44:["$","title",null,{"children":"Poncelet Phenomena in the Euclidean Plane (2019-2021) | Dan S. Reznik | Observable"}] 4c:T1746,html`

[1] Dan Reznik, Ronaldo Garcia, and Jair Koiller. Can the elliptic billiard still surprise us? Math Intelligencer, 42:6–17, 2020.

[2] Ronaldo Garcia, Dan Reznik, and Jair Koiller. New properties of triangular orbits in elliptic billiards. Amer. Math. Monthly, Oct, 2021. doi:10.1080/00029890.2021.1982360

[3] Dan Reznik, Ronaldo Garcia, and Jair Koiller. The ballet of triangle centers on the elliptic billiard. J. Geom. and Graphics, 24(1):079–101, 2020.

[4] Dan Reznik and Ronaldo Garcia. Circuminvariants of 3-periodics in the elliptic billiard. Intl. J. Geometry, 10(1):31–57, 2021.

[5] Dan Reznik, Ronaldo Garcia, and Jair Koiller. Fifty new invariants of N-periodics in the elliptic billiard. Arnold Math. J., 2021.

[6] Ronaldo Garcia and Dan Reznik. Related by similarity I: Poristic triangles and 3-periodics in the elliptic billiard. Intl. J. Geom., 10(3):52–70, 2021.

[7] Dan Reznik and Ronaldo Garcia. Related by similarity II: Poncelet 3-periodics in the homothetic pair and the Brocard porism. Intl. J. Geom., 10(4):18–31, 03 2021.

[8] Ronaldo Garcia, Dan Reznik, Hellmuth Stachel, and Mark Helman. Steiner’s hat: a constant-area deltoid associated with the ellipse. J. Croatian Soc. for Geom. Gr. (KoG), 24, 2020.

[9] Gabriela Gheorghe and Dan Reznik. A special conic associated with the Reuleaux negative pedal curve. Intl. J. Geom., 10(2):33–49, 2021.

[10] Dan Reznik, Ronaldo Garcia, and Hellmuth Stachel. Area-invariant pedal-like curves derived from the ellipse. Beiträge zur Algebra und Geometrie, 2021. doi:10.1007/s13366-021-00588-x

[11] Dan Reznik and Ronaldo Garcia. The talented Mr. Inversive Triangle in the elliptic billiard. European J. Math, July, 2021. doi:10.1007/s40879-021-00489-2

[12] Ronaldo Garcia and Dan Reznik. Family ties: Relating Poncelet 3-periodics by their properties. J. Croatian Soc. for Geom. & Gr. (KoG), to appear, 2021.

[13] Mark Helman, Ronaldo Garcia, and Dan Reznik. Intriguing invariants of centers of ellipse-inscribed triangles. J. Geometry, 112:28, July, 2021. doi:10.1007/s00022-021-00586-3

[14] Pedro Roitman, Ronaldo Garcia, and Dan Reznik. New invariants of Poncelet-Jacobi bicentric polygons. Arnold Math. J., August, 2021. doi=10.1007/s40598-021-00188-6

[15] Dominique Laurain, Daniel Jaud, and Dan Reznik. Poncelet propellers: Invariant total blade area. Intl. J. Geom., 11(1):24-32, 2022.

[16] Mark Helman, Dominique Laurain, Ronaldo Garcia, and Dan Reznik. Center power and loci of Poncelet triangles. J. Dyn. \& Contr. Sys, to appear, 2021. doi:10.1007/s10883-021-09580-z

[17] Daniel Jaud, Dan Reznik, and Ronaldo Garcia. Poncelet plectra: Harmonious properties of cosine space. Beitr. Algebra Geom., to appear, 2021. doi:10.1007/s13366-021-00596-x

`4d:Te27,html`

[18] Ronaldo Garcia, Jair Koiller, and Dan Reznik. Average elliptic billiard invariants with spatial integrals, 2021. arXiv:2102.10899.

[19] Ronaldo Garcia, Dan Reznik, and Jair Koiller. Loci of 3-periodics in an elliptic billiard: why so many ellipses? arXiv:2001.08041, 2020.

