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<h1>20614 Symmetry in STEAM (Science, Technology, Engineering, Art, and Mathematics)</h1>
<p><br><strong>Course Leaders: Tom Naps, Joseph De La Cova, Alice De La Cova, Jane Glazebrook, Ana-Marija Nedic</strong>
<br><strong>Course Assistant: Fred Cook</strong>
<br><strong>Time and Place</strong> (OLLI Course No. 20614) Symmetry in STEAM (Science, Technology, Engineering, Art, and Mathematics), 7 Sessions: Wednesdays 1/21/2026 - 3/4/2026, 12:30 PM - 2:00 PM, Community Room, Pillars of Prospect Park.
<br><strong>Parking</strong> Here are links to helpful information we've received from people at OLLI and Pillars: </p>
<ol>
<li><a href="https://docs.google.com/document/d/1sc-JQeAl-MWPS9cuXUr_GTPo6Ths6cba/edit?usp=sharing&ouid=106832221196582971686&rtpof=true&sd=true">OLLI's map and parking information for this site</a> - Parking in the lot indicated in the map will probably not be enough to accommodate all OLLI participants. Further instructions received from OLLI indicate <em>"Park at spaces with orange cones in the facility parking lot. These are put out for OLLI members! You can also use metered street parking. Please avoid the east side of Malcolm Street."</em></li>
<li><a href="https://www.minneapolismn.gov/getting-around/parking-driving/#d.en.135121">Information about using metered spots on nearby streets provided by Pillars staff</a> </li>
<li>How to use the <a href="https://youtu.be/_vgNC8hV7_E?si=VtZ0Ov1ncQPauTUe">Minneapolis city parking app on your phone</a> to make street parking more convenient. </li>
<li>The <a href="https://maps.app.goo.gl/HBF2atZumA6af84T7">UMN Prospect Park Ramp</a> is located at 390 29th Avenue SE. It costs $3 per hour up to a maximum of $13 a day.</li>
</ol>
<p><strong>Course Description</strong>: Symmetry is surprisingly pervasive in our mental and physical worlds. This course will explore our fascination with symmetry through the following lenses: </p>
<ul>
<li>Jan 21: Symmetry in everyday life (Tom, Alice, Joe) <ul>
<li><a href="JoeSession1.pdf">Joe's slides</a> <ul>
<li>Joe's recommendation on a <a href="https://www.facebook.com/groups/tiling">Facebook group that discusses Mathematical Tiling and Tessellation</a></li>
</ul>
</li>
<li><a href="Class1Tom/index.html">Tom's interlude slides</a>. Here are quick links to all the resources referenced in Tom's slides. Enjoy exploring! 😊<ul>
<li><a href="https://www.youtube.com/watch?v=ZYhyAq4Keg4">Mirrors "reverse" left to right and top-to-bottom depending on how you rotate</a>. </li>
<li><a href="https://tnaps-math-cs.website/Symmetry/p5js-Kaleido/">Simple kaleidoscope featuring my granddaughter's drawing and more...</a></li>
<li><a href="https://math.hws.edu/eck/js/symmetry/rosette.html">David Eck's (Prof. Emeritus at Hobart and William Smith) visualization of Rosette symmetry</a></li>
<li><a href="https://youtube.com/clip/Ugkx4DkneOAIGeOmP8dqu_yPqRUkfpYKLDXn?si=8MFYjKF4kRVxjtQm">What symmetry operation is illustrated in this video?</a></li>
<li><a href="https://youtube.com/clip/UgkxUDWBK4jM8TIe_K-uqte4qZm-t-vD5S05?si=Gsb4ZcVXIYmvruss">Bach's artful signature</a></li>
<li><a href="https://www.youtube.com/clip/UgkxXRtqpXftZzgUMHkxs9uqkgpyZsIeeELT">Bach's Crab Canon</a></li>
<li><a href="https://www.youtube.com/clip/Ugkx9bgkO9OdNwtbixxwDCGoCVX2-11GZvj8">Stephen Malinowski's visualization of the Crab Canon</a> </li>
<li><a href="https://www.youtube.com/watch?v=q6eVZQXkRIo">Malinowski's visualization of a "good old round"</a></li>
<li><a href="https://youtu.be/dEFPd8OznWc?si=k8WCKQvQ5P-zbUEB">Malinowski's visualization of Bach's Canone per Augmentationem in moto contrario</a>?</li>
<li><a href="https://stephenmalinowski.com/">See all the music videos available in Stephen Malinowski's music animation machine</a></li>
<li><a href="https://youtu.be/9AdQkEWq8F8?si=0w7NDur_pGJ8wxXR"><em>Gary Garrels</em>, curator at the San Francisco Museum of Art, descibes Sol Lewitt's Open Cubes</a></li>
<li><a href="https://youtu.be/_BrFKp-U8GI?si=Ob6p6SAtGBGdnZXJ">A longer video revealing the answer to the Open Cubes puzzle posed at the end of class</a></li>
</ul>
