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<urlset xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.sitemaps.org/schemas/sitemap/0.9" xmlns:image="http://www.google.com/schemas/sitemap-image/1.1" xsi:schemaLocation="http://www.sitemaps.org/schemas/sitemap/0.9 http://www.sitemaps.org/schemas/sitemap/0.9/sitemap.xsd"><url><loc>https://diagonalargument.com/2020/04/28/eschers-toroidal-print-gallery/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/print_gallery_by_m._c._escher.jpg</image:loc><image:title>Print_Gallery_by_M._C._Escher</image:title><image:caption>(From Wikimedia Commons)</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/escher-droste.png</image:loc><image:title>escher-droste</image:title></image:image><lastmod>2026-03-14T15:12:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/set-theory-jottings-the-series/</loc><lastmod>2026-03-11T16:41:04+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2026/03/05/set-theory-jottings-21-the-constructible-universe/</loc><lastmod>2026-03-11T16:37:24+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2026/03/11/set-theory-jottings-22-absoluteness/</loc><lastmod>2026-03-11T16:36:23+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/12/27/set-theory-jottings-20-consistency-of-gch-and-ac-overview/</loc><lastmod>2026-03-05T18:39:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2026/01/20/from-kepler-to-ptolemy-23/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2026/01/astronomia-frontispiece.jpg</image:loc><image:title>astronomia-frontispiece</image:title></image:image><lastmod>2026-01-21T15:17:41+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/from-ptolemy-to-kepler-the-series/</loc><lastmod>2026-01-20T21:23:26+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2025/11/24/set-theory-jottings-19-gch-implies-ac/</loc><lastmod>2025-12-27T18:53:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/11/20/set-theory-jottings-18-the-axiom-of-determinacy/</loc><lastmod>2025-12-05T20:21:03+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/08/20/set-theory-jottings-15-from-zermelo-to-zfc-formal-logic/</loc><lastmod>2025-12-05T20:19:51+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/09/set-theory-jottings-11-zermelo-to-the-rescue-part-2/</loc><lastmod>2025-12-05T20:18:17+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/23/set-theory-jottings-7-the-cantor-dedekind-schroder-bernstein-theorem/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/equiv-bullet.png</image:loc><image:title>equiv-bullet</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/ordered-equivalence-theorem.png</image:loc><image:title>ordered-equivalence-theorem</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/equivalence-theorem.png</image:loc><image:title>equivalence-theorem</image:title></image:image><lastmod>2025-12-05T20:16:45+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/16/set-theory-jottings-6-zorns-lemma/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/spanning-forest.png</image:loc><image:title>spanning-forest</image:title><image:caption>Spanning Forest</image:caption></image:image><lastmod>2025-12-05T20:15:27+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/22/set-theory-jottings-5-zermelo-to-the-rescue-part-1/</loc><lastmod>2025-12-05T20:14:11+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/08/22/set-theory-jottings-17-ordinals-revisited/</loc><lastmod>2025-12-05T20:11:27+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/08/21/set-theory-jottings-16-axioms-of-zfc/</loc><lastmod>2025-12-06T13:59:38+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/11/18/from-kepler-to-ptolemy-22/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/11/libration-force.jpg</image:loc><image:title>libration-force</image:title><image:caption>Libration Force</image:caption></image:image><lastmod>2025-12-02T19:57:06+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/11/13/from-kepler-to-ptolemy-21/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/11/stephenson-fig14.jpg</image:loc><image:title>stephenson-fig14</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/11/dipole-inverse-linear.jpg</image:loc><image:title>dipole-inverse-linear</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/11/1024px-whirlpool_playa_del_rey_california.jpg</image:loc><image:title>1024px-Whirlpool_playa_del_Rey_california</image:title></image:image><lastmod>2025-11-18T12:43:28+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/07/29/from-kepler-to-ptolemy-19/</loc><lastmod>2025-11-17T16:56:46+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/who-inverted-and-squared-gravity/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/11/ismael_boulliau.jpeg</image:loc><image:title>Ismaël_Boulliau</image:title></image:image><lastmod>2025-11-13T17:14:51+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2025/08/07/from-kepler-to-ptolemy-20/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/08/whirlpool.jpg</image:loc><image:title>whirlpool</image:title></image:image><lastmod>2025-09-19T20:57:35+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/31/from-kepler-to-ptolemy-16/</loc><lastmod>2025-09-07T23:13:52+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/08/19/set-theory-jottings-14-from-zermelo-to-zfc-replacement-and-foundation/</loc><lastmod>2025-08-20T17:27:39+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/30/set-theory-jottings-13-from-zermelo-to-zfc-everythings-a-set/</loc><lastmod>2025-08-19T15:38:45+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/07/from-kepler-to-ptolemy-17/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/06/mysterium-cosmographicum.jpg</image:loc><image:title>mysterium-cosmographicum</image:title></image:image><lastmod>2025-08-07T17:10:07+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/27/from-kepler-to-ptolemy-18/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/06/mars_actual_orbit.jpg</image:loc><image:title>Mars_actual_orbit</image:title><image:caption>Actual