[20] Ronaldo Garcia and Dan Reznik. Invariants of self-intersected and inversive N-periodics in the elliptic billiard. arXiv:2011.06640, 10 2020.

[21] Mark Helman, Dominique Laurain, Dan Reznik, and Ronaldo Garcia. A theory for locus ellipticity of Poncelet 3-periodics centers. arXiv:2106.00715, 6 2021.

[22] Dan Reznik and Ronaldo Garcia. An infinite, converging, sequence of Brocard porisms. arXiv:2010.01391, 10 2020.

[23] Ronaldo Garcia and Dan Reznik. Loci of the Brocard points over selected triangle families. arXiv:2009.08561, 9 2020.

[24] Dan Reznik, Ronaldo Garcia, and Jair Koiller. Eighty new invariants of N-periodics in the elliptic billiard. arXiv:2004.12497, 9 2020.

[25] Iverton Darlan and Dan Reznik. An App for Visual Exploration, Discovery, and Sharing of Poncelet 3-Periodic Phenomena. arXiv:2106.04521, 6 2021.

[26] Ronaldo Garcia, Boris Odehnal, and Dan Reznik. Loci of Poncelet triangles with multiple caustics. arXiv:2108.05430, 8 2021. 2021.

[27] Ronaldo Garcia, Boris Odehnal, and Dan Reznik. Poncelet porisms in hyperbolic pencils of circles}. submitted to J. Geom.Graphics, 10 2021.

[28] Dan Reznik. Poncelet Parabola Pirouettes. arXiv:2110.06356, 10 2021.

[29] Dominique Laurain, Peter Moses,and Dan Reznik. Cramer-Castillon on a triangle's incircle and excircles. arXiv:2110.13615, 10 2021.

[30] Filipe Bellio, Ronaldo Garcia, and Dan Reznik. Cramer-Castillon on a triangle's incircle and excircles, arXiv:2110.13615, 10 2021.

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Reznik","avatar_url":"https://avatars-next.observableusercontent.com/34300050560dea2b36d63efd30e3f07e6f455717f9e917936080d33429d8b426","tier":"starter_2024","bio":"Data Analytics Consultant, Instructor. Areas: Data Analytics, Geometry, Simulation, Visualization, Computer Vision, Robotics...","followed_by_you":false,"follows_you":false},"version":783,"publish_version":783,"role":null,"authored":false,"authors":[{"type":"individual","id":"bda3bb7cbffeec7d","login":"dan-reznik","name":"Dan S. Reznik","avatar_url":"https://avatars-next.observableusercontent.com/34300050560dea2b36d63efd30e3f07e6f455717f9e917936080d33429d8b426","tier":null,"bio":"Data Analytics Consultant, Instructor. Areas: Data Analytics, Geometry, Simulation, Visualization, Computer Vision, Robotics...","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"bda3bb7cbffeec7d","login":"dan-reznik","name":"Dan S. Reznik","avatar_url":"https://avatars-next.observableusercontent.com/34300050560dea2b36d63efd30e3f07e6f455717f9e917936080d33429d8b426","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":{"id":"6543aeb6f72c303d","slug":"elliptic-billiards","title":"Poncelet Phenomena","owner":{"id":"5f70011df0350296","login":"dan-reznik","name":"Dan S. Reznik"}},"type":"notebook","body":{"titling":"auto","title":"Poncelet Phenomena in the Euclidean Plane (2019-2021)","cells":[{"id":30,"value":"md`# Poncelet Phenomena in the Euclidean Plane (2019-2021)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"md`Artifacts of our exploration of Poncelet phenomena in the Euclidean plane, including:\n- (new) Book!\n- Journal Publications & Submissions\n- Videos\n- Wolfram apps\n- Javascript Interactive apps\n- Presentations\n- Webpages\n- To do: Mathematica code and GitHub repos`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":701,"value":"md`## (new) Book IMPA 33rd Colloquium of Brazilian Math.\n(250 pages)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":708,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":755,"value":"md`## (new) IMPA 33rd CBM minicourse: [playlist](https://www.youtube.com/playlist?list=PLvvfpeSf1IRI7xCZfQwjmU7M-XL4Ctkt8)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":512,"value":"html`

