{"id":1254,"date":"2022-11-09T15:46:47","date_gmt":"2022-11-09T20:46:47","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=1254"},"modified":"2022-11-09T15:46:47","modified_gmt":"2022-11-09T20:46:47","slug":"math-digests-october-2022","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-october-2022\/","title":{"rendered":"Math Digests October 2022"},"content":{"rendered":"<h3><a id=\"1\" href=\"https:\/\/www.washingtonpost.com\/kidspost\/2022\/10\/05\/chocolate-shape-affects-taste\/\"><span style=\"font-weight: 400\">How to make a tastier chocolate? Use geometry.<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Washington Post<\/span><\/i><span style=\"font-weight: 400\">, October 5, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">What makes eating chocolate so satisfying? You may like the sweetness and creaminess of a milk chocolate. Maybe you like the sharp, rich bitterness of dark chocolate. To physicist Corentin Coulais, it\u2019s all about the crunch. Coulais is a physicist who has conducted research on how the shape of a chocolate bar increases its <\/span><i><span style=\"font-weight: 400\">brittleness<\/span><\/i><span style=\"font-weight: 400\">, which in turn improves its quality. In a recent experiment, Coulais 3D-printed chocolate in various zig-zagging and swirling shapes. The most zig-zagging spiral shape was the most crunchy\u2014and the one most preferred by Coulais\u2019 ten volunteers. \u201cA pleasurable eating experience doesn\u2019t only take place in the mouth, but can be affected by the noises in your skull,\u201d writes Galadriel Watson for the <\/span><i><span style=\"font-weight: 400\">Washington Post<\/span><\/i><span style=\"font-weight: 400\">. In this article, Watson describes the research project and why it may one day change the shape of the chocolate you can buy.<\/span><\/p>\n<p><b>Classroom Activities:<\/b> <i><span style=\"font-weight: 400\">brittle geometry, chocolate math<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Low level) Watch this <\/span><a href=\"https:\/\/www.youtube.com\/watch?v=z7tRr49qZfo\"><span style=\"font-weight: 400\">Infinite Chocolate<\/span><\/a><span style=\"font-weight: 400\"> math riddle for another example of tricky geometry with math. Discuss why this trick works.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Based on this image of the <\/span><a href=\"https:\/\/www.washingtonpost.com\/wp-apps\/imrs.php?src=https:\/\/arc-anglerfish-washpost-prod-washpost.s3.amazonaws.com\/public\/BSWX2PSAYQI63CE4NL2ZKEK7QI.jpg&amp;w=916\"><span style=\"font-weight: 400\">3D printed chocolates<\/span><\/a><span style=\"font-weight: 400\">, rank the shapes from most crunchy to least crunchy. Describe why you have ranked them this way.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Do you expect that an S-shaped chocolate would be more crunchy if it were thicker (more chocolate) or less thick? Why?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Geometry factors into the design of food in other ways as well. Imagine you are a chocolatier making a spicy chocolate entirely coated in chili powder. You make 1-ounce chocolates in three different shapes: a sphere, a flat bar, and a zig-zag (like Coulais\u2019 printed treat). Each of these shapes has the same volume and weight of chocolate. Which will be the spiciest? Discuss what factor from its geometry most influences the overall spiciness of its chili coating.<\/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=\"2\" href=\"https:\/\/www.bbc.com\/future\/article\/20221019-how-a-magician-mathematician-revealed-a-casino-loophole\"><span style=\"font-weight: 400\">How a magician-mathematician revealed a casino loophole<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">BBC Future<\/span><\/i><span style=\"font-weight: 400\">, October 19, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">In a friendly game of Go Fish, it might not matter how thoroughly you mix your deck of cards. But an incomplete shuffle can make all the difference in a high-stakes casino game. The question of how to randomize a deck so that gamblers can\u2019t take advantage of patterns in the cards is practical, but also mathematical. In 1992, mathematicians Dave Bayer and Persi Diaconis proved that it takes seven riffle shuffles to fully mix a deck. With six or fewer rounds of shuffling, the deck is still biased, but seven or more shuffles basically randomize it. Diaconis, who was a professional magician before pursuing statistics, has continued to work on the math of mixing cards: he even traveled to Las Vegas to assess a new card-shuffling machine, as Shane Keating describes in an article for <\/span><i><span style=\"font-weight: 400\">BBC Future<\/span><\/i><span style=\"font-weight: 400\">.