{"id":808,"date":"2022-04-05T11:52:25","date_gmt":"2022-04-05T15:52:25","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=808"},"modified":"2022-06-28T11:55:44","modified_gmt":"2022-06-28T15:55:44","slug":"math-digests-march-2022","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-march-2022\/","title":{"rendered":"Math Digests March 2022"},"content":{"rendered":"<h3><a id=\"1\" href=\"https:\/\/dotesports.com\/general\/news\/how-to-play-nerdle-a-math-based-version-of-wordle\">How to play Nerdle, a math-based version of Wordle<\/a><\/h3>\n<p><em>Dot Esports<\/em>, February 28, 2022<\/p>\n<p>It was only a matter of time until someone came up with an even nerdier version of Wordle, the viral word game. Enter: <em>Nerdle<\/em>. Data scientist Richard Mann created Nerdle for people who enjoy math games, according to writer Sage Datuin. In Nerdle, players guess <em>equations <\/em>instead of words. Each equation contains digits, operations ($+$, $-$, $\\times$, and\/or $\\div$), and one equals sign. Players must guess equations until they have the right pieces to find the mystery equation. Much like Wordle, you only get 6 guesses, and each guess has to be mathematically correct\u2014or else the game will tell you, \u201cThis guess does not compute!\u201d In this article, Datuin highlights the differences between Nerdle and Wordle and shares some tips on how to win.<\/p>\n<p><strong>Classroom activities:<\/strong> <em>Nerdle, combinatorics<\/em><\/p>\n<ul>\n<li>(All levels) Play <a href=\"https:\/\/nerdlegame.com\/\">Nerdle<\/a> individually or as a class. For an easier game, go to the menu and select \u201cmini-Nerdle\u201d to activate a smaller board. Discuss what makes the game hard and what strategies you can use to solve the puzzle in as few guesses as possible.<\/li>\n<li>(Algebra, Statistics) Wordle relies on a fixed dictionary containing 2,315 possible words, but how many different equations are possible in Nerdle? For simplicity, let\u2019s assume that the format will always be a sum or product of two two-digit numbers, and that a three-digit solution is ok, such as 12+34=46 or 12$\\times$34=408.\n<ul>\n<li>Consider the spaces on the left side of the equation that contain digits\u2014how many are there, and how many options do we have to fill them?<\/li>\n<li>Next, how many options do we have for the operation? Now, combine these measures according to the <a href=\"https:\/\/www.mathsisfun.com\/data\/basic-counting-principle.html\">Fundamental Counting Principle<\/a>.<\/li>\n<li>Discuss why we don\u2019t need to count the permutations of the digits on the right side of the equals sign.<\/li>\n<li>(Advanced) How does the calculation change if we allow subtraction? What about division?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.quantamagazine.org\/what-a-math-party-game-tells-us-about-graph-theory-20220324\/\">What a Math Party Game Tells Us About Graph Theory<\/a><\/h3>\n<p><em>Quanta Magazine<\/em>, March 24, 2022<\/p>\n<p>Is it possible for every person at a party to shake hands with an odd number of people? Patrick Honner suggests you try it out at your next social gathering. In this article, he explains the solution using the tools of graph theory. The puzzle connects to the concept of subgraphs, which is an open area of research. The latest advance in <a href=\"https:\/\/www.quantamagazine.org\/mathematicians-answer-old-question-about-odd-graphs-20210519\/\">describing odd subgraphs<\/a>, Honner writes, came just last year.<\/p>\n<p><strong>Classroom activities: <\/strong><em>graph theory, even and odd numbers<\/em><\/p>\n<ul>\n<li>(All levels) Before students read the article, split them into groups of 5 or 6 and ask them to try to shake hands with an odd number of people. (You can use elbow bumps or verbal greetings instead.)\n<ul>\n<li>Draw graphs representing each group\u2019s handshakes.<\/li>\n<li>Discuss which groups were able to succeed and why, using the idea of a graph\u2019s \u201cdegree sum.