Journal Publications

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":500,"value":"$4c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":697,"value":"html`

Submitted Articles

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":692,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"md`## Videos

(${dt_videos.numRows()})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":568,"value":"viewof ponc_topic = Inputs.select(['All',...new Set(dt_videos_filtered.columnArray('Topic'))], {value: \"All\", label: \"video topic\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"viewof dt_videos_search = Inputs.search(dt_videos_filtered.rename({Link:'youtu.be/...'}).filter(aq.escape(d=>ponc_topic===\"All\"|d.Topic===ponc_topic)).objects())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"viewof table_videos = Inputs.table(dt_videos_search,{\n format:{'youtu.be/...':hyperlink_video(re_video)},\n width:{row:30,Topic:100,N:20,Title:400,'X(k)':50,'youtu.be/...':150},align:{row:'center',N:'left'}})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"md`## Applets

(${dt_applets.numRows()})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":590,"value":"viewof applet_topic = Inputs.select(['All',...new Set(dt_applets_filtered.columnArray('Topic'))], {value: \"All\", label: \"applet topic\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":106,"value":"viewof dt_applets_search = Inputs.search(dt_applets_filtered.filter(aq.escape(d=>applet_topic===\"All\"|d.Topic===applet_topic)).objects())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"viewof table_applets=Inputs.table(dt_applets_search,{format:{Link:hyperlink_video(re_applet)},\n width:{row:30,Topic:100,N:20,Title:400}})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"md`## Interactive Apps (in Javascript)\n(click on the pictures)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":413,"value":"html`

1. Locus Lab

docs, demo video, locus gallery, code repo`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":417,"value":"html`

