Circle Packing and the Math of Social Distancing

{ "@context": [ "http://www.w3.org/ns/anno.jsonld", "http://iiif.io/api/presentation/3/context.json" ], "type": "Manifest", "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7", "label": { "en": [ "Circle Packing and the Math of Social Distancing" ] }, "requiredStatement": { "label": { "en": [ "Attribution" ] }, "value": { "en": [ "Provided by Archipelago Deployment" ] } }, "metadata": [ { "label": { "en": [ "description" ] }, "value": { "en": [ "

What is the maximum number of people to be allowed in a certain area to practice social distancing during COVID-19? Scientists recommend that people keep at least two meters away from each other, then we can imagine each person to be at the center of a circle of radius one meter, where the circles cannot overlap. Thus, solving the aforementioned social distancing problem amounts to fitting as many non-overlapping equal-sized circles into a confined floor plan as possible. This is the so-called circle packing problem in geometry, which concerns the best (densest) way to arrange non-overlapping circles on a plane. We will calculate the density of square packing as well as hexagon packing of circles, and go over Thue's theorem, which says that hexagon packing is the optimal packing of circles.<\/p>" ] } }, { "label": { "en": [ "navDate" ] }, "value": { "en": [ "May 7th at 12:11pm" ] } }, { "label": { "en": [ "license" ] }, "value": { "en": [ "http:\/\/rightsstatements.org\/vocab\/InC-EDU\/1.0\/" ] } } ], "within": "https://arches.union.edu/steinmetzsymposium", "partOf": [ { "id": "https://arches.union.edu/steinmetzsymposium/metadata/iiifmanifest3collection/default.jsonld", "type": "Manifest" } ], "items": [{ "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/canvas/p1", "type": "Canvas", "label": { "en": [ "Video:Circle Packing and the Math of Social Distancing"]}, "width": 1280, "height": 800, "duration": 1120080, "items": [ { "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/page/p1", "type": "AnnotationPage", "items": [ { "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/annotation/p1", "type": "Annotation", "motivation": "painting", "body": { "id": "https://arches.union.edu/do/55023/iiif/495af292-ee29-4510-89ba-e917d39718a6/full/full/0/compressed_CirclePackingandtheMathofSocialDistancing_Nguyen-MyNguyen.mp4", "type": "Video", "format": "video/mp4", "duration": 1120080, "height": 800, "width": 1280 }, "target": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/canvas/p1" } ] } ] } ], "structures": [ { "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/range/r1", "type": "Range", "label": { "en": [ "Circle Packing and the Math of Social Distancing" ] }, "items": [ { "id": "https://arches.union.edu/do/1a50f6ca-78e4-4aae-b626-4b25dd7bf1d7/iiif/canvas/p1", "type": "Canvas" } ] } ] }