</li>
</ul>
</li>
<li>Jan 28: Symmetry in biology (Jane) <ul>
<li><a href="JaneSession2.pdf">Jane's slides</a></li>
<li>In-class activity<ul>
<li><a href="JaneActivityPix.pdf">Pictures</a></li>
<li><a href="Jane-Plant-symmetry-notes.pdf">Notes to guide the activity</a></li>
</ul>
</li>
</ul>
</li>
<li>Feb 4: Symmetry in physics (Ana-Marija)<ul>
<li><a href="ana-marija/OLLI_symmetry_in_physics_amnedic_pdf.pdf">Slides</a></li>
<li><a href="ana-marija/Dirac-1931-monopoles.pdf">Dirac's paper on monopoles</a> referenced during class</li>
<li><a href="ana-marija/Preskill-1984-monopoles.pdf">Preskill's paper on monopoles</a> referenced during class</li>
</ul>
</li>
<li>Feb 11: Symmetry’s operations in mathematical group theory (Tom)<ul>
<li><a href="https://tnaps-math-cs.website/Symmetry/Class4Tom/">Slides</a></li>
<li>Some quick links to references in the slides that you might enjoy exploring<ul>
<li><a href="https://rarehistoricalphotos.com/dagen-h-sweden-1967/">The Story of a Symmetry Flip - Dagen Day in Sweden</a></li>
<li><a href="https://youtu.be/pFXqps0vbLc?si=jeoW_L0Vt4JVhS5L">A 15- minute video on the <em>Legend of Galois</em></a></li>
<li><a href="https://youtu.be/jjyhUQzAIzc?si=X90zrtujb4tHIQ56">A 15-minute video describing my "Symmetrial Perfect Shuffle Challenge"</a></li>
</ul>
</li>
</ul>
</li>
<li>Feb 18: M.C. Escher’s tessellation art and its 2-D symmetries (Alice and Joe)<ul>
<li><a href="Class5-Alice-Joe/Escher-Class5.pdf">Slides</a></li>
<li>Recommended Books<ul>
<li>Bool, F.H., et al, M.C. Escher: <em>His Life and Complete Graphic Work, Henry N. Abrams Inc., 1982.</em></li>
<li>Ernst, Bruno, <em>The Magic Mirror of M.C. Escher, Taschen, 2016.</em></li>
<li>Escher, M.C., <em>Escher on Escher: Exploring the Infinite, Abrams, 1989.</em></li>
<li>Escher, M.C., <em>The Graphic Work of M.C. Escher, Ballantine Books, 1971.</em></li>
<li>MacGillavry, Caroline H., <em>Fantasy & Symmetry: The Periodic Drawings of M.C. Escher, Henry N. Abrams Inc., 1965.</em></li>
<li>Piller, Micky, et al, <em>The Amazing World of M.C. Escher, National Galleries of Scotland, 2015.</em></li>
<li>Ranucci, E.R. and Teeters, J.L., <em>Creating Escher-Type Drawings, Creative Publications, 1977.</em></li>
<li>Schattschneider, Doris, <em>M.C. Escher: Visions of Symmetry, Harry N. Abrams Inc., 2004.</em></li>
<li>Seymour, Dale and Britton, Jill, <em>Introduction to Tessellations, Dale Seymour Publications, 1989.</em></li>
</ul>
</li>
<li>Recommended Websites <ul>
<li><a href="https://escherinhetpaleis.nl/en/about-escher">Escher in Het Paleis website</a></li>
<li><a href="https://eschermath.org">Math & the Art of M.C. Escher website</a></li>
<li><a href="https://www.nga.gov/artists/2492-mc-escher/artworks">National Gallery of Art website</a></li>
<li><a href="https://mcescher.com">The M.C. Escher Company website</a></li>
<li><a href="https://www.wikiart.org/en/m-c-escher">WikiArt Visual Art Encyclopedia website</a></li>
<li><a href="https://www.youtube.com/watch?v=AmLaM6NkTDs">YouTube video of Escher working on “Snakes”</a></li>
</ul>
</li>
</ul>
</li>
<li>Feb 25: 3-D symmetry, crystals, and snowflakes (Joe)<ul>
<li><a href="Class6.pdf">Joe's slides</a></li>
<li>Books<ul>
<li>Bentley, W.A. and Humphreys, W.J., Snow Crystals, Dover Publications, Inc., 1962.</li>
<li>Libbecht, Kenneth and Wing, Rachel, Capturing Snowflakes: Winter’s Frozen Artistry, Voyageur Press, 2021.</li>
<li>Libbrecht, Kenneth, Ken Libbrecht’s Field Guide to Snowflakes, Voyageur Press, 2006.</li>
</ul>
</li>
<li>Websites<ul>
<li><a href="https://www.math.brown.edu/tbanchof/Beyond3d/chapter5/section03.html">Brown University’s “Duals of Regular Polyhedra”</a></li>
<li><a href="https://msestudent.com/what-are-point-groups-simple-explanation/">Materials Science Engineering’s “What Are Point Groups (Simple Explanation”)</a></li>
<li><a href="https://www.socratica.com/pages/platonic-solids">Socratica’s “Platonic Solids: The Five Uniform Polyhedra”</a></li>
<li><a href="https://math.ucr.edu/home/baez/platonic.html">University of California – Riverside, John Baez, “Platonic Solids in All Dimensions”</a></li>
