobhan Roberts reports for the<em> New York Times<\/em>.<\/span><\/p>\n<p><b>Classroom Activities:<\/b> <i><span style=\"font-weight: 400\">geometry, ratios, irrational numbers<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Read the <\/span><a href=\"https:\/\/mathstodon.xyz\/@johncarlosbaez\/109511663915548794\"><span style=\"font-weight: 400\">original Mastodon post<\/span><\/a><span style=\"font-weight: 400\"> about the problem, where Baez shows three possible ways to break a square into three similarly proportioned rectangles.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Draw a square on a piece of paper. Try to divide it into four similar rectangles. Then discuss your ideas with another student. If you both found a solution, did you find the same one, or two different ones?\u00a0<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) Read the first two paragraphs in the beginning of Baez\u2019s <\/span><a href=\"https:\/\/johncarlosbaez.wordpress.com\/2022\/12\/22\/dividing-a-square-into-similar-rectangles\/\"><span style=\"font-weight: 400\">blog post<\/span><\/a><span style=\"font-weight: 400\"> on the problem, then take a look at the image with the three squares. (For this activity, it may help to have printouts of <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Plastic_number#\/media\/File:Plastic_square_partitions.svg\"><span style=\"font-weight: 400\">this image<\/span><\/a><span style=\"font-weight: 400\"> of the three squares.)<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Assume that the square has dimensions 1 unit by 1 unit. For the first two pictures, label the lengths of the sides of each rectangle. For a hint, note that Baez describes these rectangles\u2019 proportions in the two bullets under the image.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Now, read the third bullet under the image, along with the paragraph that begins \u201cWhat\u2019s $x$?\u201d Label the lengths of the sides of the rectangles in the third square, using \u201c$x$\u201d the way that Baez does in his description.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">For a challenge, read through the algebraic explanation of $x$, up through the line $\\rho^3 = \\rho + 1$. Discuss: Does it seem surprising to you that the height-to-width ratio of the rectangle is an irrational number? Why or why not?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Tamar Lichter Blanks<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.swimmingworldmagazine.com\/news\/the-math-behind-the-medals-professor-ken-ono-is-helping-virginia-revolutionize-swimming-performance\/\"><span style=\"font-weight: 400\">The Math Behind the Medals: Professor Ken Ono Is Helping Virginia Revolutionize Swimming Performance<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Swimming World Magazine<\/span><\/i><span style=\"font-weight: 400\">, January 31, 2023.<\/span><\/p>\n<p><span style=\"font-weight: 400\">In 2021, when members of the University of Virginia swim team attempted to qualify for the Beijing Olympics, they had a secret weapon: mathematician Ken Ono. They needed more than just muscles to swim faster than they ever had before. By combining sensors like accelerometers with mathematical analysis, Ono carefully studied the swimmers&#8217; form and suggested tweaks to improve their speed. One swimmer named Paige had ranked seventh in a 200-meter contest and eleventh in the 400-meter. Only the top six swimmers could advance, so she considered only focusing on the 200-meter. But Ono&#8217;s data revealed a different story: &#8220;I had been telling [UVA&#8217;s head coach] and Paige, you really want to be focusing on the 400,\u201d Ono told <\/span><i><span style=\"font-weight: 400\">Swimming World <\/span><\/i><span style=\"font-weight: 400\">writer Mathew De George. \u201cOur speculation was that Paige would have almost a near lock to make the Olympic team.&#8221; That prediction came true. This article describes Ono&#8217;s analysis and how he found this niche.\u00a0<\/span><\/p>\n<p><b>Classroom Activities:<\/b> <i><span style=\"font-weight: 400\">movement analysis,<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Install an accelerometer app on your cell phone (individually or in groups) with a \u201crecord\u201d function.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The forces graphed on this app should have three components: $x$, $y$, and $z$. Which dimensions\/directions of movement does each variable correspond to? (up and down, side to side, or forward and back)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Start a recording on the accelerometer. Place your phone in your hand and move it from side to side as if waving hello. The accelerometer will produce a chart showing force versus time. Based on this chart, how long does one side-to-side movement take?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Predict how the accelerometer graphs for $x$, $y$, and $z$ will look for the following movements and sketch them. Then perform the movement and compare the graph to your prediction.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">A full circle at constant speed (as if wiping a window)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">A full circle at constant speed (as if wiping a table)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">A zig zag motion facing you<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Max Levy<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/www.nytimes.com\/2023\/02\/09\/learning\/whats-going-on-in-this-graph-feb-15-2023.html\"><span style=\"font-weight: 400\">What&#8217;s Going On in This Graph?<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">The New York Times<\/span><\/i><span style=\"font-weight: 400\">, February 15, 2023.