Orbit of Mars</image:caption></image:image><lastmod>2025-07-29T18:49:25+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/14/set-theory-jottings-12-zermelo-on-definiteness/</loc><lastmod>2025-11-12T21:37:31+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/mathnotes/first-order-categorical-logic-the-series/</loc><lastmod>2025-06-11T02:45:53+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2025/06/04/first-order-categorical-logic-13/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/06/restriction-nat-trans.png</image:loc><image:title>restriction-nat-trans</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/beck-chevalley-quantifiers.png</image:loc><image:title>beck-chevalley-quantifiers</image:title></image:image><lastmod>2025-06-11T02:42:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/09/first-order-categorical-logic-14/</loc><lastmod>2025-06-09T23:24:58+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/06/03/set-theory-jottings-10-axiomatic-set-theory/</loc><lastmod>2025-06-09T14:11:38+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/06/non-standard-models-of-arithmetic-1/</loc><lastmod>2025-06-08T16:01:17+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/07/non-standard-models-of-arithmetic-2/</loc><lastmod>2025-06-08T15:59:55+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/22/first-order-categorical-logic-12/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/nat-trans-2-1.png</image:loc><image:title>nat-trans-2</image:title><image:caption>Left Adjoints</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/nat-trans-1.png</image:loc><image:title>nat-trans-1</image:title><image:caption>A natural transformation</image:caption></image:image><lastmod>2025-06-05T00:19:58+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/about/</loc><lastmod>2025-06-03T13:41:06+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2025/05/28/set-theory-jottings-9-cantor-normal-form/</loc><lastmod>2025-06-03T12:29:20+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/06/02/first-order-categorical-logic-1/</loc><lastmod>2025-06-01T18:19:15+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/04/19/from-kepler-to-ptolemy-13/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/04/latitude.png</image:loc><image:title>latitude</image:title></image:image><lastmod>2025-05-31T10:16:29+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/04/05/nonstandard-models-of-arithmetic-32/</loc><lastmod>2025-05-31T10:13:31+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/25/set-theory-jottings-8-ordinal-arithmetic/</loc><lastmod>2025-05-31T10:10:28+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/24/from-kepler-to-ptolemy-15/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/manshurat-fig.png</image:loc><image:title>manshurat-fig</image:title><image:caption>Sawn-Off Model
(from Murschel p.45)</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/05/planetary-hyp-outer.png</image:loc><image:title>planetary-hyp-outer</image:title><image:caption>Full Shell Model</image:caption></image:image><lastmod>2025-05-31T10:09:57+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/05/20/from-kepler-to-ptolemy-14/</loc><lastmod>2025-05-31T10:08:41+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/28/from-kepler-to-ptolemy-12/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/mercury.png</image:loc><image:title>mercury</image:title></image:image><lastmod>2025-05-31T10:07:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/23/from-kepler-to-ptolemy-11/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/venus.png</image:loc><image:title>venus</image:title><image:caption>Venus</image:caption></image:image><lastmod>2025-05-31T10:06:13+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/07/26/review-smullyan-fitting-set-theory-and-the-continuum-problem/</loc><lastmod>2025-04-22T19:09:31+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/mathnotes/nonstandard-models-of-arithmetic-the-series/</loc><lastmod>2025-04-05T04:48:13+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2020/11/20/nonstandard-models-of-arithmetic-24/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/10/indicators-1.png</image:loc><image:title>indicators</image:title></image:image><lastmod>2025-04-05T04:42:06+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/10/12/non-standard-models-of-arithmetic-20/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/10/trudy.jpg</image:loc><image:title>trudy</image:title><image:caption>Trudy Campbell</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/10/arith-hierarchy.png</image:loc><image:title>arith-hierarchy</image:title></image:image><lastmod>2025-04-03T16:20:18+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/10/18/non-standard-models-of-arithmetic-21/</loc><lastmod>2025-04-03T16:17:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/04/from-kepler-to-ptolemy-10/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/outer-planet.png</image:loc><image:title>outer-planet</image:title><image:caption>Model