{"id":2452,"date":"2024-03-17T17:59:54","date_gmt":"2024-03-17T17:59:54","guid":{"rendered":"https:\/\/news.talkwithrattan.com\/index.php\/2024\/03\/17\/geometry-can-shape-our-world-in-unexpected-but-useful-ways\/"},"modified":"2024-03-17T17:59:54","modified_gmt":"2024-03-17T17:59:54","slug":"geometry-can-shape-our-world-in-unexpected-but-useful-ways","status":"publish","type":"post","link":"https:\/\/news.talkwithrattan.com\/index.php\/2024\/03\/17\/geometry-can-shape-our-world-in-unexpected-but-useful-ways\/","title":{"rendered":"Geometry can shape our world in unexpected but useful ways"},"content":{"rendered":"<div style=\"text-align:center\"><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"450\" src=\"https:\/\/i3.wp.com\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/680_Geometers_tablet-514x450.jpg?fit=514,450&amp;ssl=1\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"Geometry can shape our world in unexpected but useful ways\" title=\"Geometry can shape our world in unexpected but useful ways\" \/><\/div><p> <br \/>\n<\/p>\n<div data-component=\"video-embed\">\n<p>Have you noticed how oranges are stacked at the store? Grocers know that the most attractive and stable arrangement is a pyramid. Johannes Kepler suspected this pyramid-stacking was superior, way back in the 17th century. But the German scientist also noted that he couldn\u2019t prove it. Sadly, like Kepler, many mathematicians <a href=\"https:\/\/www.nature.com\/articles\/475166a\" rel=\"noopener\">may never live to see the confirmation of their discoveries<\/a>. Or the full impact of their insights.<\/p>\n<p>In Kepler\u2019s case, it took nearly 400 years for mathematicians to confirm his stacking theory. And their proof now has <a href=\"https:\/\/www.snexplores.org\/article\/physics-stack-fruit-display-collapse\">applications that extend well beyond grocery stands<\/a>. For instance, this concept has helped scientists improve radio communications.<\/p>\n<aside class=\"wp-block-sciencenews-inline-related-post alignleft\">\n<h4><a href=\"https:\/\/www.snexplores.org\/article\/explainer-basics-geometry\">Explainer: The basics of geometry<\/a><\/h4>\n<\/aside>\n<p>How? Scientists use the orange-stacking concept to tightly pack various messages into radio transmissions. Think of each message as an orange. The technique suggests how they can be bundled together efficiently, without overlapping. This helps maximize information flow, which has far-reaching impacts. For instance, it ensures that long-range communications \u2014 such as those done by satellites \u2014 are less noisy and garbled.<\/p>\n<p>This stacking application is one measure of the reach of <a href=\"https:\/\/www.snexplores.org\/article\/scientists-say-geometry\">geometry<\/a> \u2014 the mathematics of shapes.<\/p>\n<p>For centuries, mathematicians have studied geometry problems \u2014 often just for what they saw as the beauty of the math. Many people may find it hard to see the appeal or everyday uses of such math. But modern geometry is full of problems both beautiful and useful. They range from visualizing an unimaginable geometric shape (that does not <em>yet<\/em> have a real-world application) to studying the shapes of viruses \u2014 which could help scientists develop new vaccines.<\/p>\n<aside class=\"sn-conversion rich-text\"\/>\n<h4 class=\"wp-block-heading\">Shaping the unknown<\/h4>\n<p>Harrison Bray runs the <a href=\"https:\/\/megl.science.gmu.edu\/\" rel=\"noopener\">Mason Experimental Geometry Lab<\/a> at George Mason University. That\u2019s in Fairfax, Va. One project there challenged students to imagine what a four-dimensional, or 4-D, structure might look like.<\/p>\n<p>We live in a three-dimensional, or 3-D, world. That means we can move in three dimensions: right and left, forward and backward, and up and down. Spheres (such as oranges), cubes (like dice) and cones (party hats) can all be described by measurements in three dimensions. That is, their height, width and depth. But what would the geometry of a fourth dimension be?<\/p>\n<p>Bray\u2019s students worked to imagine a special 4-D structure. It\u2019s called a convex real projective structure. To visualize things in higher dimensions than we experience \u2014 like a fourth dimension \u2014 geometers use what\u2019s known as a <em>projection<\/em>. They take points on an object in space and then map these points onto a different space in lower dimensions.