<\/span><\/p>\n<p><span style=\"font-weight: 400\">On February 7, the basketball player LeBron James scored the 38,388th point of his career. The achievement <\/span><a href=\"https:\/\/www.nytimes.com\/interactive\/2023\/02\/07\/sports\/basketball\/lebron-james-kareem-abdul-jabbar-points.html\"><span style=\"font-weight: 400\">made headlines<\/span><\/a><span style=\"font-weight: 400\">, as it meant James had broken the record for most career points in the NBA, previously held by Kareem Abdul-Jabbar. The<\/span><i><span style=\"font-weight: 400\"> Times\u2019 <\/span><\/i><span style=\"font-weight: 400\">analysis of the event included a graph showing how the 250 top scorers in the NBA accumulated points throughout their career, highlighting the line representing James. Two days later, the Learning Network posted the graph as part of their \u201cWhat\u2019s Going On in This Graph?\u201d series, which asks students to analyze and interpret a graph and post their thoughts for others to consider.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">data analysis, point-slope form<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Answer the four questions asked by the Learning Network in activity 1. When you\u2019re done, find a partner and share your answers. What did your partner pick up on that you didn\u2019t notice? What did your answers have in common?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Algebra) <\/span><a href=\"https:\/\/www.mathsisfun.com\/algebra\/line-equation-point-slope.html\"><span style=\"font-weight: 400\">Read this online lesson<\/span><\/a><span style=\"font-weight: 400\"> on point-slope form. Now, use the graph to apply it to real data. By eyeballing two data points from James\u2019 scoring graph, estimate the formula of the line. Repeat this with 3 different choices of points. Do the same for Abdul-Jabbar.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Print out the graph, and draw the lines whose formulas you estimated. How well do they match the data? Which choices of points created a line that best matched the data?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">James is 38 years old, four years younger than Abdul-Jabbar was when he retired. Using your formula, estimate how many points James will have if he plays until he\u2019s 42. How accurate do you think your guess is?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Algebra) Create your own graph with data you collect from your daily life. For example, you might use your phone to track how many steps you take each day, and graph your total steps for the week. After one week, repeat the activity above, finding a line and predicting what the total would be if you continued for three more days. After three more days, check how good your estimates were.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Leila Sloman<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.cleveland19.com\/2023\/02\/02\/punxsutawney-phils-groundhog-day-prediction-accuracy-rate-calculated\/\"><span style=\"font-weight: 400\">Punxsutawney Phil\u2019s Groundhog Day prediction accuracy rate calculated<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Cleveland19 News<\/span><\/i><span style=\"font-weight: 400\">, February 2, 2023.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Every year, a groundhog in Pennsylvania predicts the weather. Or at least, he tries to. If Phil sees his shadow on Groundhog Day, it is believed that there will be six more weeks of winter. The tradition dates back to the 1800s, and in 2023, Phil predicted that winter would stick around for another six weeks. \u201cTo verify whether or not his predictions have been accurate, we look at temperatures across the country during the months of February and March,\u201d writes Erika Paige, in an article for <\/span><i><span style=\"font-weight: 400\">Cleveland 19 News<\/span><\/i><span style=\"font-weight: 400\">. Paige questions the accuracy of Phil\u2019s predictions and describes her process for conducting the analysis. Since records have been kept, Phil has failed to see his shadow only 20 times. Over the last 30 years, Phil&#8217;s success rate is only around 37%.\u00a0<\/span><\/p>\n<p><b>Classroom Activities:<\/b> <i><span style=\"font-weight: 400\">data analysis, spreadsheets\u00a0\u00a0<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Transfer the table of data from the article into a spreadsheet, such as Microsoft Excel. Use spreadsheet functions to do or answer the following.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">In the last 20 years, how many times did Phil see his shadow? (Use equation functions, do not count manually)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">What percent of Phil\u2019s predictions of winter were correct in the last 20 years?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">What percent of Phil\u2019s \u201cspring\u201d predictions were correct, in the last 20 years?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Use the software\u2019s Conditional Formatting options to make all \u201cverified\u201d predictions green.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">What was the longest streak of verified predictions in the last 30 years?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) The article determines a \u201ctrue\u201d winter or spring based on whether the actual temperatures are warmer or colder than average for February and March. As a class, talk about whether you believe this is a fair classification or not. If not, then how would you change it? Do you expect that this change should increase Phil\u2019s calculated accuracy or decrease it?<\/span><\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Max Levy<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/science.howstuffworks.com\/math-concepts\/collatz-conjecture.htm\"><span style=\"font-weight: 400\">Even the Smartest Mathematicians Can&#8217;t Solve the Collatz Conjecture<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">HowStuffWorks<\/span><\/i><span style=\"font-weight: 400\">, February 14, 2023.