for an Outer Planet</image:caption></image:image><lastmod>2025-03-24T17:29:01+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/02/first-order-categorical-logic-11/</loc><lastmod>2025-03-24T17:28:33+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/24/set-theory-jottings-1-philosophy-and-naive-set-theory/</loc><lastmod>2025-03-24T17:26:17+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/02/set-theory-jottings-4-ordinals/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/ordinal-tree.jpg</image:loc><image:title>ordinal-tree</image:title><image:caption>The Ordinal Tree for ω&lt;sup&gt;2&lt;/sup&gt;</image:caption></image:image><lastmod>2025-03-22T15:16:41+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/22/from-kepler-to-ptolemy-2/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/deferent-epicycle-1.png</image:loc><image:title>deferent-epicycle</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/scaling.png</image:loc><image:title>scaling</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/heliocentric-geocentric.png</image:loc><image:title>heliocentric-geocentric</image:title></image:image><lastmod>2025-03-19T21:25:06+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/03/02/from-kepler-to-ptolemy-9/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/03/moon.png</image:loc><image:title>moon</image:title><image:caption>The Moon's Orbit</image:caption></image:image><lastmod>2025-03-13T11:08:15+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/02/26/from-kepler-to-ptolemy-8/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/02/ptolemy-sun.jpg</image:loc><image:title>ptolemy-sun</image:title><image:caption>Ptolemy's Solar Model</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/02/mean-sun.png</image:loc><image:title>mean-sun</image:title><image:caption>Mean Sun and True Sun</image:caption></image:image><lastmod>2025-03-13T11:04:47+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/02/25/from-kepler-to-ptolemy-7/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/02/opposition-conjunction.png</image:loc><image:title>opposition-conjunction</image:title><image:caption>Opposition and Conjunction</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2025/02/ecliptic_grid_globe.png</image:loc><image:title>Ecliptic_grid_globe</image:title><image:caption>Ecliptic Coordinates&lt;br /&gt;(From &lt;a href="https://commons.wikimedia.org/wiki/File:Ecliptic_grid_globe.png"&gt;Wikimedia&lt;/a&gt;)</image:caption></image:image><lastmod>2025-03-13T11:02:28+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/02/23/set-theory-jottings-3-the-paradoxes/</loc><lastmod>2025-03-13T11:02:00+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/25/from-kepler-to-ptolemy-4/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/equant-area-quadrants.jpg</image:loc><image:title>equant-area-quadrants</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/speed-law-comparison.png</image:loc><image:title>speed-law-comparison</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/velocity-components.png</image:loc><image:title>velocity-components</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/area-law.png</image:loc><image:title>area-law</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/polar-coords.png</image:loc><image:title>polar-coords</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/equant.png</image:loc><image:title>equant</image:title><image:caption>(Note: Ptolemy’s equant circle had the same radius as the deferent)</image:caption></image:image><lastmod>2025-03-04T21:16:27+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/24/from-kepler-to-ptolemy-3/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/ellipticity.png</image:loc><image:title>ellipticity</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/ellipse.png</image:loc><image:title>ellipse</image:title></image:image><lastmod>2025-03-04T21:15:05+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/09/16/first-order-categorical-logic-5/</loc><lastmod>2025-03-03T20:31:59+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/06/22/first-order-categorical-logic-3/</loc><lastmod>2025-03-03T20:06:18+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/24/set-theory-jottings-2-cantors-paradise/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/11/cantor-rn-diagram.png</image:loc><image:title>Cantor-Rn-diagram</image:title></image:image><lastmod>2025-03-03T14:27:30+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/01/17/first-order-categorical-logic-10/</loc><lastmod>2025-03-03T00:00:51+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/02/09/from-kepler-to-ptolemy-6/</loc><lastmod>2025-02-25T22:09:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2025/01/05/first-order-categorical-logic-9/</loc><lastmod>2025-02-24T16:54:41+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/31/first-order-categorical-logic-8/</loc><lastmod>2025-02-24T16:54:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2024/12/26/from-kepler-to-ptolemy-5/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/trees.png</image:loc><image:title>trees</image:title><image:caption>Tree Analogy</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2024/12/retrograde_mars.jpg</image:loc><image:title>retrograde_mars</image:title><image:caption>Retrograde Motion of 