<\/span><\/p>\n<p><b>Classroom Activities:<\/b> <i><span style=\"font-weight: 400\">probability, statistics, card games, computers<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Watch Persi Diaconis <\/span><a href=\"https:\/\/youtu.be\/AxJubaijQbI\"><span style=\"font-weight: 400\">explain how to shuffle a deck<\/span><\/a><span style=\"font-weight: 400\"> in a video for Numberphile.\u00a0<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Probability\/Statistics) In the video, Diaconis shows that if you take a standard deck of cards, mix it well, and ask someone to guess the identity of the top card, then do that for each card in the deck (where you reveal the top remaining card after each guess), you should expect the guesser to make about 4.5 correct guesses on average. With a partner, try playing this game with a set of 10 cards, such as the ace through 10 of a single suit. Record the number of cards you guessed correctly, then discuss your results with other students. Find the class average of the number of correct guesses from a deck of 10 cards.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Probability\/Statistics) Now, try a smaller version of Diaconis\u2019s probability computation from the video: in a well-mixed deck of just 10 cards, what is the expected average number of correct guesses? Hint: Diaconis starts describing the 52-card version of this computation <\/span><a href=\"https:\/\/youtu.be\/AxJubaijQbI?t=137\"><span style=\"font-weight: 400\">at time 2:17<\/span><\/a><span style=\"font-weight: 400\">.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) If you watched the video above and are interested in learning more about the seven shuffles, watch this <\/span><a href=\"https:\/\/youtu.be\/1jfm42Qd7Qw\"><span style=\"font-weight: 400\">Numberphile2 follow-up video with more details.<\/span><\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Probability\/Statistics; Advanced) Some magic tricks use a special kind of shuffling, called the perfect shuffle or faro shuffle, in which the deck is cut exactly in half and the cards are interspersed one by one so that the two halves alternate perfectly. Read the <\/span><a href=\"http:\/\/jwilson.coe.uga.edu\/emt725\/Shuffle\/Shuffle.html\"><span style=\"font-weight: 400\">explanation of perfect shuffles<\/span><\/a><span style=\"font-weight: 400\"> from Jim Wilson at the University of Georgia, then try to answer as many parts of Questions 1, 2, and 4 as possible. To model the shuffles, try experimenting with Excel spreadsheet linked to on the webpage or building your own spreadsheet.<\/span><\/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=\"3\" href=\"https:\/\/www.npr.org\/transcripts\/1129531931\"><span style=\"font-weight: 400\">Choose Your Own (Math) Adventure<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Short Wave From NPR, <\/span><\/i><span style=\"font-weight: 400\">October 18, 2022.<\/span><\/p>\n<p><span style=\"font-weight: 400\">In early 2020, mathematician Pamela Harris and some of her students posted a new paper online about parking functions, which let you assign a collection of cars to parking spots along a one-way street. The paper, called <\/span><a href=\"https:\/\/arxiv.org\/abs\/2001.04817?context=math.HO\"><span style=\"font-weight: 400\">&#8220;Parking Functions: Choose Your Own Adventure&#8221;<\/span><\/a><span style=\"font-weight: 400\">, was structured as an interactive experience. At various choice points, readers can decide what kinds of parking functions they want to study \u2014 and at the end of their adventure, they\u2019re rewarded with an unanswered question about parking functions. In this episode of <\/span><i><span style=\"font-weight: 400\">Short Wave<\/span><\/i><span style=\"font-weight: 400\">, Regina Barber interviews Harris about what inspired her and her students to write this unusual paper and the basics of the math involved.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">combinatorics<\/span><\/i><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">(Mid level) Harris calls combinatorics \u201cthe art of counting\u201d, and gives an example of counting the number of ways to make 37 cents out of change. For a slightly easier exercise, count the number of ways you can make 17 cents out of change. Write out your logic.<\/span><\/li>\n<li><span style=\"font-weight: 400\">(All levels) For a more thorough introduction to combinatorics, check out the Art of Problem Solving\u2019s <\/span><a href=\"https:\/\/artofproblemsolving.com\/videos\/counting\"><span style=\"font-weight: 400\">online videos<\/span><\/a><span style=\"font-weight: 400\">.<\/span><\/li>\n<li><span style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Read this description of the parking problem, adapted from Harris et. al.