<li><a href="https://en.wikipedia.org/wiki/Crystal_growth">Wikipedia on “Crystal Growth”</a></li>
<li><a href="https://en.wikipedia.org/wiki/Crystal_polymorphism">Wikipedia on “Crystal Polymorphism”</a></li>
<li><a href="https://en.wikipedia.org/wiki/Crystal_structure">Wikipedia on “Crystal Structure”</a></li>
<li><a href="https://en.wikipedia.org/wiki/Dual_polyhedron#:~:text=In%20geometry%2C%20every%20polyhedron%20is,dual%20is%20the%20original%20polyhedron.">Wikipedia on “Dual Polyhedron”</a></li>
<li><a href="https://en.wikipedia.org/wiki/Space_group">Wikipedia on “Space Groups”</a></li>
<li><a href="https://www.youtube.com/watch?v=ao2Jfm35XeE&t=86s">YouTube video of “The Snowflake Myth” featuring Dr. Ken Libbrecht</a></li>
</ul>
</li>
</ul>
</li>
<li>Mar 4: Symmetry through software (Tom)<ul>
<li><a href="./Class7Tom">Slides</a></li>
<li>Explore links in the slides<ul>
<li><a href="https://tnaps-math-cs.website/Symmetry/symmetry/wallpaper.html">David Eck's Wallpaper Web App</a></li>
<li><a href="https://eschersket.ch/">EscherSketch Web App</a></li>
<li><a href="https://youtu.be/48sCx-wBs34?si=GZKBSdQHVGWZDxkb">Veritasium explains the story of the Penrose tiling</a><ul>
<li><a href="https://aatishb.com/patterncollider/">The Penrose Tiling App by the Aatish Bhatia</a></li>
<li><a href="https://github.com/aatishb/patterncollider?tab=readme-ov-file#readme">Bhatia's documentation for the App</a></li>
<li><a href="https://youtu.be/-eqdj63nEr4">Bhatia's video on it</a></li>
</ul>
</li>
<li><a href="https://www.youtube.com/watch?v=IfVwelta1fE">Scottish Mathematician and YouTuber Aylian MacDonald explains the discovery of the aperiodic monotile</a><a href="https://youtube.com/clip/Ugkxp1jeEUHTqel3a071HaZ_DcARtKdM_aEc?si=nTn_dNagcsYgukLh">. David Smith was the "Galois" of the authoring group</a><ul>
<li><a href="https://cs.uwaterloo.ca/~csk/spectre/">Craig Kaplan's website for the monotile paper</a></li>
<li><a href="https://cs.uwaterloo.ca/~csk/spectre/app.html">Craig Kaplan's monotile App</a> </li>
<li><a href="https://youtu.be/_ZS3Oqg1AX0?si=cdAqH90cG8tKh7WP">NumberPhile interview of Craig Kaplan</a></li>
<li><a href="https://www.nytimes.com/2023/12/10/science/mathematics-tiling-einstein.html?unlocked_article_code=1.QVA.9Q9L.G0K2zswdtJlS&smid=url-share">NYT article "What Can You Do With an Einstein tile?"</a></li>
</ul>
</li>
<li><a href="https://cgjennings.ca/articles/l-systems/#applet">An L-System App by Christopher Jennings</a></li>
<li><a href="https://sisyphus-industries.com/">Sisyphus and Kinetic Art</a> </li>
<li><a href="https://youtu.be/_Y3IA9fuXG0?si=YBHP2sEbMRK931UY">A video short by lead artist Bruce Shapiro</a></li>
<li><a href="https://youtu.be/Gl-hrMBm3L8?si=9rIXA6WffPYieSZe">A deeper look by Future Collective</a></li>
</ul>
</li>
</ul>
</li>
</ul>
<p>No prior background in any of these areas is required. Links to course materials will be provided on a week-by-week basis below</p>
<hr>
<h2>Accommodations</h2>
<p>OLLI is committed to making our courses accessible for members, and we expect our course leaders to help us make that happen. OLLI recommends that Course leaders teaching in classrooms wear voice amplifiers, and we set up our Zoom courses so that live captioning is an option. The OLLI office may contact you to make additional accommodations on a case by case basis. If you require additional accommodations, please contact <a href="OLLI@umn.edu">OLLI@umn.edu</a> and we will do our best to support your needs. </p>
<h2>Disability statement</h2>
<p>The University of Minnesota is committed to providing equitable access to learning opportunities for all students. If you have, or think you have, a disability in any area such as, mental health, attention, learning, chronic health, sensory, or physical, please contact the DRC office on your campus (UM Twin Cities - 612.626.1333) to arrange a confidential discussion regarding equitable access and reasonable accommodations. Additional information is available on the DRC website: <a href="https://disability.umn.edu/">https://disability.umn.edu</a> or email <a href="drc@umn.edu">drc@umn.edu</a>.</p>
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