2. Ellipse Echos

demo video, code repo`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":641,"value":"md`## Wolfram Community Posts\n1. D. Reznik and R. Garcia, [*Dynamics of the Circumcenter Map over Triangles*](https://community.wolfram.com/groups/-/m/t/2234577), April 2021.\n1. D. Reznik, [*Identity zones of the Isodynamic Map*](https://community.wolfram.com/groups/-/m/t/2249660), April, 2021.\n1. D. Reznik, [*Poncelet triangles and the amazing loci of the isogonal conjugates*](https://community.wolfram.com/groups/-/m/t/2392125), October, 2021\n1. D. Reznik, [*Dynamics of 3-point map in a circle: limit cycles, closures and porisms*](https://community.wolfram.com/groups/-/m/t/2392125), November, 2021.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":465,"value":"md`## Webpages\n1. w/ R. Garcia, J. Koiller, [*Invariants of N-Periodics in an Elliptic Billiard*](https://dan-reznik.github.io/Elliptical-Billiards-Triangular-Orbits/), 2019.\n1. [*Triangles and Ellipses: Pages and Media*](https://dan-reznik.github.io/Elliptical-Billiards-Triangular-Orbits/videos.html), 2020.\n1. [*Loci of N-Periodic Centers and Their Internal Triangles*](https://dan-reznik.github.io/billiard-loci/), 2020.\n1. [*Envelopes of Triangle Center Pairs*](https://dan-reznik.github.io/billiard-envelopes/), 2020.\n1. w/ M. Helman, [*Extremal Area Pedal and Antipedal Triangles*](https://dan-reznik.github.io/extremal-pedal-antipedal/), 2020.\n1. w/ I. Darlan, [*Loci of Ellipse-Mounted Triangle Centers*](https://dan-reznik.github.io/ellipse-mounted-triangles/), 2020.\n1. w/ R. Garcia, [*Loci of 3-periodics in the Elliptic Billiard: Why so many ellipses?*](https://dan-reznik.github.io/why-so-many-ellipses/), 2020.\n1. [*Isodynamic Map (live GPU)*](https://dan-reznik.github.io/Isodynamic-Map-GPU/), 2021.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":629,"value":"md`## GitHub Code Repos\n1. [Locus Visualization App](https://github.com/dan-reznik/ellipse-mounted-loci-p5js), 2020-2021.\n1. [Why So Many Ellipses?](https://dan-reznik.github.io/why-so-many-ellipses/), 2020.\n1. [Port of Fukushima's Fortran-90 Jacobi Elliptic Functions](https://github.com/dan-reznik/jacobi-elliptic), 2021.\n1. [Elliptic Billiard Original Website](https://github.com/dan-reznik/Elliptical-Billiards-Triangular-Orbits), 2019-2020.\n1. [Isodynamic Map (GPU)](https://github.com/dan-reznik/Isodynamic-Map-GPU), 2021.\n1. [Ellipse Echos](https://github.com/dan-reznik/ellipse-echo-p5js), 2021.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":398,"value":"md`## Observable Pages\n1. Billiard 3-periodics & spatio-temporal: [link](https://observablehq.com/@dan-reznik/elliptic-billiard-triangle)\n1. Claudio Esperança's 3d spatio-temporal viz: [link](https://observablehq.com/@esperanc/3-periodic-elliptical-billiards-3d-sweep)\n1. Poncelet's Closure Theorem: [link](https://observablehq.com/@dan-reznik/poncelet-iteration?collection=@dan-reznik/elliptic-billiards)\n1. Jacobi's Elliptic Functions: [link](https://observablehq.com/@dan-reznik/jacobi-elliptic-functions?collection=@dan-reznik/elliptic-billiards)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":604,"value":"ponc_anim","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":488,"value":"md`## Odds & Ends\n1. [IMPA Talk](https://youtu.be/t872mftaI2g), July, 29th, 2019, and [slides](https://dan-reznik.github.io/Elliptical-Billiards-Triangular-Orbits/ppt/IMPA_Adventures_in_Ellipses_Triangles.pdf).\n1. [IMPA Article](https://impa.br/noticias/palestra-de-dan-reznik-apresenta-novas-descobertas-na-area-dos-bilhares-elipticos/), July, 2019.\n1. [PUC-RJ Talk](https://dan-reznik.github.io/Elliptical-Billiards-Triangular-Orbits/papers/PUC_Billiard_Surprises.pdf), Sept 2019.\n1. Slides showing [Artsy Loci](https://docs.google.com/presentation/d/1pHPrM3wdiabtE1_gzp5ZUAzMZku1GB0-u0TNQBxEGhM/edit?usp=sharing)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"md`### Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":282,"value":"hyperlink_video = function(re) { return x => htl.html`${x.replace(re,\"\")}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":150,"value":"{\n viewof table_videos.classList.add(\"my_styled_table\");\n viewof table_applets.classList.add(\"my_styled_table\");\n return 'from: https://observablehq.com/@pbogden/observable-input-table';\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":384,"value":"dt_applets_filtered=dt_applets\n.select(aq.not('id','ok','Year'))\n.rename({'Section':'Topic','url':'Link'})\n.derive({row:op.row_number()},{before:0})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":254,"value":"dt_videos_filtered = dt_videos\n.select(aq.not('sound','id','Video2','Video3','Year'))\n.rename({'Section':'Topic','Kimberling Centers':'X(k)','Video1':'Link'})\n.derive({row: op.row_number()},{before:0})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":295,"value":"re_applet=new RegExp('^.*b021/')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":268,"value":"re_video = new RegExp('^.*\\/');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"dt_videos = aq.loadCSV(url_videos)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"dt_applets = aq.loadCSV(url_applets)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"url_videos='https://docs.google.com/spreadsheets/d/e/2PACX-1vQ5UGbhD_7gCMq1iISnE1TmGzVEHVNGTYrW6uyYMgGouYdNufPAiSnSpOJyGD4EuGrLekEkmiL3unaO/pub?gid=0&single=true&output=csv'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"url_applets = \"https://docs.google.com/spreadsheets/d/e/2PACX-1vQ5UGbhD_7gCMq1iISnE1TmGzVEHVNGTYrW6uyYMgGouYdNufPAiSnSpOJyGD4EuGrLekEkmiL3unaO/pub?gid=437148195&single=true&output=csv\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":600,"value":"import {ponc_anim} from '@dan-reznik/poncelet-iteration'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"import {op,aq} from '@uwdata/arquero'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 24:null