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Pick a number, any number. If it\u2019s odd, multiply it by 3 and add 1. If it\u2019s even, divide it by 2. Apply this recipe again and again until you get 1. The Collatz conjecture states that this is guaranteed to happen, no matter what number you pick. But as Jesslyn Shields writes for <\/span><i><span style=\"font-weight: 400\">HowStuffWorks<\/span><\/i><span style=\"font-weight: 400\">, no one has actually been able to prove this \u2014 they\u2019ve only been able to check all the numbers that have 19 or fewer digits. There are still infinitely many numbers for which the conjecture is still unknown.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">sequences, proofs, programming<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) As Shields writes, the sequence of numbers you get by applying the Collatz recipe step-by-step is called the \u201cHailstone sequence\u201d. Find the Hailstone sequences that start with 1, 3, 20, and 13.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Imagine a simplified version of the recipe: At each step, multiply by 3 and add 1, whether the number is odd or even. What will happen if you apply this recipe over and over?<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">What if you divide by 2 at each step? What will happen if you apply that recipe over and over?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) Change the Collatz recipe so that if you get an odd number, you simply add 1. Re-calculate the sequences from the last activity with this change. Prove that with this recipe, you\u2019ll always end up with 1.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Now tweak the recipe so that if you get an odd number, you multiply by 2 and then add 1. Re-calculate the sequences from the last activity with this change. What\u2019s different about this sequence? What do you think will happen if you follow the sequence forever?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Programming) Write a computer program that applies the Collatz recipe to every integer between 1 and 100, and outputs the number of steps it took to reach 1. Describe the results. Do they make you more or less convinced that the conjecture is true?<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Shields writes: \u201c[Terence Tao]&#8217;s results point to a new method for approaching the problem and note how rare it would be for a number to diverge from the Collatz rule. Rare, but not necessarily nonexistent.\u201d Is this consistent with the data from your program?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Leila Sloman<\/span><\/i><\/p>\n<hr \/>\n<h3>Some more of this month&#8217;s math headlines:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.smithsonianmag.com\/history\/history-monkey-bars-180981556\/\">The Surprisingly Scientific Roots of Monkey Bars<\/a><br \/>\n<em>Smithsonian Magazine<\/em>, March 2023.<\/li>\n<li><a href=\"https:\/\/www.bbc.com\/travel\/article\/20230222-nalanda-the-university-that-changed-the-world\">Nalanda: The university that changed the world<\/a><br \/>\n<em>BBC Travel<\/em>, February 23, 2023.<\/li>\n<li><a href=\"https:\/\/www.nature.com\/articles\/d41586-023-00487-2\">How will AI change mathematics? Rise of chatbots highlights discussion<\/a><br \/>\n<em>Nature<\/em>, February 17, 2023.<\/li>\n<li><a href=\"https:\/\/theconversation.com\/cancer-evolution-is-mathematical-how-random-processes-and-epigenetics-can-explain-why-tumor-cells-shape-shift-metastasize-and-resist-treatments-199398\">Cancer evolution is mathematical \u2013 how random processes and epigenetics can explain why tumor cells shape-shift, metastasize and resist treatments<\/a><br \/>\n<em>The Conversation<\/em>, February 10, 2023.<\/li>\n<li><a href=\"https:\/\/www.popsci.com\/environment\/machine-learning-bird-migration\/\">No one can predict exactly where birds go, but this mathematical model gets close<\/a><br \/>\n<em>Popular Science<\/em>, February 1, 2023.<\/li>\n<li><a href=\"https:\/\/fortune.com\/2023\/01\/30\/artificial-intelligence-cant-solve-all-problems-computer-scientist-says\/\">ChatGPT might be taking over the internet, but a computer scientist explains why some problems are still too hard to solve\u2014even for AI<\/a><br \/>\n<em>Fortune<\/em>, January 30, 2023.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The Quest to Find Rectangles in a Square The Math Behind the Medals: Professor Ken Ono Is Helping Virginia Revolutionize Swimming Performance What&#8217;s Going On in This Graph? LeBron James Breaks NBA Scoring Record. Punxsutawney Phil\u2019s Groundhog Day prediction accuracy rate calculated Even the Smartest Mathematicians Can&#8217;t Solve the Collatz<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2023\/\">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":[19,35,109,190,191,74,193,113,80,192],"class_list":["entry","author-leilasloman","post-1556","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-data-analysis","tag-geometry","tag-irrational-numbers","tag-movement-analysis","tag-point-slope-form","tag-programming","tag-proofs","tag-ratios","tag-sequences","tag-spreadsheets"],"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\/1556","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=1556"}],"version-history":[{"count":6,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1556\/revisions"}],"predecessor-version":[{"id":1562,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1556\/revisions\/1562"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=1556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=1556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=1556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}