<\/p>\n<div class=\"wp-block-image  has-alignleft\">\n<figure class=\"alignleft size-large\"><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137177\">This tablet is seen as a three-dimensional object projecting a two-dimensional shadow. Harrison Bray\u2019s group uses such a concept to map what a four-dimensional object might look like, based on its projected three-dimensional \u201cshadow.\u201d His students can then 3-D print such a potential 4-D object.<\/span><span class=\"credit wp-credit-3137177\">HAKINMHAN\/iStock\/Getty Images Plus<\/span><\/figcaption><\/figure>\n<\/div>\n<p>Think of a notebook, which exists in three dimensions. It has height, width and depth. What happens if you hold that notebook above a flat surface and shine a light down on the book? \u201cThis will cast a rectangular shadow underneath,\u201d notes Steven Schaefer. He took part in Bray\u2019s study. (Now, he is a PhD student in computer science at the University of Michigan in Ann Arbor.)<\/p>\n<p>The notebook\u2019s shadow is two-dimensional, or 2-D. It has only height and width. So that shadow does not provide a direct image of the 3-D notebook. But looking at the notebook\u2019s 2-D shadow from different directions can reveal information about the book\u2019s third dimension, Schaefer says.<\/p>\n<p>Likewise, looking at 3-D \u201cshadows\u201d of imagined 4-D objects can offer insight into what objects in a fourth dimension might look like. The students on Bray\u2019s team created a virtual 4-D shape on a computer using code. Then, they projected their 4-D shape into three dimensions. They printed out the resulting structure with a 3-D printer. This required writing computer code, or software, to build their projection.<\/p>\n<p>That code converted thousands of points from the 4-D structure into a format that the 3-D printer could understand. The code essentially \u201cmassaged\u201d those data in a way that allowed the printer to churn out a 3-D representation of the 4-D structure, Schaefer explains.<\/p>\n<div class=\"wp-block-image  has-alignright\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" width=\"1030\" height=\"1155\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed.jpg\" alt=\"a 3D printed representation of 4D shape\" class=\"wp-image-3137178\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed.jpg 1030w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-342x383.jpg 342w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-401x450.jpg 401w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-166x186.jpg 166w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-768x861.jpg 768w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-517x580.jpg 517w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_4D_3D_printed-692x776.jpg 692w\" sizes=\"(max-width: 1030px) 100vw, 1030px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137178\">Bray\u2019s students mapped a four-dimensional shape into three dimensions. This is the resulting 3-D representation of it that they produced using a 3-D printer. <\/span><span class=\"credit wp-credit-3137178\">Steven Schaefer<\/span><\/figcaption><\/figure>\n<\/div>\n<p>\u201cA great thing about modern computing is that you have all these visualization tools,\u201d says Bray. But to use them, the students had to understand the math at a really deep level. Without it, they couldn\u2019t write the code that told the printer what to do.<\/p>\n<p>\u201cWhen I was 15, I thought there were no physical [math] experiments,\u201d Schaefer says. It seemed that in math, \u201call one cares about is proofs.\u201d (<a href=\"https:\/\/www.snexplores.org\/article\/scientists-say-geometry\">Proof<\/a> is a method of showing that a mathematical statement is true.) Performing messier, engineering-like experiments has now helped him appreciate the many potential uses of math.<\/p>\n<p>Does 3-D printing of the projection of a 4-D structure have any real-world use today? Probably not. But there may be important uses in the near future. We just can\u2019t see them yet.<\/p>\n<p>Mathematics can seem like \u201cmake-believe or just pie-in-the-sky nonsense,\u201d says Casey Mann. He\u2019s a geometer at the University of Washington Bothell. But eventually, math \u201cfinds its way into some application somewhere,\u201d he says. \u201cThat\u2019s the beauty of math.\u201d<\/p>\n<h4 class=\"wp-block-heading\">From bath tiles to a better robo-vacuum<\/h4>\n<p>Mann studies a packing problem somewhat like the orange-stacking challenge faced by grocers. In Mann\u2019s case, he\u2019s exploring how to tile shapes on a flat surface.