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  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713745">
    <title>Why can’t directly get the range of l1+l2 under three constraints?</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713745</link>
    <description>three constraints are:&#xD;
&#xD;
    l1 Tan@a + l2 == Sin@a/Cos[a]^2 + 1/Sin@a, &#xD;
    l1 + l2/Tan@a == 1/(Cos@a (Sin@a)^2), 0 &amp;lt; a &amp;lt; \[Pi]/2&#xD;
&#xD;
&#xD;
Why can&amp;#039;t the following code solve the range of l1+l2? How to compute it correctly?&#xD;
&#xD;
    Reduce[{l1 Tan@a + l2 == Sin@a/Cos[a]^2 + 1/Sin@a, &#xD;
       l1 + l2/Tan@a == 1/(Cos@a (Sin@a)^2), 0 &amp;lt; a &amp;lt; \[Pi]/2, &#xD;
       t == l1 + l2}, t, {l1, l2, a}, Reals] // FullSimplify&#xD;
&#xD;
![enter image description here][1]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-05-10_075121.png&amp;amp;userId=3593842</description>
    <dc:creator>Bill Blair</dc:creator>
    <dc:date>2026-05-09T23:52:05Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713957">
    <title>Insphere (Inner sphere tangent to each side of the tetrahedron)</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713957</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/74d52d3b-de61-4316-92f3-5b500ba485b6</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-09T20:43:05Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713948">
    <title>Exespheres</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713948</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/df20a2f1-2508-46fc-827f-889fbadcc2f4</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-09T20:39:00Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713939">
    <title>Circumsphere</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713939</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/b17033b1-5762-4865-a3b1-1296d0284269</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-09T20:36:19Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713930">
    <title>Particle on a circular cone</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713930</link>
    <description>Suppose that the position function of a particle in space is given by &#xD;
 r[t] = {t Cos[t], t Sin[t], 3 t}.&#xD;
 Show that the particle moves on a circular cone.&#xD;
 Find the angle between the velocity and acceleration vectors when t = 1.5.&#xD;
 Find the tangential and normal components of the acceleration when t = 1.5.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/ffccbfd5-d3d9-45f0-94c2-c556851a9ae2</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-09T19:39:26Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713462">
    <title>Superoscillations Part I: 1D foundations, leaky functions and quantum wavefunctions</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713462</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/f7a9ddb0-2b29-4ee7-bd7e-6740cf584667</description>
    <dc:creator>Bruno Tenorio</dc:creator>
    <dc:date>2026-05-08T22:22:16Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713297">
    <title>Inverse pedal and negative-pedal surfaces of a twisted surface.</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713297</link>
    <description>In this notebook for the twisted surface, its inversion will be made with respect to a sphere with center at the origin and radius 4. Once you have the inverse you will get its pedal and negative-pedal surfaces.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/aa1ac836-ea25-4fa9-9127-4cfcac48ec1f</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-08T17:38:48Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713611">
    <title>Looking for a study partner / mentor in Mathematical Physics (Theory of Everything)</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713611</link>
    <description>Hi everyone,&#xD;
&#xD;
I’m a 3rd-year Mathematics student and I’m reaching a point where I finally start to understand what math really is. I’m fascinated by the Theory of Everything.&#xD;
&#xD;
I have a specific perspective: I believe that while physics can change based on new data, mathematics is absolute. For me, physics is like a subset of a huge axiomatic mathematical structure. I really want to study this connection, but I don’t have much background in physics yet.&#xD;
&#xD;
I live in a small city where it’s hard to find experts in this specific field, and sometimes it&amp;#039;s difficult to stay disciplined when you study everything alone. I’m looking for a study partner or a mentor who is interested in:&#xD;
&#xD;
Mathematical Physics and Axiomatic systems.&#xD;
&#xD;
String Theory or Quantum Mechanics from a math perspective.&#xD;
&#xD;
Deep scientific discussions (not just methodology, but pure science).&#xD;
&#xD;
I want to learn fast and I&amp;#039;m ready to dive into complex topics. If you are interested in exploring these &amp;#034;intersection points&amp;#034; of the universe together, please let me know!</description>
    <dc:creator>Naira naira.mndlyan2005@gmail.com</dc:creator>
    <dc:date>2026-05-08T17:17:40Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713379">
    <title>Orthogonally projected parabola</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713379</link>
    <description>A parabola on the plane XY is projected orthogonally on the plane x + y + z = 1.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/3664b4e5-6493-47a4-b00f-76db4a37c553</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-08T14:08:53Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713323">