\u201d<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Watch <a href=\"https:\/\/www.youtube.com\/watch?v=VvCytJvd4H0\">this 3Blue1Brown video<\/a> about the three-utilities problem, another popular puzzle in graph theory.\n<ul>\n<li>The three-utilities problem is impossible on a flat surface, but a solution <em>does <\/em>exist on a coffee mug. Why doesn\u2019t a similar trick work for the shaking hands puzzle?<\/li>\n<\/ul>\n<\/li>\n<li>(Upper level) Complete the exercises at the end of the article (answers are provided).<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Scott Hershberger<\/em><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/scienceline.org\/2022\/03\/inside-the-fight-to-protect-your-data-from-quantum-computers\/\">Inside the fight to protect your data from quantum computers<\/a><\/h3>\n<p><em>Scienceline<\/em>, March 4, 2022<\/p>\n<p>Every computer you own is in a sense the same under the hood: Desktops, laptops, and phones all run on the same kind of math. Encryption is designed with this in mind. But quantum computers are different, exploiting properties of quantum physics to do their calculations. This allows them to solve certain problems that have been the basis of cryptography until now, such as factoring large numbers efficiently. Quantum computers are <a href=\"https:\/\/www.nature.com\/articles\/d41586-021-03476-5\">hard to build<\/a>\u2014they require <a href=\"https:\/\/quantum-computing.ibm.com\/composer\/docs\/iqx\/guide\/the-qubit#:~:text=we%20must%20keep%20the%20temperature%20extremely%20cold%20(15%20millikelvin%20in%20a%20dilution%20refrigerator)\">extremely cold metals<\/a> and other specialized engineering\u2014but if they get big enough, they\u2019ll be able to break much of the encryption that keeps digital communications private. The US National Institute of Standards and Technology is <a href=\"https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\">running a competition<\/a> to find new methods of encryption that are safe against both regular and quantum computers. Most of the finalists rely on mathematical objects known as lattices, as Daniel Leonard writes in <em>Scienceline<\/em>.<\/p>\n<p><strong>Classroom activities:<\/strong> <em>cryptography, quantum computing, number theory<\/em><\/p>\n<ul>\n<li>(All levels) Work in pairs through the lattice-based encryption algorithm described in the <a href=\"https:\/\/scienceline.org\/2022\/03\/inside-the-fight-to-protect-your-data-from-quantum-computers\/\">graphic in Leonard\u2019s article<\/a>.\n<ul>\n<li>One person, You, should choose a secret number $S$ and perform Steps 1\u20133 and the first part of Step 4.<\/li>\n<li>The other person, Friend, should choose a secret message, $0$ or $1$, and under Step 4 carry out Friend\u2019s Steps 1 and 2 (labeled in blue).<\/li>\n<li>You should then use Steps 5\u20136 to uncover the secret message.<\/li>\n<li>You and Friend exchange roles and repeat the above steps so that each can try both sides of the algorithm.<\/li>\n<li>You and Friend share the public steps\u2014the first part of Step 4 and Friend\u2019s (blue) Step 2\u2014with another pair of students. Can they determine what secret message Friend sent? If not, what missing piece of information would allow them to find out the message?<\/li>\n<\/ul>\n<\/li>\n<li>(Advanced) Watch a video by minutephysics about <a href=\"https:\/\/www.youtube.com\/watch?v=lvTqbM5Dq4Q\">how quantum computers break encryption.<\/a>\n<ul>\n<li>Check the \u201c<a href=\"https:\/\/www.youtube.com\/watch?v=lvTqbM5Dq4Q&amp;t=682s\">repeating property<\/a>\u201d used in Shor\u2019s Algorithm for $g=5$, $N=31$, and $p=3$ by showing that $5$, $5^4$, and $5^7$ all have the same remainder after dividing by $31$.<\/li>\n<li>Show that for any integers $g$, $N$, and $p$ satisfying the equation $g^p = m \\cdot N + 1$ for some integer $m$, the numbers $g^{x+p}$ and $g^x$ have the same remainder after dividing by $N$ (where $x$ is any integer). <em>(Hint: use the fact that $g^{x+p} = g^x \\cdot g^p$.)