<\/p>\n<p>Take any triangle. Try doodling to see if you can fill a piece of paper with lots of triangles, each having that same shape. You must fill the surface completely. And there can be no overlaps or gaps between triangles. Now try doing the same thing with a four-sided shape, such as a square. Were you successful?<\/p>\n<aside class=\"wp-block-sciencenews-inline-related-post alignleft\">\n<h4><a href=\"https:\/\/www.snexplores.org\/article\/einstein-vampire-tile-shape-math-geometry-pattern-no-repeats\">An \u2018einstein\u2019 shape eluded mathematicians for 50 years. Now they found one<\/a><\/h4>\n<\/aside>\n<p>Mathematicians have proved that you can tile a surface snugly using triangles and four-sided shapes. The natural follow-up was to see if you could also do this with a pentagon (a five-sided shape). Believe it or not, this question has puzzled mathematicians for more than a century.<\/p>\n<p>In a regular pentagon, all of the angles (corners) are equally wide. The length of each side is also the same. But when you try to tile a surface with a regular pentagon, there will always be gaps \u2014 uncovered spots. If you don\u2019t require that every angle and side of each pentagon be equal, though, certain pentagons can completely cover a surface.<\/p>\n<p>Based on these rules, mathematicians in the early 20th century found a <a href=\"http:\/\/mathtourist.blogspot.com\/2010\/06\/tiling-with-pentagons.html\" rel=\"noopener\">few pentagons that could fully tile a surface<\/a>. By the 1980s, 14 such pentagons had emerged.<\/p>\n<figure class=\"wp-block-image alignwide size-full\"><img loading=\"lazy\" width=\"1030\" height=\"275\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon.png\" alt=\"a pentagon that can compltely tile a surface\" class=\"wp-image-3137179\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon.png 1030w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon-680x182.png 680w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon-800x214.png 800w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon-330x88.png 330w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_pentagon-768x205.png 768w\" sizes=\"(max-width: 1030px) 100vw, 1030px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137179\">This is an example of a pentagon that can be used to completely tile a surface (with no overlaps or gaps). The capital letters denote the angles of the shape\u2019s corners, and lowercase letters describe the relative lengths of its sides. <\/span><span class=\"credit wp-credit-3137179\">C. Mann<\/span><\/figcaption><\/figure>\n<p>Could there be more? Mann took up this challenge. In 2015, he was part of a trio at the University of Washington that found a <a href=\"https:\/\/arxiv.org\/abs\/1510.01186\" rel=\"noopener\">15th pentagon<\/a> that could completely tile a surface. Its discovery came almost 30 years after the last one.<\/p>\n<p>What about a 16th or a 17th type? A couple of years later, Micha\u00ebl Rao wrote a computer program to test other possible options. This mathematician works at the Ecole Normale Sup\u00e9rieure de Lyon, in France. He proved that no, <a href=\"https:\/\/perso.ens-lyon.fr\/michael.rao\/publi\/penta.pdf\" rel=\"noopener\">there were only 15 types of pentagons \u2014 and no more \u2014 that could tile a surface<\/a>. And all of them are now known.<\/p>\n<p>So, what\u2019s the value in finding such snug-fitting tiles?<\/p>\n<div class=\"wp-block-image  has-aligncenter\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"1030\" height=\"773\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons.jpg\" alt=\"a tiling patern made of five sided shapes\" class=\"wp-image-3137180\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons.jpg 1030w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-510x383.jpg 510w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-600x450.jpg 600w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-248x186.jpg 248w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-768x576.jpg 768w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-773x580.jpg 773w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-263x197.jpg 263w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_tiled_pentagons-560x420.jpg 560w\" sizes=\"(max-width: 1030px) 100vw, 1030px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137180\">Coloring in the pentagons shows how this particular type of five-sided shape has completely tiled a surface (with no overlaps or gaps). Only 15 particular pentagons can do this \u2014 and no more, mathematician Micha\u00ebl Rao finds. <\/span><span class=\"credit wp-credit-3137180\">C. Mann<\/span><\/figcaption><\/figure>\n<\/div>\n<p>How about making better robotic vacuums? Roombas and other squat, round, self-propelled dust- and lint-busters don\u2019t reach all of a floor\u2019s nooks and crannies. That\u2019s why engineers at the Singapore University of Technology and Design <a href=\"https:\/\/ieeexplore.ieee.org\/document\/8580529\/authors\" rel=\"noopener\">are looking to program a robot that can apply tiling theory to floor-cleaning<\/a>. Their goal: help design cleaning paths that let those automatons clean every bit of the floor.