    <title>The last one: Curious surface 7</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713323</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/52ce2049-bb9a-4631-9a3b-a0a30b466a72</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-07T21:49:35Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3713230">
    <title>Osculating sphere, plane and circle in the Slinky curve</title>
    <link>https://community.wolfram.com/groups/-/m/t/3713230</link>
    <description>In this animation osculating sphere, circle and plane are observed \&#xD;
moving along the Slinky curve.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/4e6a5830-ecb5-4c34-9909-0192da162ca6</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-07T13:52:07Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3712756">
    <title>Curious surface 6</title>
    <link>https://community.wolfram.com/groups/-/m/t/3712756</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/d6339658-cc9f-4285-b17c-8d8061a8d0e6</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-06T20:40:25Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3712398">
    <title>Bisector planes</title>
    <link>https://community.wolfram.com/groups/-/m/t/3712398</link>
    <description>1) Find the equation of the plane that passes through the intersection of the planes:&#xD;
    x + z - 1 = 0, y - z + 2 = 0, and it is perpendicular to the plane &#xD;
    z = 0. 2) Find the equation of the plane that passes through said intersection and by the origin. &#xD;
   3) Find the angle of two planes calculated in previous points. 4) Find their bisector planes.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/974f9492-1fc7-4fa9-a784-6265cb1c9610</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-06T14:53:45Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3712465">
    <title>Bottle of Klein</title>
    <link>https://community.wolfram.com/groups/-/m/t/3712465</link>
    <description>Perhaps one of the most interesting surfaces that there is. Klein&amp;#039;s bottle is an object in four dimensions, that is represented here is only in three dimensions, that&amp;#039;s why there is a self-insertion. &#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/78ace18a-df34-4632-a381-235f8286249e</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-05T20:59:08Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3712307">
    <title>Curious surface 5</title>
    <link>https://community.wolfram.com/groups/-/m/t/3712307</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/f3be4da6-6133-47b2-8003-7671696874e7</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-05T14:43:32Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3712010">
    <title>Curious surface 4</title>
    <link>https://community.wolfram.com/groups/-/m/t/3712010</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/b8452a9c-f5ab-4b8b-8ab8-88c859e4a23c</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-04T19:55:37Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3711592">
    <title>Faster and more accurate than FLRW at predicting SNe Ia distances</title>
    <link>https://community.wolfram.com/groups/-/m/t/3711592</link>
    <description>This formula is more accurate at predicting SNe Ia comoving distances than FLRW and since it&amp;#039;s analytical, it will execute upwards of 10,000 faster and give you machine precision.&#xD;
&#xD;
$D_C(z) = \frac{t_o\left(2V_0 - A t_o\right) z}{2 + z}$&#xD;
&#xD;
![enter image description here][1]&#xD;
&#xD;
That&amp;#039;s it. That&amp;#039;s all there is to it. Here&amp;#039;s how it compares to FLRW:&#xD;
&#xD;
![enter image description here][2]&#xD;
&#xD;
Red is the analytical formula, blue is FLRW. Using the full covariance matrix of the Pantheon+ SH0ES project, the reduced $\chi^2$  of 1.68 for the analytical formula is significantly better than 2.49 for the numerical FLRW solution.&#xD;
&#xD;
This is an outrageous claim, so it should be easy to debunk. The full paper is here: [Acceleration Law Article][3] and the notebook is here: [Acceleration Law Notebook][4]. I&amp;#039;d appreciate your feedback, positive or negative.&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-05-04204344.png&amp;amp;userId=20103&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=HubbleDiagram.png&amp;amp;userId=3608757&#xD;
  [3]: https://www.wolframcloud.com/obj/de2ae88c-5ea9-4334-8b9c-3edbbac38fa5&#xD;
  [4]: https://www.wolframcloud.com/obj/ed737c03-5baf-49f4-90e3-83b91b245c2a</description>
    <dc:creator>Donald Airey</dc:creator>
    <dc:date>2026-05-04T19:36:36Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3711474">
    <title>Curious surface 3</title>
    <link>https://community.wolfram.com/groups/-/m/t/3711474</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/5a1a81ee-6aaf-460c-8199-ed0c8f81ab54</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-04T15:16:04Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3711083">
    <title>Curious surface 2</title>
    <link>https://community.wolfram.com/groups/-/m/t/3711083</link>
    <description>It will be about obtaining a new surface from the original.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/4eca8e80-723d-4898-be62-0a60b31a597a</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-03T17:51:20Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3711074">
    <title>The limit cycle predator-prey models</title>
    <link>https://community.wolfram.com/groups/-/m/t/3711074</link>
    <description>One of the thousands of examples where differential equations are used, apart from Differential Geometry.&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/0b8c3cd2-69ec-4ec8-a587-42db1e7c0364</description>
    <dc:creator>Alejandro Latorre Chirot</dc:creator>
    <dc:date>2026-05-03T16:35:08Z</dc:date>
  </item>
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