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c>https://diagonalargument.com/2020/05/26/algebraic-geometry-jottings-18/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/05/semicubical-parabola-e1590241519736.png</image:loc><image:title>semicubical-parabola</image:title><image:caption>&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;=&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;3&lt;/sup&gt;</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/05/circle-tangent-x-1-e1590183206999.png</image:loc><image:title>circle-tangent-x</image:title><image:caption>&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+(&lt;em&gt;y&lt;/em&gt;–2)&lt;sup&gt;2&lt;/sup&gt;=4</image:caption></image:image><lastmod>2020-08-08T14:39:06+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/01/10/non-standard-models-of-arithmetic-14/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2019/09/pa-models-diag-2.png</image:loc><image:title>pa-models-diag</image:title></image:image><lastmod>2020-08-07T22:26:58+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/09/22/non-standard-models-of-arithmetic-7/</loc><lastmod>2025-02-01T02:13:48+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/03/algebraic-geometry-jotting-3/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/level-curves.jpg</image:loc><image:title>level-curves</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/3petal-epsilon.png</image:loc><image:title>3petal-epsilon</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/4petal-branches.png</image:loc><image:title>4petal-branches</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/3petal-branches-1.png</image:loc><image:title>3petal-branches</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/3petal-branches.png</image:loc><image:title>3petal-branches</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/3petal-2.png</image:loc><image:title>3petal</image:title><image:caption>$latex E(x,y)=(x^2+y^2)^2+3x^2y-y^3=0$</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/4petal-1.png</image:loc><image:title>4petal</image:title><image:caption>$latex F(x,y)=(x^2+y^2)^3-4x^2y^2=0$</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/3petal-1.png</image:loc><image:title>3petal</image:title><image:caption>$latex E(x,y)=(x^2+y^2)^2+3x^2y-y^3=0$</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/circles-1.png</image:loc><image:title>circles</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/cubics.png</image:loc><image:title>cubics</image:title></image:image><lastmod>2020-06-26T14:50:40+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/05/08/algebraic-geometry-jottings-17/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/rose-intersections-h-mults.png</image:loc><image:title>rose-intersections-h-mults</image:title><image:caption>res&lt;sub&gt;x&lt;/sub&gt;(&lt;em&gt;y&lt;/em&gt;)=16&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;14&lt;/sup&gt;(16&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;-5)&lt;sup&gt;2&lt;/sup&gt;</image:caption></image:image><lastmod>2020-05-26T19:10:55+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/05/06/algebraic-geometry-jottings-16/</loc><lastmod>2020-05-26T19:10:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/05/04/algebraic-geometry-jottings-15/</loc><lastmod>2020-05-26T19:09:04+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/mathnotes/algebraic-geometry-jottings/</loc><lastmod>2020-05-26T19:02:51+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://diagonalargument.com/2020/04/01/algebraic-geometry-jotting-2/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/projection-1.png</image:loc><image:title>projection</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/chessboard.jpg</image:loc><image:title>chessboard</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/durer-perspective.jpg</image:loc><image:title>durer-perspective</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/rose-intersections-ix-2.png</image:loc><image:title>rose-intersections-ix</image:title><image:caption>$latex E(ix,y)=(y^2-x^2)^2-3x^2y-y^3$
$latex F(ix,y)=(y^2-x^2)^3+4x^2y^2$</image:caption></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/rose-intersections-hlines.png</image:loc><image:title>rose-intersections-hlines</image:title><image:caption>&lt;em&gt;E&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;,&lt;em&gt;y&lt;/em&gt;)=(&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;2&lt;/sup&gt;+3&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;em&gt;y&lt;/em&gt;–&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;3&lt;/sup&gt;&lt;br /&gt;
&lt;em&gt;F&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;,&lt;em&gt;y&lt;/em&gt;)=(&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;3&lt;/sup&gt;–4&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;</image:caption></image:image><lastmod>2020-05-05T17:23:14+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/17/algebraic-geometry-jottings-9/</loc><lastmod>2020-05-04T20:11:07+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/08/algebraic-geometry-jottings-6/</loc><lastmod>2020-05-04T14:54:26+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/30/weierstrasss-smackdown-of-dirichlets-principle/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/weierstrass-example-1.png</image:loc><image:title>weierstrass-example</image:title></image:image><lastmod>2020-05-04T13:05:56+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/05/01/algebraic-geometry-jottings-14/</loc><lastmod>2020-05-04T13:04:54+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/27/algebraic-geometry-jottings-13/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/rect-hyperbolas.png</image:loc><image:title>rect-hyperbolas</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/xy-hyperbolas.png</image:loc><image:title>xy-hyperbolas</image:title></image:image><lastmod>2020-05-01T12:55:47+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/26/wallpaper-groups/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/04/escher-alhambrasketch2.jpg</image:loc><image:title>escher-AlhambraSketch2</image:title><image:caption>Escher: Alhambra Sketch</image:caption></image:image><lastmod>2020-04-30T23:45:02+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/15/algebraic-geometry-jottings-8/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/two-ellipses-e1585328950234.png</image:loc><image:title>two-ellipses</image:title><image:caption>&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt; = 1&lt;br /&gt;2&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt; = 1
</image:caption></image:image><lastmod>2020-04-29T18:50:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/06/algebraic-geometry-jotting-4/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/branch-branch.png</image:loc><image:title>branch-branch</image:title><image:caption>&lt;p style="text-align:center;"&gt;&lt;em&gt;E&lt;/em&gt;: &lt;em&gt;r&lt;/em&gt; = –sin 3&lt;em&gt;t&lt;/em&gt;
&lt;em&gt;F&lt;/em&gt;: &lt;em&gt;r&lt;/em&gt; = sin 2&lt;em&gt;t&lt;/em&gt;&lt;/p&gt;</image:caption></image:image><lastmod>2020-04-29T18:49:37+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/24/algebraic-geometry-jottings-12/</loc><lastmod>2020-04-27T20:35:47+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/22/algebraic-geometry-jottings-11/</loc><lastmod>2020-04-27T20:35:09+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/20/algebraic-geometry-jottings-10/</loc><lastmod>2020-04-27T20:34:11+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2018/07/03/under-construction/</loc><lastmod>2020-04-24T14:59:30+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/11/18/year-zero/</loc><lastmod>2020-04-24T14:58:15+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/03/20/a-fragment-from-the-archives/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/atlantis-sinks.gif</image:loc><image:title>atlantis-sinks</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/nonagon.jpg</image:loc><image:title>nonagon</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/temple-2.jpg</image:loc><image:title>temple-2</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/temple-1.jpg</image:loc><image:title>temple-1</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/archive-fragment.jpg</image:loc><image:title>archive-fragment</image:title></image:image><lastmod>2020-04-17T13:51:40+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/13/algebraic-geometry-jottings-7/</loc><lastmod>2020-04-17T13:49:12+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/03/30/algebraic-geometry-jotting-1/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/rose-intersect-at-inf-1-e1583352976896.png</image:loc><image:title>rose-intersect-at-inf</image:title></image:image><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/rose-intersections.png</image:loc><image:title>rose-intersections</image:title><image:caption>&lt;em&gt;E&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;,&lt;em&gt;y&lt;/em&gt;)=(&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;2&lt;/sup&gt;+3&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;em&gt;y&lt;/em&gt;–&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;3&lt;/sup&gt;&lt;br /&gt;
&lt;em&gt;F&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;,&lt;em&gt;y&lt;/em&gt;)=(&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;3&lt;/sup&gt;–4&lt;em&gt;x&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;em&gt;y&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt;</image:caption></image:image><lastmod>2020-04-16T15:07:06+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2020/04/08/algebraic-geometry-jotting-5/</loc><image:image><image:loc>https://diagonalargument.com/wp-content/uploads/2020/03/auxiliary-curves.png</image:loc><image:title>auxiliary-curves</image:title><image:caption>Auxiliary Curves G and H</image:caption></image:image><lastmod>2020-04-13T16:05:09+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/06/22/non-standard-models-of-arithmetic-11/</loc><lastmod>2024-05-20T19:03:58+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/06/12/non-standard-models-of-arithmetic-10/</loc><lastmod>2019-09-17T12:52:00+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/10/non-standard-models-of-arithmetic-3/</loc><lastmod>2019-09-16T20:57:09+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/09/14/algorithmic-information-theory/</loc><lastmod>2019-09-14T17:21:50+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/29/simple-sets-and-the-recursion-theorem/</loc><lastmod>2019-07-07T21:24:23+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/06/the-lambda-calculus/</loc><lastmod>2019-05-28T23:04:49+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com/2019/05/13/friedbergs-enumeration-without-duplication/</loc><lastmod>2019-05-28T22:58:32+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://diagonalargument.com</loc><changefreq>daily</changefreq><priority>1.0</priority><lastmod>2026-03-14T15:12:32+00:00</lastmod></url></urlset>