<\/p>\n<div class=\"wp-block-image  has-alignright\">\n<figure class=\"alignright size-large\"><img loading=\"lazy\" width=\"672\" height=\"450\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-672x450.jpg\" alt=\"a robot vaccum on a wood floor\" class=\"wp-image-3137181\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-672x450.jpg 672w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-572x383.jpg 572w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-278x186.jpg 278w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-768x514.jpg 768w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum-866x580.jpg 866w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_robot_vaccum.jpg 1030w\" sizes=\"(max-width: 672px) 100vw, 672px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137181\">Robotic vacuums like this one can help clean up dust and pet fur but often miss some parts of the floor repeatedly. By applying \u201ctiling\u201d math, geometers are working on a fix for this. <\/span><span class=\"credit wp-credit-3137181\">HAKINMHAN\/iStock\/Getty Images Plus<\/span><\/figcaption><\/figure>\n<\/div>\n<p>This so-called tiling theory also helps speed up video games that involve complex imagery. The computing power needed to calculate and then display visual complexity can slow down a game. Zoom in really close on a screen and \u201cyou\u2019ll see little tiles,\u201d notes Mann. \u201cThey\u2019re all fitting together to form these surfaces [of objects].\u201d Those tiles enable the graphics to compute more easily. This lets video games run faster and leads to a more seamless experience for players.<\/p>\n<p>So next time you\u2019re excited by a super-speedy video game, thank tiling theory. And, of course, tiling theory could come in handy if you want to literally tile a floor or counter using shapes more complex than rectangles.<\/p>\n<h4 class=\"wp-block-heading\">How nature uses geometry<\/h4>\n<p>Neat, orderly shapes can be found throughout nature. They appear in honeycombs, spider webs, snowflakes, seashells \u2014 and even viruses.<\/p>\n<p>Viruses come in different standard shapes, or geometries. And many viruses share certain similarities in shape. Scientists use those similarities to group viruses into families. This helps researchers relate new viruses to existing ones. It also helps scientists predict how a virus will likely behave inside the cell it infects. It can even help predict how new vaccines might target particular viruses.<\/p>\n<div class=\"wp-block-image  has-alignleft\">\n<figure class=\"alignleft size-full\"><img loading=\"lazy\" width=\"1030\" height=\"687\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming.jpg\" alt=\" a girl and a guy both concentrating on playing a video game\" class=\"wp-image-3137175\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming.jpg 1030w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming-574x383.jpg 574w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming-675x450.jpg 675w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming-279x186.jpg 279w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming-768x512.jpg 768w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_gaming-870x580.jpg 870w\" sizes=\"(max-width: 1030px) 100vw, 1030px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137175\">Gamers don\u2019t enjoy it when their video game freezes or unexpectedly goes into slo-mo action. Geometers are using math to make the images on screens \u2014 all made up of tiny tile shapes \u2014 load faster for speedier play. <\/span><span class=\"credit wp-credit-3137175\">Anastassiya Bezhekeneva\/Moment\/Getty Images Plus<\/span><\/figcaption><\/figure>\n<\/div>\n<p>One common viral structure is the icosahedron (Eye-koss-uh-HEE-drun). It\u2019s one of the oldest known geometric shapes. Greek philosophers may have discovered it around 400 B.C. But Neolithic people in Scotland may have known about this shape at least 1,000 years earlier.