\u2019s paper:<\/span><\/span>Parking spots are lined up along one side of a one-way street, and cars arrive one at a time to park. A list of numbers represents the cars\u2019 parking preferences: If there are 3 parking spots and 3 cars, the list (2, 2, 1) means the first car arriving would like to park in the second spot it encounters, the second car would also like to park in the second spot, and the last car would like to park in the first spot. Cars drive up their favorite spot; if it\u2019s full, they keep driving until they find an empty spot. They can\u2019t turn around, so that once they\u2019ve passed a spot, they can no longer park there. If they pass all the spots without finding a place to park, they drive off and never return. The list of numbers is a parking function if every car is able to find a spot.\n<ul>\n<li><span style=\"font-weight: 400\">Harris and her students write that if there are 5 spots and 5 cars, then (1, 2, 4, 2, 2) is a parking function, while (1, 2, 2, 5, 5) isn\u2019t. Can you convince yourself if this is true? If so, explain why.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">For 3 spots and 3 cars, is (2, 2, 1) a parking function?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">For 3 spots and 3 cars, is (2, 2, 2) a parking function?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">For 3 spots and 3 cars, is (1, 1, 1) a parking function?<\/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><a id=\"4\" href=\"https:\/\/www.nature.com\/articles\/d41586-022-03166-w\"><span style=\"font-weight: 400\">DeepMind AI invents faster algorithms to solve tough maths puzzles<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Nature News<\/span><\/i><span style=\"font-weight: 400\">, October 5, 2022\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Think of the hardest math problem you\u2019ve ever seen. Perhaps it\u2019s a gnarly long division problem or a quadratic equation that seems impossible to factor. Maybe it\u2019s a long, repetitive matrix multiplication, where you multiply large grids of numbers. Whatever the challenge, the sequence of steps you take to solve it are <\/span><i><span style=\"font-weight: 400\">algorithms. <\/span><\/i><span style=\"font-weight: 400\">Mathematicians and scientists have realized that they can rely on computers and artificial intelligence to carry out complicated algorithms for their hardest problems. In this article, Matthew Hutson describes a new AI for matrix multiplication that goes one step further. Rather than just fly through the standard algorithm for matrix multiplication, this AI discovers faster, better algorithms itself. And now, the math world is eager to find out which other math problems it can tackle.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">matrix multiplication, algorithms<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Low level) Follow a real-life algorithm to <\/span><a href=\"https:\/\/code.org\/curriculum\/course2\/2\/Activity2-RealLifeAlgorithms.pdf\"><span style=\"font-weight: 400\">make a paper plane<\/span><\/a><span style=\"font-weight: 400\"> (from code.org). Discuss what you think would happen to your paper plane if you skipped or messed up one of the steps?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Create your own algorithm for drawing a picture of your choice. You can come up with any picture you like, but make sure your algorithm takes no more than 10 steps, and that others can follow it easily.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Read more about how to perform matrix multiplication on this <\/span><a href=\"https:\/\/www.mathsisfun.com\/algebra\/matrix-multiplying.html\"><span style=\"font-weight: 400\">Math is Fun tutorial<\/span><\/a><span style=\"font-weight: 400\">. Solve the example about selling pies, and do questions 1, 2, 3, and 8.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) The week after this AI discovery, two people beat its record. <\/span><a href=\"https:\/\/arstechnica.com\/information-technology\/2022\/10\/deepmind-breaks-50-year-math-record-using-ai-new-record-falls-a-week-later\/\"><span style=\"font-weight: 400\">Read more here<\/span><\/a><span style=\"font-weight: 400\">.<\/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:\/\/www.sciencenews.org\/article\/huijia-lin-cryptography-sn-10-scientists-to-watch\"><span style=\"font-weight: 400\">Huijia Lin proved that a master tool of cryptography is possible<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Science News, <\/span><\/i><span style=\"font-weight: 400\">September 29, 2022.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Researchers have shown that it\u2019s possible to create a tool that allows different people access to different information, while keeping data they don\u2019t need securely locked away. That concept, called indistinguishability obfuscation (or iO), contrasts with conventional digital security, in which those possessing a key or password have free reign over all the protected information. Elizabeth Quill covers the accomplishment \u2014 by Huijia Lin, Amit Sahai, and Aayush Jain \u2014 for <\/span><i><span style=\"font-weight: 400\">Science News<\/span><\/i><span style=\"font-weight: 400\">.