<\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong><em>Related Mathematical Moments: <\/em><\/strong><a href=\"https:\/\/www.ams.org\/publicoutreach\/mathmoments\/mm158-post-quantum-cryptography\"><strong>Securing Data in the Quantum Era<\/strong><\/a><strong>.<\/strong><\/p>\n<p style=\"text-align: right\"><em>\u2014Tamar Lichter Blanks<\/em><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.scientificamerican.com\/article\/math-is-more-than-just-numbers-celebrate-pi-day-a-different-way1\/\">Math Is More Than Just Numbers: Celebrate Pi Day a Different Way<\/a><\/h3>\n<p><em>Scientific American<\/em>, March 14, 2022<\/p>\n<p>March 14, or $\\pi$ (Pi) Day, has turned $\\pi$ into the most famous number. Writing in <em>Scientific American<\/em>, mathematician Alissa S. Crans takes issue with pi\u2019s fame. \u201cI\u2019m tickled that honoring something mathematical has become a widespread phenomenon,&#8221; she writes. &#8220;But, at the same time, I\u2019m disappointed that this numerical celebrity seems to be somewhat of an accident.&#8221; Crans wants people to understand that math is more than just weird numbers. Math is full of fascinating mysteries and clever solutions to deceptively hard problems. In that spirit, the International Mathematical Union has turned March 14 into the annual <a href=\"https:\/\/www.idm314.org\/\">International Day of Mathematics<\/a>. In this article, Crans shares examples of other fascinating facets of math worth celebrating every March.<\/p>\n<p><strong>Classroom activities:<\/strong> <em>pi<\/em>, <em>cake-cutting, irrational numbers, infinity<\/em><\/p>\n<ul>\n<li>(All levels) Explore all the ways that NASA uses $\\pi$ <a href=\"https:\/\/www.jpl.nasa.gov\/edu\/learn\/list\/oh-the-places-we-go-18-ways-nasa-uses-pi\/\">to solve its space travel problems<\/a>.\n<ul>\n<li>(Geometry) Solve <a href=\"https:\/\/www.jpl.nasa.gov\/edu\/pdfs\/piday2015_dawn_handout.pdf\">this puzzle<\/a> about a space probe photographing a dwarf planet in our solar system.<\/li>\n<li>(All levels) Check out NASA\u2019s <a href=\"https:\/\/www.jpl.nasa.gov\/edu\/nasapidaychallenge\/\">many other $\\pi$-related puzzles<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Crans writes that math can teach you the scientifically perfect way of cutting a cake so that every person gets the same amount, with the fewest cuts. Watch <a href=\"https:\/\/youtu.be\/kaMKInkV7Vs\">this Numberphile video<\/a> about the cake-cutting problem to see how this works.<\/li>\n<li>(High level) The decimal representation of $\\pi$ contains a non-repeating sequence of digits after its decimal point because it is an irrational number. But Crans notes that $\\pi$ is not special in this regard. She writes: &#8220;If you asked a genie to choose a number truly at random, the likelihood it would pick an irrational number is 100 percent!&#8221; Discuss why this is true. <em>(Hint: it has to do with <a href=\"https:\/\/plus.maths.org\/content\/maths-minute-counting-numbers\">different sizes of infinity<\/a> and the fact that the rational numbers <a href=\"https:\/\/www.youtube.com\/watch?v=cyW5z-M2yzw\">have measure zero<\/a>.)<\/em><\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3>Some more of this month\u2019s math headlines:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.quantamagazine.org\/in-music-and-math-lillian-pierce-builds-landscapes-20220330\/\"><strong>In Music and Math, Lillian Pierce Builds Landscapes<\/strong><\/a><br \/>\n<em>Quanta Magazine<\/em>, March 30, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.today.com\/parents\/parents\/katherine-johnsons-great-granddaughter-nakia-boykin-talks-math-legacy-rcna21957\">Katherine Johnson\u2019s great-granddaughter inherited the late mathematician\u2019s talents<\/a><\/strong><br \/>\n<em>Today, <\/em>March 29, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.quantamagazine.org\/dennis-sullivan-uniter-of-topology-and-chaos-wins-the-abel-prize-20220323\/\">Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize<\/a><\/strong><br \/>\n<em>Quanta Magazine, <\/em>March 23, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.sciencenews.org\/article\/rounding-numbers-stochastic-machine-learning-quantum-computing\">How the way we\u2019re taught to round numbers in school falls short<\/a><br \/>\n<\/strong><i>Science News<\/i>, March 22, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.scientificamerican.com\/article\/the-evolving-quest-for-a-grand-unified-theory-of-mathematics\/\">The Evolving Quest for a Grand Unified Theory of Mathematics<\/a><\/strong><br \/>\n<em>Scientific American<\/em>, March 21, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.nytimes.com\/2022\/03\/17\/us\/columbia-university-rank.html\">U.S. News Ranked Columbia No. 2, but a Math Professor Has His Doubts<\/a><\/strong><br \/>\n<em>The New York Times, <\/em>March 17, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.scientificamerican.com\/article\/to-keep-students-in-stem-fields-lets-weed-out-the-weed-out-math-classes\/\">To Keep Students in STEM fields, Let\u2019s Weed Out the Weed-Out Math Classes<\/a><\/strong><br \/>\n<em>Scientific American,<\/em> March 15, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.wired.com\/story\/how-much-pi-do-you-really-need\/\">How Much Pi Do You Really Need?<\/a><\/strong><br \/>\n<em>WIRED, <\/em>March 14, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.npr.org\/2022\/03\/12\/1085542427\/uva-professor-swimmer-math-faster\">This professor studies each swimmer as a math problem. It&#8217;s helped them to be faster<\/a><\/strong><br \/>\n<em>NPR<\/em>, March 12, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.quantamagazine.org\/maths-oldest-problem-ever-gets-a-new-answer-20220309\/\">Math\u2019s \u2018Oldest Problem Ever\u2019 Gets a New Answer<\/a><\/strong><br \/>\n<em>Quanta Magazine, <\/em>March 9, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.wataugademocrat.com\/news\/national\/8-real-life-applications-for-math-equations-you-learned-in-high-school\/collection_1a2225aa-d6fa-5d8c-8f78-ab95e795e419.html#1\">8 real-life applications for math equations you learned in high school<\/a><\/strong><br \/>\n<em>Watauga Democrat, <\/em>March 7, 2022<\/li>\n<li><strong><a href=\"https:\/\/www.quantamagazine.org\/in-new-math-proofs-artificial-intelligence-plays-to-win-20220307\/\">In New Math Proofs, Artificial Intelligence Plays to Win<\/a><\/strong><br \/>\n<em>Quanta Magazine, <\/em>March 7, 2022<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>How to play Nerdle, a math-based version of Wordle Dot Esports, February 28, 2022 It was only a matter of time until someone came up with an even nerdier version of Wordle, the viral word game. Enter: Nerdle. Data scientist Richard Mann created Nerdle for people who enjoy math games,<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-march-2022\/\">Read More &rarr;<\/a><\/span><\/p>\n","protected":false},"author":10,"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":[108,100,18,106,105,110,109,104,61,65,107],"class_list":["entry","author-shershberger","post-808","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-cake-cutting","tag-combinatorics","tag-cryptography","tag-even-and-odd-numbers","tag-graph-theory","tag-infinity","tag-irrational-numbers","tag-nerdle","tag-number-theory","tag-pi","tag-quantum-computing"],"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\/808","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\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/comments?post=808"}],"version-history":[{"count":12,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/808\/revisions"}],"predecessor-version":[{"id":820,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/808\/revisions\/820"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=808"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=808"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=808"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}