<\/p>\n<p>An icosahedron has 20 identical faces. Each one is a triangle whose sides are all equal in length. Joining these faces are 30 edges or lines along the sides and 12 corners. Icosahedrons show up on soccer balls, 20-sided dice and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Geodesic_dome\" rel=\"noopener\">geodesic domes<\/a>.<\/p>\n<p>In viruses, the icosahedron is one of the most common shapes of the capsid. That\u2019s the sort of shell that guards the genetic material in a virus. Researchers like Laura Schaposnik are working to better understand icosahedron-shaped capsids. This geometer works at the University of Illinois Chicago.<\/p>\n<p>\u201cIt came to me as a surprise,\u201d Schaposnik says, that even though icosahedrons have been \u201cso well studied historically, certain viruses with [this] structure haven\u2019t yet been fully understood.\u201d<\/p>\n<section class=\"newsletter-signup__wrapper___lZ0W1 wp-block-house-ads wp-block-newsletter-signup\">\n<picture><source srcset=\"https:\/\/www.snexplores.org\/wp-content\/themes\/sciencenews-sns-child\/client\/src\/images\/cta-module@1x.png 1x,&#10;&#9;&#9;&#9;&#9;https:\/\/www.snexplores.org\/wp-content\/themes\/sciencenews-sns-child\/client\/src\/images\/cta-module@2x.png 2x\" media=\"(min-width: 768px)\"><source srcset=\"https:\/\/www.snexplores.org\/wp-content\/themes\/sciencenews-sns-child\/client\/src\/images\/cta-module-sm@1x.png 1x,&#10;&#9;&#9;&#9;&#9;https:\/\/www.snexplores.org\/wp-content\/themes\/sciencenews-sns-child\/client\/src\/images\/cta-module-sm@2x.png 2x\"><img decoding=\"async\" class=\"newsletter-signup__background___Eym8W\" src=\"https:\/\/www.snexplores.org\/wp-content\/themes\/sciencenews-sns-child\/client\/src\/images\/cta-module-sm@2x.png\" alt=\"\"\/><br \/>\n<\/source><\/source><\/picture>\n<div class=\"newsletter-signup__container___srNOL\" data-component=\"newsletter-signup\">\n<h3 class=\"newsletter-signup__heading___0EHmb\">\n\t\t\tEducators and Parents, Sign Up for The Cheat Sheet\t\t<\/h3>\n<div class=\"newsletter-signup__message___pemaq\">\n<p>Weekly updates to help you use <em>Science News Explores<\/em> in the learning environment<\/p>\n<\/p><\/div>\n<p class=\"newsletter-signup__thankyou___K6GGN\">Thank you for signing up!<\/p>\n<p class=\"newsletter-signup__error___hCsJI\">There was a problem signing you up.<\/p>\n<\/p><\/div>\n<\/section>\n<h4 class=\"wp-block-heading\">Viral geometry<\/h4>\n<p>Each of the 20 sides of an icosahedral capsid is made up of <a href=\"https:\/\/www.snexplores.org\/article\/scientists-say-protein\">proteins<\/a>. Those proteins are packed tightly in a symmetric way, filling up the structure\u2019s triangular faces. These faces repeat themselves over and over across the whole outer surface of a capsid.<\/p>\n<p>Mathematicians refer to the symmetry of the capsid\u2019s icosahedral shapes as having a 2-3-5 pattern. What does this mean? Consider how you might rotate an icosahedron.<\/p>\n<div class=\"wp-block-image  has-alignleft\">\n<figure class=\"alignleft size-full\"><img loading=\"lazy\" width=\"1030\" height=\"1030\" decoding=\"async\" src=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus.jpg\" alt=\"a computer generated model of an adenovirus\" class=\"wp-image-3137176\" srcset=\"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus.jpg 1030w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-383x383.jpg 383w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-450x450.jpg 450w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-186x186.jpg 186w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-768x768.jpg 768w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-580x580.jpg 580w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-776x776.jpg 776w, https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/1030_Geometers_adenovirus-214x214.jpg 214w\" sizes=\"(max-width: 1030px) 100vw, 1030px\"\/><figcaption class=\"wp-element-caption\"><span class=\"caption wp-caption-3137176\">A capsid is sort of a shell that guards the genetic material of a virus. Among capsids, an icosahedral shape (seen illustrated here) is one of the most common forms. <\/span><span class=\"credit wp-credit-3137176\">TUMEGGY\/SCIENCE PHOTO LIBRARY\/Science Photo Library\/Getty Images<\/span><\/figcaption><\/figure>\n<\/div>\n<p>Try rotating it clockwise along an edge, half-way round. The shape on one side of that edge is a mirror image of what\u2019s on the other side. Rotate again and you reach your starting structure. This implies that when you rotate it twice along the edge, you are back to where you started. Mathematicians call this two-fold symmetry.