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">cryptography, zero-knowledge proofs<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Quill writes that Lin was taken with cryptography as a graduate student, especially zero-knowledge proofs. Embedded in the article is a video of Amit Sahai explaining what a zero-knowledge proof is to 5 different people. Click <\/span><a href=\"https:\/\/youtu.be\/fOGdb1CTu5c?t=205\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\"> to watch the section where Sahai explains to a teen.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">In the clip, Sahai illustrates the idea of a zero-knowledge proof by reading out Daila\u2019s secret which she placed in a locked box. Come up with your own example of a zero-knowledge proof. Then partner up with a classmate and use your example to convince your classmate you know something, without revealing what it is.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">After trading your zero-knowledge proofs, answer these questions about your partner\u2019s example:<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Did they convince you?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Did they reveal any information they didn\u2019t mean to? If so, what?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Read your partner\u2019s feedback and improve your proof if necessary. Now, change partners and repeat the exercise again.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) For students interested in learning more about cryptography, Khan Academy has a <\/span><a href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/cryptography\"><span style=\"font-weight: 400\">cryptography unit online<\/span><\/a><span style=\"font-weight: 400\">. After learning about the Caesar cipher and frequency analysis, encode a secret message with it using the Caesar cipher exploration tool. Then trade messages with a partner and see if they can crack it using this <\/span><a href=\"https:\/\/www.101computing.net\/frequency-analysis\/\"><span style=\"font-weight: 400\">frequency analysis tool<\/span><\/a><span style=\"font-weight: 400\">.<\/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>Some more of this month&#8217;s math headlines:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/statistics-are-being-abused-but-mathematicians-are-fighting-back\/\">Statistics Are Being Abused, but Mathematicians Are Fighting Back<\/a><br \/>\n<em>Scientific American, <\/em>September 30, 2022<\/li>\n<li><a href=\"https:\/\/www.dailyprincetonian.com\/article\/2022\/10\/princeton-mathematics-professor-june-huh-macarthur-fellows\">Princeton mathematics professor June Huh and Melanie Matchett Wood GS \u201909 named 2022 MacArthur Fellows<\/a><br \/>\n<em>The Daily Princetonian, <\/em>October 13, 2022<\/li>\n<li><a href=\"https:\/\/www.standard.co.uk\/news\/uk\/ada-lovelace-day-mathematician-b1031781.html\">Ada Lovelace Day: who was the mathematician and what is she known for?<\/a><br \/>\n<em>Evening Standard<\/em>, October 11, 2022<\/li>\n<li><a href=\"https:\/\/pandaily.com\/mathematician-yitang-zhangs-pursuit-of-the-landau-siegel-zeros-conjecture\/\">Mathematician Yitang Zhang\u2019s Pursuit of the Landau-Siegel Zeros Conjecture<\/a><br \/>\n<em>Pandaily<\/em>, October 18, 2022<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>How to make a tastier chocolate? Use geometry. Washington Post, October 5, 2022 What makes eating chocolate so satisfying? You may like the sweetness and creaminess of a milk chocolate. Maybe you like the sharp, rich bitterness of dark chocolate. To physicist Corentin Coulais, it\u2019s all about the crunch. Coulais<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-october-2022\/\">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":[2],"tags":[7,159,157,100,160,18,35,158,161,73,84,162],"class_list":["entry","author-leilasloman","post-1254","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-algorithms","tag-card-games","tag-chocolate","tag-combinatorics","tag-computers","tag-cryptography","tag-geometry","tag-math","tag-matrix-multiplication","tag-probability","tag-statistics","tag-zero-knowledge-proofs"],"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\/1254","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=1254"}],"version-history":[{"count":13,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1254\/revisions"}],"predecessor-version":[{"id":1267,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1254\/revisions\/1267"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=1254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=1254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=1254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}