<\/p>\n<p>What happens when you rotate the icosahedron along its face? Now it takes three rotations to get back to the starting structure. This is a three-fold symmetry. If you instead rotate the icosahedron along a corner, it takes 5 turns to get back the initial shape.<\/p>\n<p>Hence, an icosahedron shows 2-3-5 symmetry. Each number identifies how many rotations you need before you reach your initial shape, depending on how the structure was rotated \u2014 along its edge, its face or its corner.<\/p>\n<p>Studying the symmetry of virus capsids is crucial to understanding the stability of viruses. The more stable a virus is, the better it can defend itself from the body\u2019s immune system. So, understanding viral symmetry helps scientists create antidotes against viruses.<\/p>\n<aside class=\"wp-block-sciencenews-inline-related-post alignleft\">\n<h4><a href=\"https:\/\/www.snexplores.org\/article\/explainer-what-virus\">Explainer: What is a virus?<\/a><\/h4>\n<\/aside>\n<p>Based on the 2-3-5 symmetry of viral capsids, scientists have grouped just a little more than 2,800 viruses into categories. Those categories can help pinpoint the best ways to fight different types of viruses. But <a href=\"https:\/\/journals.asm.org\/doi\/10.1128\/mmbr.00061-19\" rel=\"noopener\">studies estimate<\/a> there are at least 10<sup>31<\/sup> (or 10 million trillion trillion) individual viruses on Earth, many of which are as yet unidentified. While biologists work to identify these viruses, Schaposnik uses geometry to study possible viral symmetries.<\/p>\n<p>She investigates which mix of symmetries along edges, triangles and vertices (and their repetitions) <a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/28111328\/\" rel=\"noopener\">are possible in icosahedrons<\/a>. This could help group viruses with those capsid shapes if and when they are identified. And that could help scientists more quickly identify vulnerabilities of those viruses.<\/p>\n<p>But Schaposnik\u2019s research has now raised a big question: Do viruses take advantage of all these possible icosahedron geometries? Or only some of them?<\/p>\n<p>This is proving hard to answer.<\/p>\n<h4 class=\"wp-block-heading\">Lots of work ahead<\/h4>\n<p>Some capsids with symmetry along certain edges are possible, Schaposnik\u2019s work suggests. But many of these possible configurations have never been seen in nature. \u00a0<\/p>\n<p>\u201cIf we haven\u2019t discovered certain types of viruses in nature,\u201d Schaposnik says, but mathematically they should \u2014 or could \u2014 exist, \u201cyou [can] start being prepared with antivirals for those types.\u201d<\/p>\n<p>Studies like hers could help narrow down potential viral shapes, preparing scientists for new mystery germs. Such data could help many experts \u2014 from vaccine developers and scientists who study viruses to government officials \u2014 limit the risk of another pandemic.<\/p>\n<p>Geometry\u2019s tremendous reach extends far beyond finding areas of triangles in the classroom. The fruits of Kepler\u2019s labors revealed unusual applications several centuries later. It remains to be seen whether other current research will one day find important uses in real life \u2014 much as those on viral geometry and tiling already are.<\/p>\n<aside class=\"sn-conversion rich-text\"\/><\/div>\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Have you noticed how oranges are stacked at the store? Grocers know that the most attractive and stable arrangement is a pyramid. Johannes Kepler suspected this pyramid-stacking was superior, way back in the 17th century. But the German scientist also noted that he couldn\u2019t prove it. Sadly, like Kepler, many mathematicians may never live to [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":2453,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","fifu_image_url":"https:\/\/www.snexplores.org\/wp-content\/uploads\/2024\/02\/680_Geometers_tablet-514x450.jpg","fifu_image_alt":"","footnotes":""},"categories":[606],"tags":[4353,1972,4354,4355,1052],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/posts\/2452"}],"collection":[{"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2452"}],"version-history":[{"count":1,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/posts\/2452\/revisions"}],"predecessor-version":[{"id":2454,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/posts\/2452\/revisions\/2454"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/media\/2453"}],"wp:attachment":[{"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/news.talkwithrattan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}